arXiv subjects

Paris A. Karakasis

Publications and source records attributed to Paris A. Karakasis.

5 recordsLinked to original sources

arXiv2026

Latent Semantic State Estimation for Reliable Swarming of UAVs under Intermittent Connectivity

Cooperative multi-unmanned aerial vehicle (UAV) reconnaissance is often hindered by intermittent air-to-air communications where link dropouts lead to uncoordinated exploration and redundant mapping. Existing approaches rely on explicit exchange of high-dimensional spatial data or raw observations, incurring significant overhead, and often revert to reactive individual exploration during outages. This paper proposes a memory-augmented framework in which each UAV maintains a structured latent state decomposed into map, task, and memory components. During dropout, a generative predictor conditioned on the memory state infers substitute peer messages in the latent space, making the estimation task more tractable and directly aligned with the cooperative objective. The framework is trained end-to-end under the centralized training with decentralized execution paradigm. Simulation results demonstrate that the proposed framework closely matches the performance of a fully connected swarm, while remaining robust across a wide range of link failure conditions.

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arXiv2026

Penalizing Localized Dirichlet Energies in Low Rank Tensor Products

We study low-rank tensor-product B-spline (TPBS) models for regression tasks and investigate Dirichlet energy as a measure of smoothness. We show that TPBS models admit a closed-form expression for the Dirichlet energy, and reveal scenarios where perfect interpolation is possible with exponentially small Dirichlet energy. This renders global Dirichlet energy-based regularization ineffective. To address this limitation, we propose a novel regularization strategy based on local Dirichlet energies defined on small hypercubes centered at the training points. Leveraging pretrained TPBS models, we also introduce two estimators for inference from incomplete samples. Comparative experiments with neural networks demonstrate that TPBS models outperform neural networks in the overfitting regime for most datasets, and maintain competitive performance otherwise. Overall, TPBS models exhibit greater robustness to overfitting and consistently benefit from regularization, while neural networks are more sensitive to overfitting and less effective in leveraging regularization.

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arXiv2025

Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering

We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data, our formulation directly models each data sample as a matrix and clusters them according to their underlying subspaces. We establish conceptual links to Subspace Clustering and Generalized Canonical Correlation Analysis (GCCA), and clarify key differences that arise in this more general setting. Our approach is based on a Block Term Decomposition (BTD) of a third-order tensor constructed from the input matrices, enabling joint estimation of cluster memberships and partially shared subspaces. We provide the first identifiability results for this formulation and propose scalable optimization algorithms tailored to large datasets. Experiments on real-world hyperspectral imaging datasets demonstrate that our method achieves superior clustering accuracy and robustness, especially under high noise and interference, compared to existing subspace clustering techniques. These results highlight the potential of the proposed framework in challenging high-dimensional applications where structure exists beyond individual data vectors.

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arXiv2023

Revisiting Deep Generalized Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened our capabilities in terms of revealing common random factors from multiview datasets. In this work, we first revisit the most recent deterministic extensions of deep CCA and highlight the strengths and limitations of these state-of-the-art methods. Some methods allow trivial solutions, while others can miss weak common factors. Others overload the problem by also seeking to reveal what is not common among the views -- i.e., the private components that are needed to fully reconstruct each view. The latter tends to overload the problem and its computational and sample complexities. Aiming to improve upon these limitations, we design a novel and efficient formulation that alleviates some of the current restrictions. The main idea is to model the private components as conditionally independent given the common ones, which enables the proposed compact formulation. In addition, we also provide a sufficient condition for identifying the common random factors. Judicious experiments with synthetic and real datasets showcase the validity of our claims and the effectiveness of the proposed approach.

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arXiv2022

Multisubject Task-Related fMRI Data Processing via a Two-Stage Generalized Canonical Correlation Analysis

Functional magnetic resonance imaging (fMRI) is one of the most popular methods for studying the human brain. Task-related fMRI data processing aims to determine which brain areas are activated when a specific task is performed and is usually based on the Blood Oxygen Level Dependent (BOLD) signal. The background BOLD signal also reflects systematic fluctuations in regional brain activity which are attributed to the existence of resting-state brain networks. We propose a new fMRI data generating model which takes into consideration the existence of common task-related and resting-state components. We first estimate the common task-related temporal component, via two successive stages of generalized canonical correlation analysis and, then, we estimate the common task-related spatial component, leading to a task-related activation map. The experimental tests of our method with synthetic data reveal that we are able to obtain very accurate temporal and spatial estimates even at very low Signal to Noise Ratio (SNR), which is usually the case in fMRI data processing. The tests with real-world fMRI data show significant advantages over standard procedures based on General Linear Models (GLMs).

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