Search Results (22)

Manifold learning is a significant computer vision task used to describe high-dimensional visual data in lower-dimensional manifolds without sacrificing the intrinsic structural properties required for 3D reconstruction. Isomap, Locally Linear Embedding (LLE), Laplacian Eigenmaps, and t-SNE are helpful in data topology preservation but are typically indifferent to the intrinsic differential geometric characteristics of the manifolds, thus leading to deformation of spatial relations and reconstruction accuracy loss. This research proposes an Optimization of Manifold Learning using Differential Geometry Framework (OML-DGF) to overcome the drawbacks of current manifold learning techniques in 3D reconstruction. The framework employs intrinsic geometric properties—like curvature preservation, geodesic coherence, and local–global structure correspondence—to produce structurally correct and topologically consistent low-dimensional embeddings. The model utilizes a Riemannian metric-based neighborhood graph, approximations of geodesic distances with shortest path algorithms, and curvature-sensitive embedding from second-order derivatives in local tangent spaces. A curvature-regularized objective function is derived to steer the embedding toward facilitating improved geometric coherence. Principal Component Analysis (PCA) reduces initial dimensionality and modifies LLE with curvature weighting. Experiments on the ModelNet40 dataset show an impressive improvement in reconstruction quality, with accuracy gains of up to 17% and better structure preservation than traditional methods. These findings confirm the advantage of employing intrinsic geometry as an embedding to improve the accuracy of 3D reconstruction. The suggested approach is computationally light and scalable and can be utilized in real-time contexts such as robotic navigation, medical image diagnosis, digital heritage reconstruction, and augmented/virtual reality systems in which strong 3D modeling is a critical need. Full article

With the rapid advancement of remote-sensing technology, the spectral information obtained from hyperspectral remote-sensing imagery has become increasingly rich, facilitating detailed spectral analysis of Earth’s surface objects. However, the abundance of spectral information presents certain challenges for data processing, such as the “curse of dimensionality” leading to the “Hughes phenomenon”, “strong correlation” due to high resolution, and “nonlinear characteristics” caused by varying surface reflectances. Consequently, dimensionality reduction of hyperspectral data emerges as a critical task. This paper begins by elucidating the principles and processes of hyperspectral image dimensionality reduction based on manifold theory and learning methods, in light of the nonlinear structures and features present in hyperspectral remote-sensing data, and formulates a dimensionality reduction process based on manifold learning. Subsequently, this study explores the capabilities of feature extraction and low-dimensional embedding for hyperspectral imagery using manifold learning approaches, including principal components analysis (PCA), multidimensional scaling (MDS), and linear discriminant analysis (LDA) for linear methods; and isometric mapping (Isomap), locally linear embedding (LLE), Laplacian eigenmaps (LE), Hessian locally linear embedding (HLLE), local tangent space alignment (LTSA), and maximum variance unfolding (MVU) for nonlinear methods, based on the Indian Pines hyperspectral dataset and Pavia University dataset. Furthermore, the paper investigates the optimal neighborhood computation time and overall algorithm runtime for feature extraction in hyperspectral imagery, varying by the choice of neighborhood k and intrinsic dimensionality d values across different manifold learning methods. Based on the outcomes of feature extraction, the study examines the classification experiments of various manifold learning methods, comparing and analyzing the variations in classification accuracy and Kappa coefficient with different selections of neighborhood k and intrinsic dimensionality d values. Building on this, the impact of selecting different bandwidths t for the Gaussian kernel in the LE method and different Lagrange multipliers λ for the MVU method on classification accuracy, given varying choices of neighborhood k and intrinsic dimensionality d, is explored. Through these experiments, the paper investigates the capability and effectiveness of different manifold learning methods in feature extraction and dimensionality reduction within hyperspectral imagery, as influenced by the selection of neighborhood k and intrinsic dimensionality d values, identifying the optimal neighborhood k and intrinsic dimensionality d value for each method. A comparison of classification accuracies reveals that the LTSA method yields superior classification results compared to other manifold learning approaches. The study demonstrates the advantages of manifold learning methods in processing hyperspectral image data, providing an experimental reference for subsequent research on hyperspectral image dimensionality reduction using manifold learning methods. Full article

Process safety plays a vital role in the modern process industry. To prevent undesired accidents caused by malfunctions or other disturbances in complex industrial processes, considerable attention has been paid to data-driven fault detection techniques. To explore the underlying manifold structure, manifold learning methods including Laplacian eigenmaps, locally linear embedding, and Hessian eigenmaps have been utilized in data-driven fault detection. However, only the partial local structure information is extracted from the aforementioned methods. This paper proposes fused local manifold learning (FLML), which synthesizes the typical manifold learning methods to find the underlying manifold structure from different angles. A more comprehensive local structure is discovered under a unified framework by constructing an objection optimization function for process data dimension reduction. The proposed method takes advantage of different manifold learning methods. Based on the proposed dimension reduction method, a new data-driven fault detection method is developed. Hotelling’s $T^2$ and Q statistics are established for the purpose of fault detection. Experiments on an industrial benchmark Tennessee Eastman process whose average MDR and average FAR of FLML $T^2$ are $7.58\%$ and $0.21\%$ and a real blast furnace ironmaking process whose MDR and FAR of FLML $T^2$ are $2.80\%$ and $0.00\%$ are carried out to demonstrate the superiority and effectiveness of the proposed method. Full article

Enhancing the generalization capability of time-series models for streamflow prediction using dimensionality reduction (DR) techniques remains a major challenge in water resources management (WRM). In this study, we investigated eight DR techniques and their effectiveness in mitigating the curse of dimensionality, which hinders the performance of machine learning (ML) algorithms in the field of WRM. Our study delves into the most non-linear unsupervised representative DR techniques, including principal component analysis (PCA), kernel PCA (KPCA), multi-dimensional scaling (MDS), isometric mapping (ISOMAP), locally linear embedding (LLE), t-distributed stochastic neighbor embedding (t-SNE), Laplacian eigenmaps (LE), and autoencoder (AE), examining their effectiveness in multi-step ahead (MSA) streamflow prediction. In this study, we conducted a conceptual comparison of these techniques. Subsequently, we focused on their performance in four different case studies in the USA. Moreover, we assessed the quality of the transformed feature spaces in terms of the MSA streamflow prediction improvement. Through our investigation, we gained valuable insights into the performance of different DR techniques within linear/dense/convolutional neural network (CNN)/long short-term memory neural network (LSTM) and autoregressive LSTM (AR-LSTM) architectures. This study contributes to a deeper understanding of suitable feature extraction techniques for enhancing the capabilities of the LSTM model in tackling high-dimensional datasets in the realm of WRM. Full article

In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used in dimension reduction such as isometric feature mapping, Laplacian Eigenmaps, fast independent component analysis, kernel ridge regression, and t-distributed stochastic neighbor embedding. We then give a brief overview of some of the topological notions used in topological data analysis, such as barcodes, persistent homology, and Wasserstein distance. Theoretically, when these methods are applied on a data set, they can be interpreted differently. From EEG data embedded into a manifold of high dimension, we discuss these methods and we compare them across persistent homologies of dimensions 0, 1, and 2, that is, across connected components, tunnels and holes, shells around voids, or cavities. We find that from three dimension clouds of points, it is not clear how distinct from each other the methods are, but Wasserstein and Bottleneck distances, topological tests of hypothesis, and various methods show that the methods qualitatively and significantly differ across homologies. We can infer from this analysis that topological persistent homologies do change dramatically at seizure, a finding already obtained in previous analyses. This suggests that looking at changes in homology landscapes could be a predictor of seizure. Full article

In machine learning and data analysis, dimensionality reduction and high-dimensional data visualization can be accomplished by manifold learning using a t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm. We significantly improve this manifold learning scheme by introducing a preprocessing strategy for the t-SNE algorithm. In our preprocessing, we exploit Laplacian eigenmaps to reduce the high-dimensional data first, which can aggregate each data cluster and reduce the Kullback–Leibler divergence (KLD) remarkably. Moreover, the k-nearest-neighbor (KNN) algorithm is also involved in our preprocessing to enhance the visualization performance and reduce the computation and space complexity. We compare the performance of our strategy with that of the standard t-SNE on the MNIST dataset. The experiment results show that our strategy exhibits a stronger ability to separate different clusters as well as keep data of the same kind much closer to each other. Moreover, the KLD can be reduced by about $30\%$ at the cost of increasing the complexity in terms of runtime by only 1–2%. Full article

The second leading cause of death and one of the most common causes of disability in the world is stroke. Researchers have found that brain–computer interface (BCI) techniques can result in better stroke patient rehabilitation. This study used the proposed motor imagery (MI) framework to analyze the electroencephalogram (EEG) dataset from eight subjects in order to enhance the MI-based BCI systems for stroke patients. The preprocessing portion of the framework comprises the use of conventional filters and the independent component analysis (ICA) denoising approach. Fractal dimension ($FD$) and Hurst exponent ($Hur$) were then calculated as complexity features, and Tsallis entropy ($TsEn$) and dispersion entropy ($DispEn$) were assessed as irregularity parameters. The MI-based BCI features were then statistically retrieved from each participant using two-way analysis of variance (ANOVA) to demonstrate the individuals’ performances from four classes (left hand, right hand, foot, and tongue). The dimensionality reduction algorithm, Laplacian Eigenmap ($LE$), was used to enhance the MI-based BCI classification performance. Utilizing k-nearest neighbors (KNN), support vector machine (SVM), and random forest (RF) classifiers, the groups of post-stroke patients were ultimately determined. The findings show that $LE$ with RF and KNN obtained 74.48% and 73.20% accuracy, respectively; therefore, the integrated set of the proposed features along with ICA denoising technique can exactly describe the proposed MI framework, which may be used to explore the four classes of MI-based BCI rehabilitation. This study will help clinicians, doctors, and technicians make a good rehabilitation program for people who have had a stroke. Full article

Ranking sports teams generally relies on supervised techniques, requiring either prior knowledge or arbitrary metrics. In this paper, we offer a purely unsupervised technique. We apply this to operational decision-making, specifically, the controversial European Super League for association football, demonstrating how this approach can select dominant teams to form the new league. We first use random forest regression to select important variables predicting goal difference, which we use to calculate the Euclidian distances between teams. Creating a Laplacian eigenmap, we bisect the Fiedler vector to identify the natural clusters in five major European football leagues. Our results show how an unsupervised approach could identify four clusters based on five basic performance metrics: shots, shots on target, shots conceded, possession, and pass success. The top two clusters identify teams that dominate their respective leagues and are the best candidates to create the most competitive elite super league. Full article

Today, introducing useful and practical solutions to residential load disaggregation as subsets of energy management has created numerous challenges. In this study, an intelligence hybrid solution based on manifold learning and deep learning applications is presented. The proposed solution presents a combined structure of Laplacian eigenmaps (LE), a convolutional neural network (CNN), and a recurrent neural network (RNN), called LE-CRNN. In the proposed model architecture, LE, with its high ability in dimensional reduction, transfers the salient features and specific values of power consumption curves (PCCs) of household electrical appliances (HEAs) to a low-dimensional space. Then, the combined model of CRNN significantly improves the structure of CNN in fully connected layers so that the process of identification and separation of the HEA type can be performed without overfitting problems and with very high accuracy. In order to implement the suggested model, two real-world databases have been used. In a separate scenario, a conventional CNN is applied to the data for comparing the performance of the suggested model with the CNN. The designed networks are trained and validated using the PCCs of HEAs. Then, the whole energy consumption of the building obtained from the smart meter is used for load disaggregation. The trained networks, which contain features extracted from PCCs of HEAs, prove that they can disaggregate the total power consumption for houses intended for the Reference Energy Disaggregation Data Set (REDD) and Almanac of Minutely Power Dataset (AMPds) with average accuracies (Acc) of 97.59% and 97.03%, respectively. Finally, in order to show the accuracy of the developed hybrid model, the obtained results in this study are compared with the results of similar works for the same datasets. Full article

Laser-induced breakdown spectroscopy (LIBS) spectra often include many intensity lines, and obtaining meaningful information from the input dataset and condensing the dimensions of the original data has become a significant challenge in LIBS applications. This study was conducted to classify five different types of aluminum alloys rapidly and noninvasively, utilizing the manifold dimensionality reduction technique and a support vector machine (SVM) classifier model integrated with LIBS technology. The augmented partial residual plot was used to determine the nonlinearity of the LIBS spectra dataset. To circumvent the curse of dimensionality, nonlinear manifold learning techniques, such as local tangent space alignment (LTSA), local linear embedding (LLE), isometric mapping (Isomap), and Laplacian eigenmaps (LE) were used. The performance of linear techniques, such as principal component analysis (PCA) and multidimensional scaling (MDS), was also investigated compared to nonlinear techniques. The reduced dimensions of the dataset were assigned as input datasets in the SVM classifier. The prediction labels indicated that the Isomap-SVM model had the best classification performance with the classification accuracy, the number of dimensions and the number of nearest neighbors being 96.67%, 11, and 18, respectively. These findings demonstrate that the combination of nonlinear manifold learning and multivariate analysis has the potential to classify the samples based on LIBS with reasonable accuracy. Full article

Classification performances for some classes of electrocardiographic (ECG) and electroencephalographic (EEG) signals processed to dimensionality reduction with different degrees are investigated. Results got with various classification methods are given and discussed. So far we investigated three techniques for reducing dimensionality: Laplacian eigenmaps (LE), locality preserving projections (LPP) and compressed sensing (CS). The first two methods are related to manifold learning while the third addresses signal acquisition and reconstruction from random projections under the supposition of signal sparsity. Our aim is to evaluate the benefits and drawbacks of various methods and to find to what extent they can be considered remarkable. The assessment of the effect of dimensionality decrease was made by considering the classification rates for the processed biosignals in the new spaces. Besides, the classification accuracies of the initial input data were evaluated with respect to the corresponding accuracies in the new spaces using different classifiers. Full article

A nonlinear feature extraction-based approach using manifold learning algorithms is developed in order to improve the classification accuracy in an electronic tongue sensor array. The developed signal processing methodology is composed of four stages: data unfolding, scaling, feature extraction, and classification. This study aims to compare seven manifold learning algorithms: Isomap, Laplacian Eigenmaps, Locally Linear Embedding (LLE), modified LLE, Hessian LLE, Local Tangent Space Alignment (LTSA), and t-Distributed Stochastic Neighbor Embedding (t-SNE) to find the best classification accuracy in a multifrequency large-amplitude pulse voltammetry electronic tongue. A sensitivity study of the parameters of each manifold learning algorithm is also included. A data set of seven different aqueous matrices is used to validate the proposed data processing methodology. A leave-one-out cross validation was employed in 63 samples. The best accuracy ($96.83\%$) was obtained when the methodology uses Mean-Centered Group Scaling (MCGS) for data normalization, the t-SNE algorithm for feature extraction, and k-nearest neighbors (kNN) as classifier. Full article

Most of the available hyperspectral image (HSI) visualization methods can be considered as data-oriented approaches. These approaches are based on global data, so it is difficult to optimize display of a specific object. Compared to data-oriented approaches, object-oriented visualization approaches show more pertinence and would be more practical. In this paper, an object-oriented hyperspectral color visualization approach with controllable separation is proposed. Using supervised information, the proposed method based on manifold dimensionality reduction methods can simultaneously display global data information, interclass information, and in-class information, and the balance between the above information can be adjusted by the separation factor. Output images are visualized after considering the results of dimensionality reduction and separability. Five kinds of manifold algorithms and four HSI data were used to verify the feasibility of the proposed approach. Experiments showed that the visualization results by this approach could make full use of supervised information. In subjective evaluations, t-distributed stochastic neighbor embedding (T-SNE), Laplacian eigenmaps (LE), and isometric feature mapping (ISOMAP) demonstrated a sharper detailed pixel display effect within individual classes in the output images. In addition, T-SNE and LE showed clarity of information (optimum index factor, OIF), good correlation (ρ), and improved pixel separability (δ) in objective evaluation results. For Indian Pines data, T-SNE achieved the best results in regard to both OIF and $\delta$ , which were 0.4608 and 23.83, respectively. However, compared with other methods, the average computing time of this method was also the longest (1521.48 s). Full article

Euclidean distance between instances is widely used to capture the manifold structure of data and for graph-based dimensionality reduction. However, in some circumstances, the basic Euclidean distance cannot accurately capture the similarity between instances; some instances from different classes but close to the decision boundary may be close to each other, which may mislead the graph-based dimensionality reduction and compromise the performance. To mitigate this issue, in this paper, we proposed an approach called Laplacian Eigenmaps based on Clustering-Adjusted Similarity (LE-CAS). LE-CAS first performs clustering on all instances to explore the global structure and discrimination of instances, and quantifies the similarity between cluster centers. Then, it adjusts the similarity between pairwise instances by multiplying the similarity between centers of clusters, which these two instances respectively belong to. In this way, if two instances are from different clusters, the similarity between them is reduced; otherwise, it is unchanged. Finally, LE-CAS performs graph-based dimensionality reduction (via Laplacian Eigenmaps) based on the adjusted similarity. We conducted comprehensive empirical studies on UCI datasets and show that LE-CAS not only has a better performance than other relevant comparing methods, but also is more robust to input parameters. Full article