Search Results (18)

Point cloud denoising is essential for improving 3D data quality, yet traditional K-means methods relying on Euclidean distance struggle with non-uniform noise. This paper proposes a K-means algorithm leveraging Total Bregman Divergence (TBD) to better model geometric structures on manifolds, enhancing robustness against noise. Specifically, TBDs—Total Logarithm, Exponential, and Inverse Divergences—are defined on symmetric positive-definite matrices, each tailored to capture distinct local geometries. Theoretical analysis demonstrates the bounded sensitivity of TBD-induced means to outliers via influence functions, while anisotropy indices quantify structural variations. Numerical experiments validate the method’s superiority over Euclidean-based approaches, showing effective noise separation and improved stability. This work bridges geometric insights with practical clustering, offering a robust framework for point cloud preprocessing in vision and robotics applications. Full article

Predicting water inrush in coal mines faces significant challenges due to limited data, model generalization, and a lack of interpretability. Current approaches often neglect the inherent geometrical symmetries and structured patterns within the complex hydrological parameter space, rely on local parameter optimization, and struggle with interpretability, leading to insufficient predictive accuracy and engineering applicability under complex geological conditions. This study addresses these limitations by integrating Gaussian mixture modeling (GMM), manifold learning, and data augmentation to effectively capture multimodal hydrological data distributions and reveal their intrinsic symmetrical configurations and manifold structures, thereby reducing feature dimensionality. We then apply a whale optimization algorithm (WOA)-enhanced XGBoost model to forecast water inrush probabilities. Our model achieved an R² of 0.92, demonstrating a greater than 60% error reduction across various metrics. Validation at the Yangcheng Coal Mine confirmed that this balanced approach significantly enhances predictive accuracy, interpretability, and cross-scenario applicability. The synergy between high accuracy and transparency provides decision makers with reliable risk insights, enabling bidirectional validation with geological mechanisms and supporting the implementation of targeted, proactive safety measures. Full article

Automated handwritten signature verification continues to pose significant challenges. A common approach for developing writer-independent signature verifiers involves the use of a dichotomizer, a function that generates a dissimilarity vector with the differences between similar and dissimilar pairs of signature descriptors as components. The Dichotomy Transform was applied within a Euclidean or vector space context, where vectored representations of handwritten signatures were embedded in and conformed to Euclidean geometry. Recent advances in computer vision indicate that image representations to the Riemannian Symmetric Positive Definite (SPD) manifolds outperform vector space representations. In offline signature verification, both writer-dependent and writer-independent systems have recently begun leveraging Riemannian frameworks in the space of SPD matrices, demonstrating notable success. This work introduces, for the first time in the signature verification literature, a Riemannian dichotomizer employing Riemannian dissimilarity vectors (RDVs). The proposed framework explores a number of local and global (or common pole) topologies, as well as simple serial and parallel fusion strategies for RDVs for constructing robust models. Experiments were conducted on five popular signature datasets of Western and Asian origin, using blind intra- and cross-lingual experimental protocols. The results indicate the discriminative capabilities of the proposed Riemannian dichotomizer framework, which can be compared to other state-of-the-art and computationally demanding architectures. Full article

Social bots increasingly mimic real users and collaborate in large-scale influence campaigns, distorting public perception and making their detection both critical and challenging. Traditional bot detection methods, constrained by single-source features, often fail to capture the complete behavioral and contextual characteristics of social bots, especially their dynamic behavioral evolution and group coordination tactics, resulting in feature incompleteness and reduced detection performance. To address this challenge, we propose CB-MTE, a social bot detection framework based on multi-source heterogeneous feature fusion. CB-MTE adopts a hierarchical architecture: user metadata is used to construct behavioral portraits, deep semantic representations are extracted from textual content via DistilBERT, and community-aware graph embeddings are learned through a combination of random walk and Skip-gram modeling. To mitigate feature redundancy and preserve structural consistency, manifold learning is applied for nonlinear dimensionality reduction, ensuring both local and global topology are maintained. Finally, a CatBoost-based collaborative reasoning mechanism enhances model robustness through ordered target encoding and symmetric tree structures. Experiments on the TwiBot-22 benchmark dataset demonstrate that CB-MTE significantly outperforms mainstream detection models in recognizing dynamic behavioral traits and detecting collaborative bot activities. These results confirm the framework’s capability to capture the complete behavioral and contextual characteristics of social bots through multi-source feature integration. Full article

In the current article, we examine Lorentzian para-Kenmotsu (shortly, LP-Kenmotsu) manifolds with regard to the generalized symmetric metric connection ${\nabla }^{\mathcal{G}}$ of type $(\alpha ,\beta )$. First, we obtain the expressions for curvature tensor, Ricci tensor and scalar curvature of an LP-Kenmotsu manifold with regard to the connection ${\nabla }^{\mathcal{G}}$. Next, we analyze LP-Kenmotsu manifolds equipped with the connection ${\nabla }^{\mathcal{G}}$ that are locally symmetric, Ricci semi-symmetric, and $\phi$-Ricci symmetric and also demonstrated that in all these situations the manifold is an Einstein one with regard to the connection ${\nabla }^{\mathcal{G}}$. Moreover, we obtain some conclusions about projectively flat, projectively semi-symmetric and $\phi$-projectively flat LP-Kenmotsu manifolds concerning the connection ${\nabla }^{\mathcal{G}}$ along with several consequences through corollaries. Ultimately, we provide a 5-dimensional LP-Kenmotsu manifold example to validate the derived expressions. Full article

This study introduces a novel method for classifying sets of images, called Riemannian geodesic discriminant analysis–minimum Riemannian mean distance (RGDA-MRMD). This method first converts image data into symmetric positive definite (SPD) matrices, which capture important features related to the variability within the data. These SPD matrices are then mapped onto simpler, flat spaces (tangent spaces) using a mathematical tool called the logarithm operator, which helps to reduce their complexity and dimensionality. Subsequently, regularized local Fisher discriminant analysis (RLFDA) is employed to refine these simplified data points on the tangent plane, focusing on local data structures to optimize the distances between the points and prevent overfitting. The optimized points are then transformed back into a complex, curved space (SPD manifold) using the exponential operator to enhance robustness. Finally, classification is performed using the minimum Riemannian mean distance (MRMD) algorithm, which assigns each data point to the class with the closest mean in the Riemannian space. Through experiments on the ETH-80 (Eidgenössische Technische Hochschule Zürich-80 object category), AFEW (acted facial expressions in the wild), and FPHA (first-person hand action) datasets, the proposed method demonstrates superior performance, with accuracy scores of 97.50%, 37.27%, and 88.47%, respectively. It outperforms all the comparison methods, effectively preserving the unique topological structure of the SPD matrices and significantly boosting image set classification accuracy. Full article

In this research paper, we establish geometric inequalities that characterize the relationship between the squared mean curvature and the warping functions of a doubly warped product pointwise bi-slant submanifold. Our investigation takes place in the context of locally conformal almost cosymplectic manifolds, which are equipped with a quarter-symmetric metric connection. We also consider the cases of equality in these inequalities. Additionally, we derive some geometric applications of our obtained results. Full article

The main objective of this paper is to study semi-symmetric almost $\alpha$-cosymplectic three-manifolds. We present basic formulas for almost $\alpha$-cosymplectic manifolds. Using curvature properties, we obtain some necessary and sufficient conditions on semi-symmetric almost $\alpha$-cosymplectic three-manifolds. We obtain the main results under an additional condition. The paper concludes with two illustrative examples. Full article

A class of nearly Sasakian manifolds is considered in this paper. We discuss the geometric effects of some symmetries on such manifolds and show, under a certain condition, that the class of Ricci semi-symmetric nearly Sasakian manifolds is a subclass of Einstein manifolds. We prove that a Codazzi-type Ricci nearly Sasakian space form is either a Sasakian manifold with a constant $\varphi$-holomorphic sectional curvature $\mathcal{H}=1$ or a 5-dimensional proper nearly Sasakian manifold with a constant $\varphi$-holomorphic sectional curvature $\mathcal{H}>1$. We also prove that the spectrum of the operator $H^2$ generated by the nearly Sasakian space form is a set of a simple eigenvalue of 0 and an eigenvalue of multiplicity 4, and we induce that the underlying space form carries a Sasaki–Einstein structure. We show that there exist integrable distributions with totally geodesic leaves on the same manifolds, and we prove that there are no proper nearly Sasakian space forms with constant sectional curvature. Full article

Considered herein is the initial-boundary value problem for a semilinear parabolic equation with a memory term and non-local source $w_t-{\mathrm{\Delta }}_{\mathbb{B}}w-{\mathrm{\Delta }}_{\mathbb{B}}{w}_t+{\int }_0^{t}g(t-\tau ){\mathrm{\Delta }}_{\mathbb{B}}w\left(\tau \right)d\tau ={|w|}^{p-1}w-\frac{1}{|\mathbb{B}|}{\int }_{\mathbb{B}}{|w|}^{p-1}w\frac{d{x}_1}{x_1}d{x}^{\prime }$ on a manifold with conical singularity, where the Fuchsian type Laplace operator ${\mathrm{\Delta }}_{\mathbb{B}}$ is an asymmetry elliptic operator with conical degeneration on the boundary $x_1=0$. Firstly, we discuss the symmetrical structure of invariant sets with the help of potential well theory. Then, the problem can be decomposed into two symmetric cases: if $w_0\in W$ and $\mathrm{\Pi }\left(w_0\right)>0$, the global existence for the weak solutions will be discussed by a series of energy estimates under some appropriate assumptions on the relaxation function, initial data and the symmetric structure of invariant sets. On the contrary, if $w_0\in V$ and $\mathrm{\Pi }\left(w_0\right)<0$, the nonexistence of global solutions, i.e., the solutions blow up in finite time, is obtained by using the convexity technique. Full article

Gaussian Mixture Models (GMMs) are used in many traditional expert systems and modern artificial intelligence tasks such as automatic speech recognition, image recognition and retrieval, pattern recognition, speaker recognition and verification, financial forecasting applications and others, as simple statistical representations of underlying data. Those representations typically require many high-dimensional GMM components that consume large computing resources and increase computation time. On the other hand, real-time applications require computationally efficient algorithms and for that reason, various GMM similarity measures and dimensionality reduction techniques have been examined to reduce the computational complexity. In this paper, a novel GMM similarity measure is proposed. The measure is based on a recently presented nonlinear geometry-aware dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices. The algorithm is applied over SPD representations of the original data. The local neighborhood information from the original high-dimensional parameter space is preserved by preserving distance to the local mean. Instead of dealing with high-dimensional parameter space, the method operates on much lower-dimensional space of transformed parameters. Resolving the distance between such representations is reduced to calculating the distance among lower-dimensional matrices. The method was tested within a texture recognition task where superior state-of-the-art performance in terms of the trade-off between recognition accuracy and computational complexity has been achieved in comparison with all baseline GMM similarity measures. Full article

The objective of this paper is to explore the complete lifts of a quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle. A relationship between the Riemannian connection and the quarter-symmetric metric connection from a Sasakian manifold to its tangent bundle was established. Some theorems on the curvature tensor and the projective curvature tensor of a Sasakian manifold with respect to the quarter-symmetric metric connection to its tangent bundle were proved. Finally, locally $\varphi$-symmetric Sasakian manifolds with respect to the quarter-symmetric metric connection to its tangent bundle were studied. Full article

A detailed analysis of the electronic structure and decay dynamics in a symmetric system with three electrons in three linearly aligned binding sites representing quantum dots (QDs) is given. The two outer A QDs are two-level potentials and can act as (virtual) photon emitters, whereas the central B QD can be ionized from its one level into a continuum confined on the QD axis upon absorbing virtual photons in the inter-Coulombic decay (ICD) process. Two scenarios in such an $ABA$ array are explored. One ICD process is from a singly excited resonance state, whose decay releasing one virtual photon we find superimposed with resonance energy transfer among both A QDs. Moreover, the decay-process manifold for a doubly excited (DE) resonance is explored, in which collective ICD among all three sites and excited ICD among the outer QDs engage. Rates for all processes are found to be extremely low, although ICD rates with two neighbors are predicted to double compared to ICD among two sites only. The slowing is caused by Coulomb barriers imposed from ground or excited state electrons in the A sites. Outliers occur on the one hand at short distances, where the charge transfer among QDs mixes the possible decay pathways. On the other hand, we discovered a shape resonance-enhanced DE-ICD pathway, in which an excited and localized $B^{*}$ shape resonance state forms, which is able to decay quickly into the final ICD continuum. Full article

Electrocardiograms (ECG) analysis is one of the most important ways to diagnose heart disease. This paper proposes an efficient ECG classification method based on Wasserstein scalar curvature to comprehend the connection between heart disease and the mathematical characteristics of ECG. The newly proposed method converts an ECG into a point cloud on the family of Gaussian distribution, where the pathological characteristics of ECG will be extracted by the Wasserstein geometric structure of the statistical manifold. Technically, this paper defines the histogram dispersion of Wasserstein scalar curvature, which can accurately describe the divergence between different heart diseases. By combining medical experience with mathematical ideas from geometry and data science, this paper provides a feasible algorithm for the new method, and the theoretical analysis of the algorithm is carried out. Digital experiments on the classical database with large samples show the new algorithm’s accuracy and efficiency when dealing with the classification of heart disease. Full article

Dimensionality reduction techniques are often used by researchers in order to make high dimensional data easier to interpret visually, as data visualization is only possible in low dimensional spaces. Recent research in nonlinear dimensionality reduction introduced many effective algorithms, including t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection (UMAP), dimensionality reduction technique based on triplet constraints (TriMAP), and pairwise controlled manifold approximation (PaCMAP), aimed to preserve both the local and global structure of high dimensional data while reducing the dimensionality. The UMAP algorithm has found its application in bioinformatics, genetics, genomics, and has been widely used to improve the accuracy of other machine learning algorithms. In this research, we compare the performance of different fuzzy information discrimination measures used as loss functions in the UMAP algorithm while constructing low dimensional embeddings. In order to achieve this, we derive the gradients of the considered losses analytically and employ the Adam algorithm during the loss function optimization process. From the conducted experimental studies we conclude that the use of either the logarithmic fuzzy cross entropy loss without reduced repulsion or the symmetric logarithmic fuzzy cross entropy loss with sufficiently large neighbor count leads to better global structure preservation of the original multidimensional data when compared to the loss function used in the original UMAP algorithm implementation. Full article