arXiv subjects

Alaeddine Zahir

Publications and source records attributed to Alaeddine Zahir.

5 recordsLinked to original sources

arXiv2025

Higher order multi-dimension reduction methods via Einstein product

This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompassing both linear and nonlinear approaches, within both supervised and unsupervised learning paradigms. Additionally, we investigate variants such as repulsion graphs and kernel methods for linear approaches. Furthermore, we present two generalizations for each method, based on single or multiple weights. We demonstrate the straightforward nature of these generalizations and provide theoretical insights. Numerical experiments are conducted, and results are compared with original methods, highlighting the efficiency of our proposed methods, particularly in handling high-dimensional data such as color images.

math.NA↗

arXiv2025

High-dimensional multi-view clustering methods

Multi-view clustering has been widely used in recent years in comparison to single-view clustering, for clear reasons, as it offers more insights into the data, which has brought with it some challenges, such as how to combine these views or features. Most of recent work in this field focuses mainly on tensor representation instead of treating the data as simple matrices. This permits to deal with the high-order correlation between the data which the based matrix approach struggles to capture. Accordingly, we will examine and compare these approaches, particularly in two categories, namely graph-based clustering and subspace-based clustering. We will conduct and report experiments of the main clustering methods over a benchmark datasets.

cs.LG↗

arXiv2025

Trace Ratio vs Ratio Trace Methods for Multidimensional Dimensionality Reduction

We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace Ratio and its surrogate, the Ratio Trace (RT) formulation. Building on these foundations, we design a Newton-type iterative algorithm that operates directly in the tensor domain via the Einstein product, avoiding data flattening and preserving multi-dimensional structure. This approach extends classical Linear Discriminant Analysis (LDA) to higher-order tensors, offering a natural generalization of trace-based dimensionality reduction from matrices to tensors. Numerical experiments on several benchmark datasets confirm the efficiency and robustness of the proposed methods, showing consistent improvements over existing matrix- and tensor-based techniques.

math.NA↗

arXiv2025

A low-rank non-convex norm method for multiview graph clustering

This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning as it requires the integration of information from multiple data sources or views to cluster data points accurately. The suggested approach makes use of the structural characteristics of multi-view data tensors, introducing a non-convex tensor norm to identify correlations between these views. In contrast to conventional methods, this approach demonstrates superior clustering accuracy across several benchmark datasets. Despite the non-convex nature of the tensor norm used, the proposed method remains amenable to efficient optimization using existing algorithms. The approach provides a valuable tool for multi-view data analysis and has the potential to enhance our understanding of complex systems in various fields. Further research can explore the application of this method to other types of data and extend it to other machine-learning tasks.

cs.LG↗

arXiv2025

Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms

In this paper, we propose a new approaches for low rank approximation of quaternion tensors \cite{chen2019low,zhang1997quaternions,hamilton1866elements}. The first method uses quasi-norms to approximate the tensor by a low-rank tensor using the QT-product \cite{miao2023quaternion}, which generalizes the known L-product to N-mode quaternions. The second method involves Non-Convex norms to approximate the Tucker and TT-rank for the completion problem. We demonstrate that the proposed methods can effectively approximate the tensor compared to the convexifying of the rank, such as the nuclear norm. We provide theoretical results and numerical experiments to show the efficiency of the proposed methods in the Inpainting and Denoising applications.

math.NA↗