arXiv subjects

Ammar Mian

Publications and source records attributed to Ammar Mian.

11 recordsLinked to original sources

arXiv2026

FedSPDnet: Geometry-Aware Federated Deep Learning with SPDnet

We introduce two federated learning frameworks for the classical SPDnet model operating on symmetric positive definite (SPD) matrices with Stiefel-constrained parameters. Unlike standard Euclidean averaging, which violates orthogonality, our approach preserves geometric structure through two efficient aggregation strategies: ProjAvg, projecting arithmetic means onto the Stiefel manifold, and RLAvg, approximating tangent-space averaging via retractions and liftings. Both methods are computationally efficient, independent of the optimizer, and enable scalable federated learning for signal processing applications whose features are SPD matrices. Simulations on EEG motor imagery benchmarks show that FedSPDnet outperforms federated EEGnet in F1 score and robustness to federation and partial participation, while using fewer parameters per communication round.

stat.ML↗

arXiv2026

SPD Learn: A Geometric Deep Learning Python Library for Neural Decoding Through Trivialization

Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages. Existing implementations often employ ad hoc handling of manifold constraints and non-unified training setups, which hinders reproducibility and integration into modern deep-learning workflows. To address this gap, we introduce SPD Learn, a unified and modular Python package for geometric deep learning with SPD matrices. SPD Learn provides core SPD operators and neural-network layers, including numerically stable spectral operators, and enforces Stiefel/SPD constraints via trivialization-based parameterizations. This design enables standard backpropagation and optimization in unconstrained Euclidean spaces while producing manifold-constrained parameters by construction. The package also offers reference implementations of representative SPDNet-based models and interfaces with widely used brain computer interface/neuroimaging toolkits and modern machine-learning libraries (e.g., MOABB, Braindecode, Nilearn, and SKADA), facilitating reproducible benchmarking and practical deployment.

q-bio.NC↗

arXiv2025

Generalized Nonnegative Structured Kruskal Tensor Regression

This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity constraints. Our approach accommodates both linear and logistic regression formulations for diverse response variables while addressing the structural heterogeneity inherent in multidimensional tensor data. We integrate fused LASSO, total variation, and ridge regularizers, each tailored to specific tensor modes, and develop an efficient alternating direction method of multipliers (ADMM) based algorithm for parameter estimation. Comprehensive experiments on synthetic signals and real hyperspectral datasets demonstrate that NS-KTR consistently outperforms conventional tensor regression methods. The framework's ability to preserve distinct structural characteristics across tensor dimensions while ensuring physical interpretability makes it especially suitable for applications in signal processing and hyperspectral image analysis.

eess.SP↗

arXiv2024

Classification of Buried Objects from Ground Penetrating Radar Images by using Second Order Deep Learning Models

In this paper, a new classification model based on covariance matrices is built in order to classify buried objects. The inputs of the proposed models are the hyperbola thumbnails obtained with a classical Ground Penetrating Radar (GPR) system. These thumbnails are then inputs to the first layers of a classical CNN, which then produces a covariance matrix using the outputs of the convolutional filters. Next, the covariance matrix is given to a network composed of specific layers to classify Symmetric Positive Definite (SPD) matrices. We show in a large database that our approach outperform shallow networks designed for GPR data and conventional CNNs typically used in computer vision applications, particularly when the number of training data decreases and in the presence of mislabeled data. We also illustrate the interest of our models when training data and test sets are obtained from different weather modes or considerations.

cs.CV↗

arXiv2024

Random matrix theory improved Fréchet mean of symmetric positive definite matrices

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fréchet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine-learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory-based method that estimates Fréchet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.

stat.ML↗

arXiv2024

Robust Detection for Mills Cross Sonar

Multi-array systems are widely used in sonar and radar applications. They can improve communication speeds, target discrimination, and imaging. In the case of a multibeam sonar system that can operate two receiving arrays, we derive new adaptive to improve detection capabilities compared to traditional sonar detection approaches. To do so, we more specifically consider correlated arrays, whose covariance matrices are estimated up to scale factors, and an impulsive clutter. In a partially homogeneous environment, the 2-step Generalized Likelihood ratio Test (GLRT) and Rao approach lead to a generalization of the Adaptive Normalized Matched Filter (ANMF) test and an equivalent numerically simpler detector with a well-established texture Constant False Alarm Rate (CFAR) behavior. Performances are discussed and illustrated with theoretical examples, numerous simulations, and insights into experimental data. Results show that these detectors outperform their competitors and have stronger robustness to environmental unknowns.

stat.AP↗

arXiv2023

Online Change Detection in SAR Time-Series with Kronecker Product Structured Scaled Gaussian Models

We develop the information geometry of scaled Gaussian distributions for which the covariance matrix exhibits a Kronecker product structure. This model and its geometry are then used to propose an online change detection (CD) algorithm for multivariate image times series (MITS). The proposed approach relies mainly on the online estimation of the structured covariance matrix under the null hypothesis, which is performed through a recursive (natural) Riemannian gradient descent. This approach exhibits a practical interest compared to the corresponding offline version, as its computational cost remains constant for each new image added in the time series. Simulations show that the proposed recursive estimators reach the Intrinsic Cramér-Rao bound. The interest of the proposed online CD approach is demonstrated on both simulated and real data.

stat.AP↗

arXiv2023

Learning Graphical Factor Models with Riemannian Optimization

Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within graph learning processes. This paper therefore addresses this issue by proposing a flexible algorithmic framework for graph learning under low-rank structural constraints on the covariance matrix. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution (a generalization of Gaussian graphical models to possibly heavy-tailed distributions), where the covariance matrix is optionally constrained to be structured as low-rank plus diagonal (low-rank factor model). The resolution of this class of problems is then tackled with Riemannian optimization, where we leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models. Numerical experiments on real-world data sets illustrate the effectiveness of the proposed approach.

stat.ML↗

arXiv2022

Riemannian classification of EEG signals with missing values

This paper proposes a strategy to handle missing data for the classification of electroencephalograms using covariance matrices. It relies on the observed-data likelihood within an expectation-maximization algorithm. This approach is compared to two existing state-of-the-art methods: (i) covariance matrices computed with imputed data; (ii) Riemannian averages of partially observed covariance matrix. All approaches are combined with the minimum distance to Riemannian mean classifier and applied to a classification task of two widely known paradigms of brain-computer interfaces. In addition to be applicable for a wider range of missing data scenarios, the proposed strategy generally performs better than other methods on the considered real EEG data.

cs.HC↗

arXiv2020

Block-wise Minimization-Majorization algorithm for Huber's criterion: sparse learning and applications

Huber's criterion can be used for robust joint estimation of regression and scale parameters in the linear model. Huber's (Huber, 1981) motivation for introducing the criterion stemmed from non-convexity of the joint maximum likelihood objective function as well as non-robustness (unbounded influence function) of the associated ML-estimate of scale. In this paper, we illustrate how the original algorithm proposed by Huber can be set within the block-wise minimization majorization framework. In addition, we propose novel data-adaptive step sizes for both the location and scale, which are further improving the convergence. We then illustrate how Huber's criterion can be used for sparse learning of underdetermined linear model using the iterative hard thresholding approach. We illustrate the usefulness of the algorithms in an image denoising application and simulation studies.

stat.ML↗

arXiv2020

Riemannian geometry for Compound Gaussian distributions: application to recursive change detection

A new Riemannian geometry for the Compound Gaussian distribution is proposed. In particular, the Fisher information metric is obtained, along with corresponding geodesics and distance function. This new geometry is applied on a change detection problem on Multivariate Image Times Series: a recursive approach based on Riemannian optimization is developed. As shown on simulated data, it allows to reach optimal performance while being computationally more efficient.

stat.ML↗