arXiv subjects

Abd-Krim Seghouane

Publications and source records attributed to Abd-Krim Seghouane.

8 recordsLinked to original sources

arXiv2026

Projection Pursuit CPCANet for Domain Generalization

Domain Generalization (DG) aims to learn representations robust to distribution shifts. Recent geometric alignment methods, such as CPCANet, extract domain-invariant structures through batch-wise Common Principal Component Analysis (CPCA). However, CPCANet suffers from rank-deficient covariance estimation due to the small-sample-size issue in mini-batch training. To address this limitation, we propose Projection Pursuit CPCANet (PP-CPCANet), a covariance-free framework that learns a global orthogonal basis on the Stiefel manifold and jointly optimizes it with network parameters via the Cayley transform. We further introduce a symmetry-breaking detached-median PP dispersion objective to extract common principal components (CPCs) with dense and robust optimization signals. Experiments on four DG benchmarks show that PP-CPCANet achieves SOTA performance while maintaining stable training.

cs.CV↗

arXiv2026

CPCANet: Deep Unfolding Common Principal Component Analysis for Domain Generalization

Domain Generalization (DG) aims to learn representations that remain robust under out-of-distribution (OOD) shifts and generalize effectively to unseen target domains. While recent invariant learning strategies and architectural advances have achieved strong performance, explicitly discovering a structured domain-invariant subspace through second-order statistics remains underexplored. In this work, we propose CPCANet, a novel framework grounded in Common Principal Component Analysis (CPCA), which unrolls the iterative Flury-Gautschi (FG) algorithm into fully differentiable neural layers. This approach integrates the statistical properties of CPCA into an end-to-end trainable framework, enforcing the discovery of a shared subspace across diverse domains while preserving interpretability. Experiments on four standard DG benchmarks demonstrate that CPCANet achieves state-of-the-art (SOTA) performance in zero-shot transfer. Moreover, CPCANet is architecture-agnostic and requires no dataset-specific tuning, providing a simple and efficient approach to learning robust representations under distribution shift. Code is available at https://github.com/wish44165/CPCANet.

cs.CV↗

arXiv2025

Robust Regression under Adversarial Contamination: Theory and Algorithms for the Welsch Estimator

Convex and penalized robust regression methods often suffer from a persistent bias induced by large outliers, limiting their effectiveness in adversarial or heavy-tailed settings. In this work, we study a smooth redescending non-convex M-estimator, specifically the Welsch estimator, and show that it can eliminate this bias whenever it is statistically identifiable. We focus on high-dimensional linear regression under adversarial contamination, where a fraction of samples may be corrupted by an adversary with full knowledge of the data and underlying model. A central technical contribution of this paper is a practical algorithm that provably finds a statistically valid solution to this non-convex problem. We show that the Welsch objective remains locally convex within a well-characterized basin of attraction, and our algorithm is guaranteed to converge into this region and recover the desired estimator. We establish three main guarantees: (a) non-asymptotic minimax-optimal deviation bounds under contamination, (b) improved unbiasedness in the presence of large outliers, and (c) asymptotic normality, yielding statistical efficiency as the sample size grows. Finally, we support our theoretical findings with comprehensive experiments on synthetic and real datasets, demonstrating the estimator's superior robustness, efficiency, and effectiveness in mitigating outlier-induced bias relative to state-of-the-art robust regression methods.

math.ST↗

arXiv2024

Joint Approximate Partial Diagonalization of Large Matrices

Given a set of $p$ symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these $p$ matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural generalization of this problem is to seek an orthonormal basis of a certain subspace that is a near eigenspace for all the matrices in the set. We refer to this as the problem of ``partial joint diagonalization of matrices.'' The approach proposed first finds this approximate common near eigenspace and then proceeds to a joint diagonalization of the restrictions of the input matrices in this subspace. A few solution methods for this problem are proposed and illustrations of its potential applications are provided.

math.NA↗

arXiv2022

A Guide to Image and Video based Small Object Detection using Deep Learning : Case Study of Maritime Surveillance

Small object detection (SOD) in optical images and videos is a challenging problem that even state-of-the-art generic object detection methods fail to accurately localize and identify such objects. Typically, small objects appear in real-world due to large camera-object distance. Because small objects occupy only a small area in the input image (e.g., less than 10%), the information extracted from such a small area is not always rich enough to support decision making. Multidisciplinary strategies are being developed by researchers working at the interface of deep learning and computer vision to enhance the performance of SOD deep learning based methods. In this paper, we provide a comprehensive review of over 160 research papers published between 2017 and 2022 in order to survey this growing subject. This paper summarizes the existing literature and provide a taxonomy that illustrates the broad picture of current research. We investigate how to improve the performance of small object detection in maritime environments, where increasing performance is critical. By establishing a connection between generic and maritime SOD research, future directions have been identified. In addition, the popular datasets that have been used for SOD for generic and maritime applications are discussed, and also well-known evaluation metrics for the state-of-the-art methods on some of the datasets are provided.

cs.CV↗

arXiv2018

Find the dimension that counts: Fast dimension estimation and Krylov PCA

High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these covariance matrices and obtaining an approximation to the subspace. This problem arises in the popular principal component analysis (PCA), and in many applications of machine learning, data analysis, signal and image processing, and others. We first present a novel method for estimating the dimension of the principal subspace. We then show how this method can be coupled with a Krylov subspace method to simultaneously estimate the dimension and obtain an approximation to the subspace. The dimension estimation is achieved at no additional cost. The proposed method operates on a model selection framework, where the novel selection criterion is derived based on random matrix perturbation theory ideas. We present theoretical analyses which (a) show that the proposed method achieves strong consistency (i.e., yields optimal solution as the number of data-points $n\rightarrow \infty$), and (b) analyze conditions for exact dimension estimation in the finite $n$ case. Using recent results, we show that our algorithm also yields near optimal PCA. The proposed method avoids forming the sample covariance matrix (associated with the data) explicitly and computing the complete eigen-decomposition. Therefore, the method is inexpensive, which is particularly advantageous in modern data applications where the covariance matrices can be very large. Numerical experiments illustrate the performance of the proposed method in various applications.

math.NA↗

arXiv2018

Hybrid Joint Diagonalization Algorithms

This paper deals with a hybrid joint diagonalization (JD) problem considering both Hermitian and transpose congruences. Such problem can be encountered in certain non-circular signal analysis applications including blind source separation. We introduce new Jacobi-like algorithms using Givens or a combination of Givens and hyperbolic rotations. These algorithms are compared with state-of-the-art methods and their performance gain, especially in the high dimensional case, is assessed through simulation experiments including examples related to blind separation of non-circular sources.

eess.SP↗

arXiv2016

Fast estimation of approximate matrix ranks using spectral densities

In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the approximate ranks of such large matrices. These techniques exploit approximate spectral densities, popular in physics, which are probability density distributions that measure the likelihood of finding eigenvalues of the matrix at a given point on the real line. Integrating the spectral density over an interval gives the eigenvalue count of the matrix in that interval. Therefore the rank can be approximated by integrating the spectral density over a carefully selected interval. Two different approaches are discussed to estimate the approximate rank, one based on Chebyshev polynomials and the other based on the Lanczos algorithm. In order to obtain the appropriate interval, it is necessary to locate a gap between the eigenvalues that correspond to noise and the relevant eigenvalues that contribute to the matrix rank. A method for locating this gap and selecting the interval of integration is proposed based on the plot of the spectral density. Numerical experiments illustrate the performance of these techniques on matrices from typical applications.

math.NA↗