arXiv subjects

Ioannis D. Schizas

Publications and source records attributed to Ioannis D. Schizas.

5 recordsLinked to original sources

arXiv2026

Manifold Navigation Learning Using Recurrent Networks: Efficient Training Techniques

Position tracking is a well-studied problem in Euclidean navigation, yet comparatively little attention has been given to navigation on general manifolds, where motion is governed by the underlying geometry of the space. In this work, we formalize the problem of manifold navigation as a velocity-driven tracking task and propose a coordinate-chart-based learning framework in which learning models operate entirely in a Euclidean representation. Predicted trajectories are mapped to the manifold via an immersion function prior to error computation, allowing geometric consistency to be evaluated without explicitly enforcing manifold constraints during learning. Within this framework, we focus on Gated Recurrent Units (GRUs) for sequential position prediction on curved manifolds after comparisons with alternative recurrent architectures. We evaluate our GRU models, trained with pertinent custom loss functions, against both a standard MSE loss function and a naive vector-addition baseline. We evaluate our approach on both analytically (and numerically) defined manifolds, as well as a surface reconstructed from a LiDAR point cloud. Our results show that recurrent models can learn to approximate manifold-constrained dynamics from velocity sequences and consistently outperform Euclidean baselines. Our results demonstrate that certain custom loss functions significantly improve long-horizon prediction accuracy compared to conventional point-wise loss functions.

cs.CV↗

arXiv2026

From Classical to Topological Neural Networks Under Uncertainty

This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial intelligence in the military domain. Throughout the chapter, we highlight practical applications spanning image, video, audio, and time-series recognition, fraud detection, and link prediction for graphical data, illustrating how topology-aware and uncertainty-aware models can enhance robustness, interpretability, and generalization.

cs.LG↗

arXiv2018

Graph filtering for data reduction and reconstruction

A novel approach is put forth that utilizes data similarity, quantified on a graph, to improve upon the reconstruction performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph filtering operations, that enable the exploitation of data node connectivity in a graph via the adjacency matrix. The unknown reducing and reconstruction filters are determined by optimizing a mean-square error cost that entails the data, as well as their graph adjacency matrix. Working in the graph spectral domain enables the derivation of simple gradient descent recursions used to update the matrix filter taps. Numerical tests in real image datasets demonstrate the better reconstruction performance of the novel method over standard principal component analysis.

stat.ML↗

arXiv2015

Decentralized learning for wireless communications and networking

This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and recast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of parallelization. Without exchanging elements from the distributed training sets and keeping inter-node communications at affordable levels, the local (per-node) learners consent to the desired quantity inferred globally, meaning the one obtained if the entire training data set were centrally available. Impact of the decentralized learning framework to contemporary wireless communications and networking tasks is illustrated through case studies including target tracking using wireless sensor networks, unveiling Internet traffic anomalies, power system state estimation, as well as spectrum cartography for wireless cognitive radio networks.

math.OC↗

arXiv2012

Covariance Eigenvector Sparsity for Compression and Denoising

Sparsity in the eigenvectors of signal covariance matrices is exploited in this paper for compression and denoising. Dimensionality reduction (DR) and quantization modules present in many practical compression schemes such as transform codecs, are designed to capitalize on this form of sparsity and achieve improved reconstruction performance compared to existing sparsity-agnostic codecs. Using training data that may be noisy a novel sparsity-aware linear DR scheme is developed to fully exploit sparsity in the covariance eigenvectors and form noise-resilient estimates of the principal covariance eigenbasis. Sparsity is effected via norm-one regularization, and the associated minimization problems are solved using computationally efficient coordinate descent iterations. The resulting eigenspace estimator is shown capable of identifying a subset of the unknown support of the eigenspace basis vectors even when the observation noise covariance matrix is unknown, as long as the noise power is sufficiently low. It is proved that the sparsity-aware estimator is asymptotically normal, and the probability to correctly identify the signal subspace basis support approaches one, as the number of training data grows large. Simulations using synthetic data and images, corroborate that the proposed algorithms achieve improved reconstruction quality relative to alternatives.

stat.AP↗