Discrete Semantics-Guided Asymmetric Hashing for Large-Scale Multimedia Retrieval

: Cross-modal hashing technology is a key technology for real-time retrieval of large-scale multimedia data in real-world applications. Although the existing cross-modal hashing methods have achieved impressive accomplishment, there are still some limitations: (1) some cross-modal hashing methods do not make full consider the rich semantic information and noise information in labels, resulting in a large semantic gap, and (2) some cross-modal hashing methods adopt the relaxation-based or discrete cyclic coordinate descent algorithm to solve the discrete constraint problem, resulting in a large quantization error or time consumption. Therefore, in order to solve these limitations, in this paper, we propose a novel method, named D iscrete S emantics-Guided A symmetric H ashing (DSAH). Speciﬁcally, our proposed DSAH leverages both label information and similarity matrix to enhance the semantic information of the learned hash codes, and the (cid:96) 2,1 norm is used to increase the sparsity of matrix to solve the problem of the inevitable noise and subjective factors in labels. Meanwhile, an asymmetric hash learning scheme is proposed to efﬁciently perform hash learning. In addition, a discrete optimization algorithm is proposed to fast solve the hash code directly and discretely. During the optimization process, the hash code learning and the hash function learning interact, i.e., the learned hash codes can guide the learning process of the hash function and the hash function can also guide the hash code generation simultaneously. Extensive experiments performed on two benchmark datasets highlight the superiority of DSAH over several state-of-the-art methods.


Introduction
In recent years, due to the rapid development of multimedia Internet of Things technologies, there has been an explosive growth in the amount of multimedia network data. Consequently, the current unimodal search methods can no longer meet the multimedia data retrieval requirements in the complex environment of the new information era. Therefore, cross-modal retrieval methods [1][2][3] have received increasing attention from the information retrieval community and have become a hot research topic in both academia and industry. Specifically, given a query in one modality (such as text), users expect to return its semantically related modality (text) or different modalities (such as images or videos). For decades, as a branch of nearest neighbor search (NNS), the hashing technique has been an active research field in information retrieval community due to the following advantages: (1) Lower storage cost and (2) improved retrieval speed with the hardwarefriendly bit-wise XOR and bit-count operations [4]. In the hash code learning process, the learned hash codes should meet a condition, that is, similar instances have similar hash codes in the Hamming space, and vice versa. Among the practical applications are the image retrieval [5,6] and person re-identification [7,8].

1.
A novel supervised cross-modal hashing method, i.e., DSAH, is proposed to learn the discriminative compact hash codes for large-scale retrieval tasks. DSAH takes the label information and similarity matrix into consideration, which can improve the discriminative capability of the learned hash codes, and solves the problems of matrix sparseness and outlier processing.

2.
An asymmetric learning scheme with real-valued embeddings is proposed to effectively learn the hash function and the hash codes.

3.
Comprehensive experiments are conducted on two famous datasets. The experimental results demonstrate that DSAH outperforms some state-of-the-art baselines.
The remainder of this paper is organized as follows. Section 2 briefly reviews the related works. Section 3 introduces the details of the DSAH model and presents the alternative optimization algorithm. In Section 4, we give the results of experiments performed. Finally, we present the conclusions in Section 5.

Related Works
Cross-modal hashing retrieval has been a widely used technology in the field of information retrieval, machine intelligence, and computer vision. As mentioned above, cross-modal hashing retrieval technology can be divided into supervised and unsupervised categories. However, due to the space limitation, we refer readers to some surveys [4,24] for a more comprehensive coverage of popular hashing methods.

Unsupervised Hashing
Unsupervised hashing methods do not leverage label information for the training dataset. For example, Local Sensitive Hashing (LSH) [25] and its variants [26,27] use random projections to map instances into a Hamming space. Iterative Quantization (ITQ) [28] optimizes the projection by PCA, and then learns an orthogonal rotation matrix to bridge the quantization gap. Unsupervised semantic deep hashing (USDH) [29] uses semantic information to guide the training of hash mapping function. Unsupervised Deep Video Hashing (UDVH) [30] learns the hash codes in a self-taught manner by jointly integrating discriminative video representation with optimal code learning. Neighborhood Discriminant Hashing (NDH) [31] learns hash function by preserving the neighborhood discriminative information in Hamming space. Collective Matrix Factorization Hashing (CMFH) [32] learns a shared common latent space by a collective matrix factorization algorithm, and then adopts a thresholding operation to generate the hash codes. Fusion Similarity Hashing (FSH) [33] proposes a novel fusion similarity method for hash learning by capturing the latent relations between different heterogeneous modalities.

Supervised Hashing
Unlike unsupervised hashing methods, supervised ones utilize the labels to improve the retrieval performance. For example, Semantic Correlation Maximization (SCM) [34] preserves the pairwise similarities of the training dataset to learn the hash functions. Semantic Preserving Hashing (SePH) [35] constructs a new semantic affinity matrix into a probability distribution, and then learns the hash codes by using an approximate-based scheme. Discrete Cross-modal Hashing (DCH) [36] learns the hash codes in a bit-by-bit manner by using the discrete cyclic coordinate descent (DCC) algorithm. Label Consistent Matrix Factorization Hashing (LCMFH) [37] directly uses semantic labels to guide the hashing learning procedure. Scalable Discrete Matrix Factorization Hashing (SCRATCH) [38] is a two-step hashing method, which first generates the hash codes, and then learns the hash functions based on the learned hash codes. Nonlinear Robust Discrete Hashing (NRDH) [39] uses a nonlinear model to solve the generalization error caused by kernelization, and generates compact hash codes by constructing an asymmetric hash framework and discrete optimization algorithms. Scalable Deep Asymmetric Hashing (SDAH) [40] builds an asymmetric unequal-dimensional hash learning framework by exploring the information content of different modalities. Nonlinear Supervised Discrete Hashing (NSDH) [41] consists of two parts, the first part is a semantic enhancement descriptor, which is used to extract comprehensive latent representations of heterogeneous multimedia data, and the second part is a fast discrete optimization module, which is used to learn discriminative compact hash codes. Subspace Relation Learning for Cross-modal Hashing (SRLCH) [42] handles relationships of labels in a semantic subspace to make similar instances from different modalities closer in the binary Hamming space.

Deep Hashing
Recently, with the great success of deep learning in the field of representation learning, many deep hashing methods [13,15,40,43] have been proposed. For example, Deep Semantic-Alignment Hashing (DSAH) [44] is an unsupervised hashing method, which explores the similarity information of different modalities and proposes a semantic-alignment loss to learn the hash codes. Unsupervised Deep Cross-modal Hashing with Virtual Label Regression (UDCH-VLR) [45] proposes a novel unified learning framework to jointly perform deep hash function training, virtual label learning, and regression. Deep Saliency Hashing (DSaH) [46] is a two-step end-to-end model, which mines salient regions and learns semantic-preserving hash codes simultaneously. Supervised Hierarchical Deep Cross-modal Hashing (SHDCH) [47] learns the hash codes by explicitly delving into the hierarchical labels. Deep Semantic cross-modal hashing with Correlation Alignment (DSCA) [48] designs two deep neural networks for image and text modality separately, and learns two hash functions. First, due to the non-smooth property of the discrete optimization causing the problem of unavailable gradient in back-propagation, these methods use the relaxation-based optimization strategies to handle the problem. Even though high retrieval performance is considered to be achieved, these methods still have a large quantization error and can only produce sub-optimal hash codes. Second, they all need large computing resources (e.g., GPUs) and a massive training dataset, which makes them fairly computationally expensive.

The Proposed DSAH Framework
In this section, we introduce our proposed DSAH model. The framework of DSAH is shown in Figure 1, which consists of three main parts: hash function learning, label alignment scheme and asymmetric learning framework. We demonstrate each part in the following section in detail.

Image Modality
Pairwise Similarity Supervision S Pairwise Similarity Supervision S The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
A rose is a woody perennial flowering plant of the genus Rosa, in the family Rosaceae, or the flower it bears. There are over three hundred species and thousands of cultivars. They form a group of plants that can be erect shrubs, climbing, or trailing, with stems that are often armed with sharp prickles. Flowers vary in size and shape and are usually large and showy, in colours ranging from white through yellows and reds. Most species are native to Asia, with smaller numbers native to Europe, North America, and northwestern Africa. Species, cultivars and hybrids are all widely grown for their beauty and often are fragrant. Roses have acquired cultural significance in many societies.
Elephants are large mammals of the family Elephantidae in the order Proboscidea. Three species are currently recognised: the African bush elephant (Loxodonta africana), the African forest elephant (L. cyclotis), and the Asian elephant (Elephas maximus). Elephants are scattered throughout sub-Saharan Africa, South Asia, and Southeast Asia. Elephantidae is the only surviving family of the order Proboscidea; other, now extinct, members of the order include deinotheres, gomphotheres, mastodons, anancids and stegodontids; Elephantidae itself also contains several now extinct groups, such as the mammoths and straight-tusked elephants.
A dragonfly is an insect belonging to the order Odonata, infraorder Anisoptera (from Greek ἄνισος anisos, "unequal" and πτερόν pteron, "wing", because the hindwing is broader than the forewing). Adult dragonflies are characterized by large, multifaceted eyes, two pairs of strong, transparent wings, sometimes with coloured patches, and an elongated body. Dragonflies can be mistaken for the related group, damselflies (Zygoptera), which are similar in structure, though usually lighter in build; however, the wings of most dragonflies are held flat and away from the body, while damselflies hold the wings folded at rest, along or above the abdomen.
Mangoes are juicy stone fruit (drupe) from numerous species of tropical trees belonging to the flowering plant genus Mangifera, cultivated mostly for their edible fruit. The majority of these species are found in nature as wild mangoes. The genus belongs to the cashew family Anacardiaceae. Mangoes are native to South Asia, [1][2] from where the "common mango" or "Indian mango", Mangifera indica, has been distributed worldwide to become one of the most widely cultivated fruits in the tropics. Other Mangifera species (e.g. horse mango, Mangifera foetida) are grown on a more localized basis. Bats are mammals of the order Chiroptera;[a] with their forelimbs adapted as wings, they are the only mammals naturally capable of true and sustained flight. Bats are more manoeuvrable than birds, flying with their very long spread-out digits covered with a thin membrane or patagium. The smallest bat, and arguably the smallest extant mammal, is Kitti's hog-nosed bat, which is 29-34 mm (1.14-1.34 in) in length, 15 cm (5.91 in) across the wings and 2-2.6 g (0.07-0.09 oz) in mass. The largest bats are the flying foxes and the giant goldencrowned flying fox, Acerodon jubatus, which can weigh 1.6 kg (4 lb) and have a wingspan of 1.7 m (5 ft 7 in).
A hedgehog is any of the spiny mammals of the subfamily Erinaceinae, in the eulipotyphlan family Erinaceidae. There are seventeen species of hedgehog in five genera found through parts of Europe, Asia, and Africa, and in New Zealand by introduction. There are no hedgehogs native to Australia and no living species native to the Americas (the extinct genus Amphechinus was once present in North America). Hedgehogs share distant ancestry with shrews (family Soricidae), with gymnures possibly being the intermediate link, and they have changed little over the last 15 million years. [2] Like many of the first mammals, they have adapted to a nocturnal way of life. [3] The reindeer (Rangifer tarandus), also known as the caribou in North America, [3] is a species of deer with circumpolar distribution, native to Arctic, sub-Arctic, tundra, boreal, and mountainous regions of northern Europe, Siberia, and North America. [2] This includes both sedentary and migratory populations. Rangifer herd size varies greatly in different geographic regions. The Taimyr herd of migrating Siberian tundra reindeer (R. t. sibiricus) in Russia is the largest wild reindeer herd in the world, [4] [5] varying between 400,000 and 1,000,000. What was once the second largest herd is the migratory boreal woodland caribou (R. t. caribou) George River herd in Canada, with former variations between 28,000 and 385,000.
Gibbons are apes in the family Hylobatidae. The family historically contained one genus, but now is split into four genera and 18 species. Gibbons live in tropical and subtropical rainforests from eastern Bangladesh and northeast India to southern China and Indonesia (including the islands of Sumatra, Borneo, and Java). Also called the smaller apes or lesser apes, gibbons differ from great apes (chimpanzees, bonobos, gorillas, orangutans, and humans) in being smaller, exhibiting low sexual dimorphism, and not making nests. [3] In certain anatomical details, they superficially more closely resemble monkeys than great apes do, but like all apes, gibbons are tailless.
Rabbits are small mammals in the family Leporidae of the order Lagomorpha (along with the hare and the pika). Oryctolagus cuniculus includes the European rabbit species and its descendants, the world's 305 breeds [1] of domestic rabbit. Sylvilagus includes 13 wild rabbit species, among them the 7 types of cottontail. The European rabbit, which has been introduced on every continent except Antarctica, is familiar throughout the world as a wild prey animal and as a domesticated form of livestock and pet. With its widespread effect on ecologies and cultures, the rabbit (or bunny) is, in many areas of the world, a part of daily life-as food, clothing, a companion, and as a source of artistic inspiration.
A raven is one of several larger-bodied species of the genus Corvus. These species do not form a single taxonomic group within the genus. There is no consistent distinction between "crows" and "ravens", and these appellations have been assigned to different species chiefly on the basis of their size, crows generally being smaller than ravens. The largest raven species are the common raven and the thick-billed raven. The term "raven" originally referred to the common raven (Corvus corax), the type species of the genus Corvus, which has a larger distribution than any other species of Corvus, ranging over much of the Northern Hemisphere.
Monkey is a common name that may refer to groups or species of mammals, in part, the simians of infraorder Simiiformes. The term is applied descriptively to groups of primates, such as families of new world monkeys and old world monkeys. Many monkey species are tree-dwelling (arboreal), although there are species that live primarily on the ground, such as baboons. Most species are also active during the day (diurnal). Monkeys are generally considered to be intelligent, especially the old world monkeys of Catarrhini. Simians and tarsiers emerged within haplorrhines some 60 million years ago. New World monkeys and catarrhine monkeys emerged within the simians some 35 million years ago.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
Rabbits are small mammals in the family Leporidae of the order Lagomorpha (along with the hare and the pika). Oryctolagus cuniculus includes the European rabbit species and its descendants, the world's 305 breeds [1] of domestic rabbit. Sylvilagus includes 13 wild rabbit species, among them the 7 types of cottontail. The European rabbit, which has been introduced on every continent except Antarctica, is familiar throughout the world as a wild prey animal and as a domesticated form of livestock and pet. With its widespread effect on ecologies and cultures, the rabbit (or bunny) is, in many areas of the world, a part of daily life-as food, clothing, a companion, and as a source of artistic inspiration.
A raven is one of several larger-bodied species of the genus Corvus. These species do not form a single taxonomic group within the genus. There is no consistent distinction between "crows" and "ravens", and these appellations have been assigned to different species chiefly on the basis of their size, crows generally being smaller than ravens. The largest raven species are the common raven and the thick-billed raven. The term "raven" originally referred to the common raven (Corvus corax), the type species of the genus Corvus, which has a larger distribution than any other species of Corvus, ranging over much of the Northern Hemisphere.
Monkey is a common name that may refer to groups or species of mammals, in part, the simians of infraorder Simiiformes. The term is applied descriptively to groups of primates, such as families of new world monkeys and old world monkeys. Many monkey species are tree-dwelling (arboreal), although there are species that live primarily on the ground, such as baboons. Most species are also active during the day (diurnal). Monkeys are generally considered to be intelligent, especially the old world monkeys of Catarrhini. Simians and tarsiers emerged within haplorrhines some 60 million years ago. New World monkeys and catarrhine monkeys emerged within the simians some 35 million years ago.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing.

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The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
A rose is a woody perennial flowering plant of the genus Rosa, in the family Rosaceae, or the flower it bears. There are over three hundred species and thousands of cultivars. They form a group of plants that can be erect shrubs, climbing, or trailing, with stems that are often armed with sharp prickles. Flowers vary in size and shape and are usually large and showy, in colours ranging from white through yellows and reds. Most species are native to Asia, with smaller numbers native to Europe, North America, and northwestern Africa. Species, cultivars and hybrids are all widely grown for their beauty and often are fragrant. Roses have acquired cultural significance in many societies.
Elephants are large mammals of the family Elephantidae in the order Proboscidea. Three species are currently recognised: the African bush elephant (Loxodonta africana), the African forest elephant (L. cyclotis), and the Asian elephant (Elephas maximus). Elephants are scattered throughout sub-Saharan Africa, South Asia, and Southeast Asia. Elephantidae is the only surviving family of the order Proboscidea; other, now extinct, members of the order include deinotheres, gomphotheres, mastodons, anancids and stegodontids; Elephantidae itself also contains several now extinct groups, such as the mammoths and straight-tusked elephants.
A dragonfly is an insect belonging to the order Odonata, infraorder Anisoptera (from Greek ἄνισος anisos, "unequal" and πτερόν pteron, "wing", because the hindwing is broader than the forewing). Adult dragonflies are characterized by large, multifaceted eyes, two pairs of strong, transparent wings, sometimes with coloured patches, and an elongated body. Dragonflies can be mistaken for the related group, damselflies (Zygoptera), which are similar in structure, though usually lighter in build; however, the wings of most dragonflies are held flat and away from the body, while damselflies hold the wings folded at rest, along or above the abdomen.
Mangoes are juicy stone fruit (drupe) from numerous species of tropical trees belonging to the flowering plant genus Mangifera, cultivated mostly for their edible fruit. The majority of these species are found in nature as wild mangoes. The genus belongs to the cashew family Anacardiaceae. Mangoes are native to South Asia, [1][2] from where the "common mango" or "Indian mango", Mangifera indica, has been distributed worldwide to become one of the most widely cultivated fruits in the tropics. Other Mangifera species (e.g. horse mango, Mangifera foetida) are grown on a more localized basis. Bats are mammals of the order Chiroptera;[a] with their forelimbs adapted as wings, they are the only mammals naturally capable of true and sustained flight. Bats are more manoeuvrable than birds, flying with their very long spread-out digits covered with a thin membrane or patagium. The smallest bat, and arguably the smallest extant mammal, is Kitti's hog-nosed bat, which is 29-34 mm (1.14-1.34 in) in length, 15 cm (5.91 in) across the wings and 2-2.6 g (0.07-0.09 oz) in mass. The largest bats are the flying foxes and the giant goldencrowned flying fox, Acerodon jubatus, which can weigh 1.6 kg (4 lb) and have a wingspan of 1.7 m (5 ft 7 in).
A hedgehog is any of the spiny mammals of the subfamily Erinaceinae, in the eulipotyphlan family Erinaceidae. There are seventeen species of hedgehog in five genera found through parts of Europe, Asia, and Africa, and in New Zealand by introduction. There are no hedgehogs native to Australia and no living species native to the Americas (the extinct genus Amphechinus was once present in North America). Hedgehogs share distant ancestry with shrews (family Soricidae), with gymnures possibly being the intermediate link, and they have changed little over the last 15 million years. [2] Like many of the first mammals, they have adapted to a nocturnal way of life. [3] The reindeer (Rangifer tarandus), also known as the caribou in North America, [3] is a species of deer with circumpolar distribution, native to Arctic, sub-Arctic, tundra, boreal, and mountainous regions of northern Europe, Siberia, and North America. [2] This includes both sedentary and migratory populations. Rangifer herd size varies greatly in different geographic regions. The Taimyr herd of migrating Siberian tundra reindeer (R. t. sibiricus) in Russia is the largest wild reindeer herd in the world, [4] [5] varying between 400,000 and 1,000,000. What was once the second largest herd is the migratory boreal woodland caribou (R. t. caribou) George River herd in Canada, with former variations between 28,000 and 385,000.
Gibbons are apes in the family Hylobatidae. The family historically contained one genus, but now is split into four genera and 18 species. Gibbons live in tropical and subtropical rainforests from eastern Bangladesh and northeast India to southern China and Indonesia (including the islands of Sumatra, Borneo, and Java). Also called the smaller apes or lesser apes, gibbons differ from great apes (chimpanzees, bonobos, gorillas, orangutans, and humans) in being smaller, exhibiting low sexual dimorphism, and not making nests. [3] In certain anatomical details, they superficially more closely resemble monkeys than great apes do, but like all apes, gibbons are tailless.
Rabbits are small mammals in the family Leporidae of the order Lagomorpha (along with the hare and the pika). Oryctolagus cuniculus includes the European rabbit species and its descendants, the world's 305 breeds [1] of domestic rabbit. Sylvilagus includes 13 wild rabbit species, among them the 7 types of cottontail. The European rabbit, which has been introduced on every continent except Antarctica, is familiar throughout the world as a wild prey animal and as a domesticated form of livestock and pet. With its widespread effect on ecologies and cultures, the rabbit (or bunny) is, in many areas of the world, a part of daily life-as food, clothing, a companion, and as a source of artistic inspiration.
A raven is one of several larger-bodied species of the genus Corvus. These species do not form a single taxonomic group within the genus. There is no consistent distinction between "crows" and "ravens", and these appellations have been assigned to different species chiefly on the basis of their size, crows generally being smaller than ravens. The largest raven species are the common raven and the thick-billed raven. The term "raven" originally referred to the common raven (Corvus corax), the type species of the genus Corvus, which has a larger distribution than any other species of Corvus, ranging over much of the Northern Hemisphere.
Monkey is a common name that may refer to groups or species of mammals, in part, the simians of infraorder Simiiformes. The term is applied descriptively to groups of primates, such as families of new world monkeys and old world monkeys. Many monkey species are tree-dwelling (arboreal), although there are species that live primarily on the ground, such as baboons. Most species are also active during the day (diurnal). Monkeys are generally considered to be intelligent, especially the old world monkeys of Catarrhini. Simians and tarsiers emerged within haplorrhines some 60 million years ago. New World monkeys and catarrhine monkeys emerged within the simians some 35 million years ago.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. In some species, this is done in a large group. The foam is laid above a water source, so the tadpoles fall into the water once they hatch. [1] The species within this family vary in size from 1.5 to 12 cm (0.59 to 4.72 in). [1] Like other arboreal frogs, they have toe discs, and those of the genus Chiromantis have two opposable fingers on each hand. This family also contains the Old World flying frogs, including Wallace's flying frog (Rhacophorus nigropalmatus). These frogs have extensive webbing between their forelimbs and hindlimbs, allowing them to glide through the air.
Rabbits are small mammals in the family Leporidae of the order Lagomorpha (along with the hare and the pika). Oryctolagus cuniculus includes the European rabbit species and its descendants, the world's 305 breeds [1] of domestic rabbit. Sylvilagus includes 13 wild rabbit species, among them the 7 types of cottontail. The European rabbit, which has been introduced on every continent except Antarctica, is familiar throughout the world as a wild prey animal and as a domesticated form of livestock and pet. With its widespread effect on ecologies and cultures, the rabbit (or bunny) is, in many areas of the world, a part of daily life-as food, clothing, a companion, and as a source of artistic inspiration.
A raven is one of several larger-bodied species of the genus Corvus. These species do not form a single taxonomic group within the genus. There is no consistent distinction between "crows" and "ravens", and these appellations have been assigned to different species chiefly on the basis of their size, crows generally being smaller than ravens. The largest raven species are the common raven and the thick-billed raven. The term "raven" originally referred to the common raven (Corvus corax), the type species of the genus Corvus, which has a larger distribution than any other species of Corvus, ranging over much of the Northern Hemisphere.
Monkey is a common name that may refer to groups or species of mammals, in part, the simians of infraorder Simiiformes. The term is applied descriptively to groups of primates, such as families of new world monkeys and old world monkeys. Many monkey species are tree-dwelling (arboreal), although there are species that live primarily on the ground, such as baboons. Most species are also active during the day (diurnal). Monkeys are generally considered to be intelligent, especially the old world monkeys of Catarrhini. Simians and tarsiers emerged within haplorrhines some 60 million years ago. New World monkeys and catarrhine monkeys emerged within the simians some 35 million years ago.
The Rhacophoridae are a family of frog species, which occur in tropical sub-Saharan Africa, South India and Sri Lanka, Japan; northeastern India to eastern China south through the Philippines and Greater Sundas, and Sulawesi. They are commonly known as shrub frogs, or more ambiguously as "moss frogs" or "bush frogs". Some Rhacophoridae are called "tree frogs". Among the most spectacular members of this family are numerous "flying frogs". Although a few groups are primarily terrestrial, rhacophorids are predominantly treefrogs which are arboreal. Mating frogs, while in amplexus, hold on to a branch, and beat their legs to form a foam. The eggs are laid in the foam, and covered with seminal fluid, before the foam hardens into a protective casing. . In our proposed DSAH, we first handle the nonlinear relations in different modalities with the kernelization, then an asymmetric learning scheme is proposed to effectively perform the hash learning process; meanwhile, our proposed method fully considers the label information to enhance the semantic information. In addition, a discrete optimization algorithm is proposed to solve the discrete problems.

Definitions
Suppose that the multimedia training data contains M modalities, represented by n } ∈ R d m ×n is the m-th modality data features and d m is the dimension of modality X (m) . In this paper, we focus on the supervised hashing paradigm; therefore, label information L ∈ {0, 1} c×n is available, c denotes the number of categories, and l j i = 1 indicates the j-th instance belongs to category i, and l ij = 0 otherwise. B ∈ R k×n denotes the hash codes, where k is the length of hash codes. f (·) denotes the hash function. The main notations used in this paper are listed in Table 1.

Notation
Explanations Hash mapping matrix D ∈ R c×c Projection matrix for label information Dimension of modality X (m) n Number of instances c Number of categories q Number of Kernelized features

Kernelization
Kernelization is a widely used technique to handle the nonlinear relations in different modalities. Therefore, in this paper, we use Radical Basis Function (RBF) kernel to express the nonlinear correlations among original high dimensional features [49][50][51]. Specifically, we define the RBF function φ(·) as follows: where A = [a 1 , a 2 , ..., a q ] denotes the randomly chosen q anchors from the database and σ is the free parameter. Therefore, the complex original feature X (m) ∈ R d m ×n can be converted into a nonlinear relation representation φ(X (m) ) ∈ R q×n .

Feature Mapping
The aim of DSAH is to project the original features to compact hash codes. In this paper, we adopt two linear projections as the hash mapping functions for image modality X (1) and text modality X (2) , respectively. f 1 (X (1) ) = sgn(P 1 φ(X (1) )), f 2 (X (2) ) = sgn(P 2 φ(X (2) )), where P 1 ∈ R k×q and P 2 ∈ R k×q are the hash mapping matrices, which map specific kernel features into Hamming subspace, and f 1 (·) and f 2 (·) are hash functions for image modality and text modality, respectively.

Label Alignment Scheme
As described above, labels contain rich semantic information, directly converting the complex label vectors into binary semantic matrix will cause the loss of semantic information. The results of Gui's work [52] demonstrate that the ordinary least squares regression is sensitive to the boundary contour. Inspired by the work in [53], we consider p,q norm instead of 2 norm to handle the problem, the p,q norm can be formulated as where E = R B − L and R ∈ R k×c is the semantic projection matrix. It is easy to find that when p = q = 2, Equation (3) is a standard Frobenius norm. However, in order to improve the robustness of the model for outliers and the sparsity of the label alignment matrix, we need to redefine the values of p, q. In general, the sparsity of the model can be guaranteed when the constraint conditions satisfy p ≥ 2 and 0 ≤ q ≤ 2. Therefore, in the paper, we set p = 2 and q = 1, as if q = 0, the problem is not convex. Then, we can rewrite the Equation (3) where D ∈ R c×c is the diagonal matrix, and the i-th element of D is defined as where e (i) is the i-th row of E.

Asymmetric Learning Framework
We briefly review the related work Supervised Hashing with Kernels (KSH) [51], the symmetric learning framework can be formulated as where B is the learned hash codes. However, there are two major problems of Equation (5): (1) It is very time-consuming to directly compute S, as the similarity information S is a n × n matrix. (2) Some works [54,55] show that the use of an asymmetric learning framework can not only solve the problem of high time consumption, but also improves retrieval accuracy, because the value range of the asymmetric learning framework is wider than that of symmetric learning. Therefore, in this paper, we construct an asymmetric learning framework to learn the compact hash codes, that is, min B,P 1 ,P 2 The advantages of Equation (6) are as follows: 1.
The learning mode uses an efficient asymmetric learning architecture instead of a time-consuming symmetric one.

2.
The use of the real-valued embeddings instead of the binary embeddings produces a close semantic similarity relation, and the value of the objective function is smaller.

3.
The last term is used to reduce the quantization errors, which leads to a better retrieval performance.
However, there is a limitation of Equation (6) that is for the purpose of cross-modal retrieval tasks, we need to obtain a unified hash codes. Therefore, we need to consider another discrete constraint, i.e., min F . In order to make the optimization easy, we set a unified hash code B = B 1 = B 2 instead of minimizing the constraint min (6) can be rewritten as min B,P 1 ,P 2 where α is the balance parameter.

The Joint Framework
Combining the above constraints and individual objective function, we obtain min B,R,P 1 ,P 2 where γ is the trade-off parameter, P * i = P i φ(X (i) ), Re(·) = || · || 2 F is the Frobenius norm regularization term, which is used to prevent overfitting.

Optimization
In this part, we use an alternating strategy to solve the four variables B, R, P 1 , P 2 in Equation (8), as the four variables are coupled with each other. The problem is split into four steps as follows.
Fix R, P 1 , P 2 , update B. The sub-problem of Equation (8) related to B can be formulated as min B ||(P 1 φ(X (1) )) B − kS|| 2 F + ||(P 2 φ(X (2) )) B − kS|| 2 F + tr(E DE) In the next step, we need to solve the following problem: where C = 0.5(P 1 φ(X (1) ) + P 2 φ(X (2) )). As the B is the discrete value, it is challenging to directly solve the value of B. In this solution, we propose an augmented Lagrangian multiplier (ALM) [39] to compute B. Specifically, we introduce an auxiliary value V ∈ {−1, 1} k×n to replace the B of second term, i.e., B RDR B. Then, we obtain the following formula: where J b measures the gap between B and V.
Then, the value of B can be solved with a closed-form solution: However, the computational complexity of P * φ(X ( * ) )S| 2 * =1 is O(n 2 ), which is not suitable for large-scale retrieval tasks. To address this problem, we use the label matrix L ∈ R c×n to replace the similarity matrix S ∈ R n×n . Specifically, we letL ij = l ij /||l i || 2 , as the element at the i-th row and the j-th column in the matrix L. Then, the similarity matrix S can be rewritten as where 1 n is a vector with all elements being 1. Therefore, we can rewrite the term P * φ(X ( * ) )S| 2 * =1 as which consumes O((q + c)kn). Fix B, update V. The sub-problem related to V can be formulated as Then, the value of V can be solved with a closed-form solution, Update J b . The sub-problem related to J b can be updated as where ρ is a parameter to control the convergence speed. Fix B, P 1 , P 2 , update R. The sub-problem of Equation (8) In the next step, we need to solve the following problem: Setting the derivative Equation (20) w.r.t R to 0, we obtain We transform Equation (20) into Then, it can be seen that Equation (21) is a Sylvester equation. Therefore, the value of R can be easily solved. Due to the space limitation, the detail about the solution is not given here.
The objective function is solved by iteratively updating four variables until the objective function converges or reaches the preset maximum number of iterations. The iterative optimization for solving the Equation (8) is summarized in Algorithm 1.
Output: Hash mapping functions P 1 and P 2 .
Until up to T.

Out-of-Sample Extension
In the query phase, the proposed DSAH can easily map the original high-dimensional instances into compact hash codes. Specifically, given a new query x (t) q X (m) , DSAH learns its corresponding hash codes by where φ(x (t) q ) is the nonlinear kernelized embedding of x (t) q .

Complexity Analysis
For each iteration, the time complexity is analyzed as follows. The time computational complexity of B is O(k 2 c + kc 2 + (q + c + k)kn), V is O(kc 2 + k 2 c + k 2 n), R is O((k 2 + kc)n + k 2 c + kc 2 + c 3 ), P 1 and P 2 are all O(q 3 + kq 2 + (kq + kc + qc + q 2 )n). As {k, c, q} n, the training complexity is O((kq + k 2 + kc + q 2 )n). Given the iteration T, the overall training complexity for DSAH is O((kq + k 2 + kc + q 2 )nT), where T {k, c, q} is very small , which is linear to the training set size. Therefore, DSAH is highly scalable for large-scale cross-modal retrieval tasks.

Datasets
To evaluate the performance of DSAH, we conducted experiments on two widely used datasets, i.e., MIRFlickr [56] and NUS-WIDE [57] datasets.

MIRFlickr
It contains 25,000 instances collected from open website, which are annotated by at least one of 24 tags. Similar to the work in [38], we ignored the instances that textual tags appear less than 20 times and finally selected 20,015 instances. We randomly selected 2k instances as the query set and the rest as the retrieval set. Each image is represented as a 512-D GIST feature and each text is represented as a 1386-D bag-of-word (BOW) vector.

NUS-WIDE
It contains 269,648 instances collected from Flick with 5018 unique tags and 81 groundtruth concepts that can be used for evaluation. Similar to the work in [38], we selected the ten most frequent tags and corresponding 186,577 instances. We randomly selected 2000 instances as the query set and the rest as the retrieval set. Each image is represented as a 500-D SIFT feature and each text is represented as a 1000-D bag-of-word (BOW) vector.

Methodology
To verify the effectiveness of our proposed DSAH method, seven state-of-the-art cross-modal hashing methods are compared. Among them, CMFH [32] and FSH [33] are unsupervised cross-modal hashing methods, and SCM-Seq [34], SePH-km [35], DCH [36], LCMFH [37], and SRLCH [42] are supervised ones. We have briefly introduced the compared baselines in Section 2. For fair comparison, the experimental results with citations are copied from the corresponding works.
To evaluate our proposed DSAH, we conducted two cross-modal retrieval tasks: (1) "Image2Text" using an image query to retrieve texts; (2) "Text2Image" using a text query to retrieve images. In this paper, three widely-used evaluation measures are used to evaluate the retrieval performance, i.e., mean average precision (mAP), precision-recall curves (PR) and precisions w.r.t top-k returned image (P@k).

Implementation Details
DSAH consists of several parameters, i.e., α and γ. We tune the balance parameters, i.e., α and γ using grid search, and the best performance is achieve when {α = 10 −1 , γ = 10 −3 } and {α = 10 −2 , γ = 10 −3 } on MIRFlickr and NUS-WIDE datasets, respectively. q is the number of kernel and optimal performance is obtained when q = 2000. ξ and ρ are used for ALM algorithm and the best performance is obtained when {ξ = 10 −2 , ρ = 1.5} and {ξ = 10 −1 , ρ = 1.5} on MIRFlickr and NUS-WIDE datasets, respectively. All our experiments are conducted on a workstation with a Intel Xeon Silver 4210 CPU@2.20 GHz of 10 cores and 128 G RAM. Tables 2 and 3 show the mAP scores of different compared cross-modal hashing methods at 8 bits, 16 bits, 32 bits, 64 bits, and 128 bits on MIRFlickr and NUS-WIDE datasets, respectively. Note that the mAP metric is one of the comprehensive evaluation criterions used to measure the effectiveness of the proposed method. From these tables, it can be observed that the mAP scores of DSAH are higher than most compared baselines with different code lengths on the two datasets. In the seven compared baselines, only SRLCH, LCMFH, and DCH obtain satisfactory retrieval performance. The main reason is that they learn the common latent representation across different modalities through matrix factorization operations, thus the common latent representation can be used as a bridge to solve the heterogeneous gap between different modalities. However, they ignore the use of an asymmetric learning framework to enhance the semantic similarity of different modalities and the noises contained in the labels. In contrast, our proposed DSAH leverages both the similarity matrix and label information to enhance the semantic information of the learned hash codes, and solves the problem of noises contained in the labels. Specifically, on the MIRFlickr dataset, compared to the best baselines, i.e., SRLCH, the mAP scores of DSAH have an increase of 2.7% on average, and on the NUS-WIDE dataset, DSAH obtains the highest mAP scores of all compared baselines, which demonstrates the efficacy of DSAH. Meanwhile, by comparing supervised cross-modal hashing methods and unsupervised ones on the two datasets, we find that the supervised hashing methods, i.e., SCM-Seq, SePH-km, DCH, LCMFH, and SRLCH, can always outperform the unsupervised hashing methods, i.e., CMFH and FSH, as the supervised information can improve the ability of hash learning process. In addition, the mAP scores of most cross-modal hashing methods increase as the length of the hash codes becomes longer, revealing that the longer codes can handle more discriminative information. The performance on the T2I task, i.e., the use of text modality to retrieve image modality is better than that on the I2T task, i.e., the use of image modality to retrieve text modality. The reason is that the semantic information in text modality is more than that in image modality.  Figure 2 plots the precision-recall and P@k curves in the cases of 64-bit code length for all compared baselines on two datasets. From the figure, we can draw the following observations.

1.
From the precision-recall curves, we can observe that the area under the precisionrecall curves of DSAH is larger than the compared baselines, which shows the effectiveness of DSAH.

2.
From the P@k curves, we can observe that DSAH outperforms the compared baselines in most cases, which further demonstrate its superiority.

Effects of Discrete Optimization
To validate the effects of the proposed discrete optimization strategy, we denote a variant of DSAH, named DSAH-Re. Specifically, we first relax the discrete constraints, then Equation (9) can be solved as Setting the derivative Equation (29) w.r.t. B to 0, and the value of B can be solved with a closed-form solution: B = (RDR ) −1 α(P 1 φ(X (1) ) + P 2 φ(X (2) )) + RDL .
Then, we obtain the hash codes by mean-thresholding operation. The mAP results of DSAH and DSAH-Re on two datasets are shown in Table 4 and 5. From the table, we can observe that the performance of DSAH is better than that of DSAH-Re on two datasets. These results demonstrate that our proposed discrete optimization algorithm performs well in avoiding quantization errors and improving the performance of crossmodal retrieval tasks.  In this paper, DSAH adopts a kernelization technique to handle the nonlinear relations between different heterogeneous modalities to improve the retrieval accuracy and efficiency. To demonstrate the effects of kernelization, we denote a variant of DSAH, named DSAH-ke, which directly uses the original features to learn the hash codes. We conduct experiments on two datasets with the code length varying from 8 bits to 128 bits to evaluate the performance of DSAH-ke. The mAP results of DSAH-ke are reported in Tables 4 and 5. From the tables, we can observe that the lack of using kernelization will reduce the retrieval performance.

Effects of 2,1 Norm
As shown in Section 3.3, the p,q norm, i.e., 2,1 , is used to improve the robustness for outliers. Therefore, in this section, to verify its effectiveness, we denote a variant of DSAH, named DSAH-Nm, which replaced the term ||R B − L|| 2,1 in Equation (8) with ||R B − L|| 2 F . The mAP results on two datasets with the code length varying from 8 bits to 128 bits are reported in Table 4 and 5. From the table, we can observe that the 2,1 norm is effective to improve the performance of DSAH, the reason may be that the label information often inevitably contains some noises or subjective factors.

Effects of Word Embeddings
In order to verify the impact of different word embeddings on the performance of cross-modal retrieval. We denote a Bidirectional Encoder Representations from Transformers (BERT)-based [58] variant of DSAH, named DSAH-BERT. The BERT-based word embeddings are generated by summing the 786-D features from the last 4-hidden layers of a 12 layers BERT trained in an uncased way (https://github.com/huggingface/transformers, accessed on 13 July 2021). We conduct experiments on NUS-WIDE dataset to evaluate the effects of word embeddings. The mAP scores on NUS-WIDE dataset with the code length varying from 8 bits to 128 bits are reported in Table 6. From the table, we can find that BERT-based word embedding provides a slightly higher average mAP scores than those with bag-ofword embedding.  [59]. The mAP scores on NUS-WIDE dataset with the code length varying from 8 bits to 128 bits are shown in Table 7. From the table, we can observe that the use of deep learning based representation for cross-modal retrieval improves the accuracy of retrieving text through images, but reduces the accuracy of retrieving images through text. The reason may be that deep learning-based representation improves the semantics of the image representation, but the difficulty of retrieving images is increased due to the increase of the dimensionality simultaneously. In this section, we conduct parameter sensitivity analysis experiments to observe the variation of mAP scores under different α and γ. In this experiment, by prefixing the code length as 64 bits, we vary the parameters α and γ in the range of {10 −5 , 10 −4 , ..., 10 4 , 10 5 }. Figures 3 and 4 report the results. From these results, we observe that the performance of our proposed DSAH is relatively stable on a wide range of α and γ values. Specifically, on the MIRFlickr dataset, when α < 10 0 and γ < 10 1 , the retrieval performance becomes stable. On the NUS-WIDE dataset, when α < 10 2 and γ < 10 1 , the scores of mAP have a very small fluctuation. Therefore, our proposed method can be easily tuned for practical implementations.

Convergence Analysis
In order to show the convergence of our proposed DSAH, we conduct the experiments on two datasets with the codes length fixed as 64 bits. Similar results can be obtained on other lengths of hash codes. The results are shown in Figure 5. Note that, in order to visually represent the convergence of the objective function, the value can be normalized by dividing by the maximum value on each dataset. From the figure, we can easily see that the values of objective function can converge very fast, i.e., less than 12 iterations, which demonstrates the efficiently of the closed-form solutions of the optimization algorithm.

Limitations
The main potential limitation of our proposed DSAH is that the time complexity of constructing the pairwise similarity matrix is O(n 2 ). Although the method we proposed uses label matrices instead of a pairwise similarity matrix for matrix decomposition, it cannot effectively solve the large time complexity problem. Therefore, compared with the hash methods that only use label information for learning, the time cost of DSAH is slightly high. In addition, without point-to-point label information, there is no general algorithm to process similarity matrices on all datasets.

Conclusions
In this paper, we present a novel cross-modal hashing method, named DSAH, for largescale cross-modal retrieval. In detail, to enhance the feature representation in the linear model, we handle the nonlinear relations with a kernelization technique. Meanwhile, DSAH incorporates the label information and semantic matrix into the learning process. Therefore, DSAH can obtain more semantic information to improve the discriminative capability of the learned hash codes. However, due to the inevitable noise and subjective factors in labels for large-scale dataset, the 2,1 norm is used to sparse the matrix and effectively deal with outliers. In addition, a discrete optimization algorithm is proposed to solve the quantization errors and improve the optimization efficiency. Extensive experiments on two datasets demonstrate the superiority of DSAH on cross-modal retrieval tasks.