arXiv subjects

Eleftherios Kofidis

Publications and source records attributed to Eleftherios Kofidis.

18 recordsLinked to original sources

arXiv2026

Kernel Regression with Tensor Trains and Hadamard Overparameterization

Kernel regression with tensor trains and Hadamard overparameterization (KReTTaH) is introduced as a training-data-free, interpretable, and nonparametric framework for multi-way data imputation. The imputation problem is reformulated as regression in reproducing kernel Hilbert spaces (RKHS), where the tensor regression coefficients are explicitly constrained to lie on fixed-rank tensor-train (TT) manifolds and structured via Hadamard overparameterization to promote sparsity and high representational efficiency. Rather than relying on costly cross-validation, KReTTaH jointly optimizes the TT coefficient tensors and the kernel covariance matrices within a Riemannian product-manifold framework -- the former on fixed-rank TT manifolds, the latter on the manifold of positive-definite matrices -- thereby enabling automated kernel-hyperparameter selection. Numerical tests on two challenging applications -- imputation of high-dimensional functional magnetic resonance imaging (fMRI) data and recovery of missing edge flows in dynamic graphs -- demonstrate that KReTTaH consistently outperforms state-of-the-art tensor-, Bayesian-, and neural-network-based baselines in terms of modeling accuracy.

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arXiv2026

Beyond Tensor Probabilistic Independent Component Analysis -- Putting Block-Term Decomposition and Independent Vector Analysis Together

Tensor probabilistic independent component analysis (TPICA) is a popular approach to analyzing functional magnetic resonance imaging (fMRI) data, which draws its popularity from its ability to enrich the advantages of the statistics-based ICA with the awareness of the multi-way nature of these data, brought about and exploited via a deterministic 3-way (time $\times$ space $\times$ subjects) tensor decomposition (Canonical Polyadic Decomposition (CPD)) model. It has, however, received critique concerning its robustness in realistic fMRI unmixing scenarios, notably those involving sources that are strongly overlapped in space. Such cases may not meet the assumption of statistical independence required in ICA. They can instead be better described as independent vectors (or subspaces) of dependent components, pointing to the adoption of alternative statistical approaches, notably independent vector analysis (IVA). On the other hand, on the deterministic side, CPD is often restrictive and is outperformed by the more flexible block-term decomposition (BTD) model, also in the fMRI source unmixing context. Given the above, plus strong evidence of links between IVA and BTD, it is deemed worthwhile to consider the possibilities of generalizing TPICA to a BTD-based ``TPIVA" extension, which would more successfully combine the power of statistics and tensor decomposition. This could also entail a generalization of the BTD model, where (non)collinearity would be replaced by statistical (in)dependence. This note aims to outline the state-of-the-art and the above ideas in more detail, serving as a preliminary, motivating step in this research direction.

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arXiv2026

Block-Term Decomposition Approach to Blind Multi-trial Functional Ultrasound Unmixing

Functional ultrasound (fUS) has emerged as a powerful neuroimaging modality due to its high resolution in both space and time, low cost and potential portability. Nevertheless, fUS signals provide only indirect observations of neuronal activity through the neurovascular coupling, and hence require the blind separation of latent neuronal sources while also deconvolving their hemodynamic responses. In this work, we propose a data-driven convolutive block-term tensor decomposition-based model for multi-trial fUS measurements, where each source has a spatiotemporal representation comprising a low-rank spatial map and a piecewise-constant neuronal activation signal convolved with a trial- and source-dependent hemodynamic response function (HRF) with a physiologically plausible shape. We propose a constrained optimization framework for the model computation, which consists of alternating projected gradient descent iterations. Simulation results are reported that demonstrate accurate recovery of spatial maps and reliable estimation of activation temporal profiles across various noise levels, while confirming that HRF estimation remains the most challenging part of the problem.

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arXiv2025

Kernel Regression of Multi-Way Data via Tensor Trains with Hadamard Overparametrization: The Dynamic Graph Flow Case

A regression-based framework for interpretable multi-way data imputation, termed Kernel Regression via Tensor Trains with Hadamard overparametrization (KReTTaH), is introduced. KReTTaH adopts a nonparametric formulation by casting imputation as regression via reproducing kernel Hilbert spaces. Parameter efficiency is achieved through tensors of fixed tensor-train (TT) rank, which reside on low-dimensional Riemannian manifolds, and is further enhanced via Hadamard overparametrization, which promotes sparsity within the TT parameter space. Learning is accomplished by solving a smooth inverse problem posed on the Riemannian manifold of fixed TT-rank tensors. As a representative application, the estimation of dynamic graph flows is considered. In this setting, KReTTaH exhibits flexibility by seamlessly incorporating graph-based (topological) priors via its inverse problem formulation. Numerical tests on real-world graph datasets demonstrate that KReTTaH consistently outperforms state-of-the-art alternatives-including a nonparametric tensor- and a neural-network-based methods-for imputing missing, time-varying edge flows.

cs.LG↗

arXiv2024

Federated Learning Using Coupled Tensor Train Decomposition

Coupled tensor decomposition (CTD) can extract joint features from multimodal data in various applications. It can be employed for federated learning networks with data confidentiality. Federated CTD achieves data privacy protection by sharing common features and keeping individual features. However, traditional CTD schemes based on canonical polyadic decomposition (CPD) may suffer from low computational efficiency and heavy communication costs. Inspired by the efficient tensor train decomposition, we propose a coupled tensor train (CTT) decomposition for federated learning. The distributed coupled multi-way data are decomposed into a series of tensor trains with shared factors. In this way, we can extract common features of coupled modes while maintaining the different features of uncoupled modes. Thus the privacy preservation of information across different network nodes can be ensured. The proposed CTT approach is instantiated for two fundamental network structures, namely master-slave and decentralized networks. Experimental results on synthetic and real datasets demonstrate the superiority of the proposed schemes over existing methods in terms of both computational efficiency and communication rounds. In a classification task, experimental results show that the CTT-based federated learning achieves almost the same accuracy performance as that of the centralized counterpart.

cs.DC↗

arXiv2022

Tensor-based Channel Tracking for RIS-Empowered Multi-User MIMO Wireless Systems

The accurate estimation of Channel State Information (CSI) is of crucial importance for the successful operation of Multiple-Input Multiple-Output (MIMO) communication systems, especially in a Multi-User (MU) time-varying environment and when employing the emerging technology of Reconfigurable Intelligent Surfaces (RISs). Their predominantly passive nature renders the estimation of the channels involved in the user-RIS-base station link a quite challenging problem. Moreover, the time-varying nature of most of the realistic wireless channels drives up the cost of real-time channel tracking significantly, especially when RISs of massive size are deployed. In this paper, we develop a channel tracking scheme for the uplink of RIS-enabled MU MIMO systems in the presence of channel fading. The starting point is a tensor representation of the received signal and we rely on its PARAllel FACtor (PARAFAC) analysis to both get the initial estimate and track the channel time variation. Simulation results for various system settings are reported, which validate the feasibility and effectiveness of the proposed channel tracking approach.

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arXiv2021

Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Uniqueness conditions and fitting methods have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms, $R$, and their individual ranks, $L_r$, has only recently started to attract significant attention, mainly through regularization-based approaches which entail the need to tune the regularization parameter(s). In this work, we build on ideas of sparse Bayesian learning (SBL) and put forward a fully automated Bayesian approach. Through a suitably crafted multi-level \emph{hierarchical} probabilistic model, which gives rise to heavy-tailed prior distributions for the BTD factors, structured sparsity is \emph{jointly} imposed. Ranks are then estimated from the numbers of blocks ($R$) and columns ($L_r$) of non-negligible energy. Approximate posterior inference is implemented, within the variational inference framework. The resulting iterative algorithm completely avoids hyperparameter tuning, which is a significant defect of regularization-based methods. Alternative probabilistic models are also explored and the connections with their regularization-based counterparts are brought to light with the aid of the associated maximum a-posteriori (MAP) estimators. We report simulation results with both synthetic and real-word data, which demonstrate the merits of the proposed method in terms of both rank estimation and model fitting as compared to state-of-the-art relevant methods.

stat.ME↗

arXiv2021

Online Rank-Revealing Block-Term Tensor Decomposition

The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{block} components of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. The challenging problem of estimating the BTD model structure, namely the number of block terms (rank) and their individual (block) ranks, is of crucial importance in practice and has only recently started to attract significant attention. In data-streaming scenarios and/or big data applications, where the tensor dimension in one of its modes grows in time or can only be processed incrementally, it is essential to be able to perform model selection and computation in a recursive (incremental/online) manner. To date there is only one such work in the literature concerning the (general rank-$(L,M,N)$) BTD model, which proposes an incremental method, however with the BTD rank and block ranks assumed to be a-priori known and time invariant. In this preprint, a novel approach to rank-$(L_r,L_r,1)$ BTD model selection and tracking is proposed, based on the idea of imposing column sparsity jointly on the factors and estimating the ranks as the numbers of factor columns of nonnegligible magnitude. An online method of the alternating iteratively reweighted least squares (IRLS) type is developed and shown to be computationally efficient and fast converging, also allowing the model ranks to change in time. Its time and memory efficiency are evaluated and favorably compared with those of the batch approach. Simulation results are reported that demonstrate the effectiveness of the proposed scheme in both selecting and tracking the correct BTD model.

math.NA↗

arXiv2020

Block-Term Tensor Decomposition: Model Selection and Computation

The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a scenario encountered in numerous and diverse applications. Its uniqueness and approximation have thus been thoroughly studied. Nevertheless, the challenging problem of estimating the BTD model structure, namely the number of block terms and their individual ranks, has only recently started to attract significant attention. In this paper, a novel method of BTD model selection and computation is proposed, based on the idea of imposing column sparsity \emph{jointly} on the factors and in a \emph{hierarchical} manner and estimating the ranks as the numbers of factor columns of non-negligible magnitude. Following a block successive upper bound minimization (BSUM) approach for the proposed optimization problem is shown to result in an alternating hierarchical iteratively reweighted least squares (HIRLS) algorithm, which is fast converging and enjoys high computational efficiency, as it relies in its iterations on small-sized sub-problems with closed-form solutions. Simulation results for both synthetic examples and a hyper-spectral image de-noising application are reported, which demonstrate the superiority of the proposed scheme over the state-of-the-art in terms of success rate in rank estimation as well as computation time and rate of convergence.

math.NA↗

arXiv2020

Early soft and flexible fusion of EEG and fMRI via tensor decompositions

Data fusion refers to the joint analysis of multiple datasets which provide complementary views of the same task. In this preprint, the problem of jointly analyzing electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) data is considered. Jointly analyzing EEG and fMRI measurements is highly beneficial for studying brain function because these modalities have complementary spatiotemporal resolution: EEG offers good temporal resolution while fMRI is better in its spatial resolution. The fusion methods reported so far ignore the underlying multi-way nature of the data in at least one of the modalities and/or rely on very strong assumptions about the relation of the two datasets. In this preprint, these two points are addressed by adopting for the first time tensor models in the two modalities while also exploring double coupled tensor decompositions and by following soft and flexible coupling approaches to implement the multi-modal analysis. To cope with the Event Related Potential (ERP) variability in EEG, the PARAFAC2 model is adopted. The results obtained are compared against those of parallel Independent Component Analysis (ICA) and hard coupling alternatives in both simulated and real data. Our results confirm the superiority of tensorial methods over methods based on ICA. In scenarios that do not meet the assumptions underlying hard coupling, the advantage of soft and flexible coupled decompositions is clearly demonstrated.

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arXiv2019

A Tensor-based Approach to Joint Channel Estimation / Data Detection in Flexible Multicarrier MIMO Systems

Filter bank-based multicarrier (FBMC) systems have attracted increasing attention recently in view of their many advantages over the classical cyclic prefix (CP)-based orthogonal frequency division multiplexing (CP-OFDM) modulation. However, their more advanced structure (resulting in, for example, self interference) complicates signal processing tasks at the receiver, including synchronization, channel estimation and equalization. In a multiple-input multiple-output (MIMO) configuration, the multi-antenna interference has also to be taken into account. (Semi-) blind receivers, of increasing interest in (massive) MIMO systems, have been little studied so far for FBMC and mainly for the single-antenna case only. The design of such receivers for flexible MIMO FBMC systems, unifying a number of existing FBMC schemes, is considered in this paper through a tensor-based approach, which is shown to encompass existing joint channel estimation and data detection approaches as special cases, adding to their understanding and paving the way to further developments. Simulation-based results are included, for realistic transmission models, demonstrating the estimation and detection performance gains from the adoption of these receivers over their training only-based counterparts.

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arXiv2016

Assisted Dictionary Learning for fMRI Data Analysis

Extracting information from functional magnetic resonance (fMRI) images has been a major area of research for more than two decades. The goal of this work is to present a new method for the analysis of fMRI data sets, that is capable to incorporate a priori available information, via an efficient optimization framework. Tests on synthetic data sets demonstrate significant performance gains over existing methods of this kind.

stat.ML↗

arXiv2016

Joint Channel Estimation / Data Detection in MIMO-FBMC/OQAM Systems - A Tensor-Based Approach

Filter bank-based multicarrier (FBMC) systems are currently being considered as a prevalent candidate for replacing the long established cyclic prefix (CP)-based orthogonal frequency division multiplexing (CP-OFDM) in the physical layer of next generation communications systems. In particular, FBMC/OQAM has received increasing attention due to, among other features, its potential for maximum spectral efficiency. It suffers, however, from an intrinsic self-interference effect, which complicates signal processing tasks at the receiver, including synchronization, channel estimation and equalization. In a multiple-input multiple-output (MIMO) configuration, the multi-antenna interference has also to be taken into account. (Semi-)blind FBMC/OQAM receivers have been little studied so far and mainly for single-antenna systems. The problem of joint channel estimation and data detection in a MIMO-FBMC/OQAM system, given limited or no training information, is studied in this paper through a tensor-based approach in the light of the success of such techniques in OFDM applications. Simulation-based comparisons with CP-OFDM are included, for realistic transmission models.

cs.IT↗

arXiv2016

Higher-Order Block Term Decomposition for Spatially Folded fMRI Data

The growing use of neuroimaging technologies generates a massive amount of biomedical data that exhibit high dimensionality. Tensor-based analysis of brain imaging data has been proved quite effective in exploiting their multiway nature. The advantages of tensorial methods over matrix-based approaches have also been demonstrated in the characterization of functional magnetic resonance imaging (fMRI) data, where the spatial (voxel) dimensions are commonly grouped (unfolded) as a single way/mode of the 3-rd order array, the other two ways corresponding to time and subjects. However, such methods are known to be ineffective in more demanding scenarios, such as the ones with strong noise and/or significant overlapping of activated regions. This paper aims at investigating the possible gains from a better exploitation of the spatial dimension, through a higher- (4 or 5) order tensor modeling of the fMRI signal. In this context, and in order to increase the degrees of freedom of the modeling process, a higher-order Block Term Decomposition (BTD) is applied, for the first time in fMRI analysis. Its effectiveness is demonstrated via extensive simulation results.

math.NA↗

arXiv2016

A Unified Multicarrier Modulation Framework

Orthogonal frequency division multiplexing (OFDM) has been recently recognized as inadequate to meet the increased requirements of the next generation of communication systems. A number of alternative modulation solutions, based on the use of filter banks, have thus been proposed and are currently being considered as candidate waveforms for the envisaged air interface of the future networks. A unified view of these schemes would largely facilitate a systematic comparison of their pros and cons as well as the study of methods for related signal processing problems. To this end, a generic modulator is developed in this paper, following a structured matrix formulation. With appropriate parameter settings, existing modulation schemes can result as special cases. Three such popular examples are presented in detail.

cs.IT↗

arXiv2016

Blind Source Separation: Fundamentals and Recent Advances (A Tutorial Overview Presented at SBrT-2001)

Blind source separation (BSS), i.e., the decoupling of unknown signals that have been mixed in an unknown way, has been a topic of great interest in the signal processing community for the last decade, covering a wide range of applications in such diverse fields as digital communications, pattern recognition, biomedical engineering, and financial data analysis, among others. This course aims at an introduction to the BSS problem via an exposition of well-known and established as well as some more recent approaches to its solution. A unified way is followed in presenting the various results so as to more easily bring out their similarities/differences and emphasize their relative advantages/disadvantages. Only a representative sample of the existing knowledge on BSS will be included in this course. The interested readers are encouraged to consult the list of bibliographical references for more details on this exciting and always active research topic.

stat.ML↗

arXiv2014

Preamble-based Channel Estimation in FBMC/OQAM Systems: A Time-Domain Approach

Filter bank-based multicarrier (FBMC) systems based on offset QAM (FBMC/OQAM) have recently attracted increased interest in several applications due to their enhanced flexibility, higher spectral efficiency, and better spectral containment compared to conventional OFDM. They suffer, however, from an inter-carrier/inter-symbol interference that complicates signal processing tasks such as channel estimation. Most of the methods reported thus far rely on the assumption of (almost) flat subchannels to more easily tackle this problem, addressing it in a way similar to OFDM. However, this assumption may be often quite inaccurate, due to the high freq. selectivity of the channel and/or the small number of subcarriers employed to cope with frequency dispersion in fast fading. In such cases, severe error floors are exhibited at medium to high SNR values, which cancel the advantage of FBMC over OFDM. Moreover, the existing methods provide estimates of the subchannel responses, most commonly in the frequency domain. The goal of this paper is to revisit this problem through an alternative formulation that focuses on the estimation of the channel impulse response itself and makes no assumption on the degree of frequency selectivity of the subchannels. The possible gains in estimation performance offered by such an approach are investigated through the design of optimal (in the MSE sense) preambles, of both the full and sparse types, and of the smallest possible duration of only one pilot FBMC symbol. Existing designs for flat subchannels are then shown to result as special cases. Longer preambles, consisting of two consecutive pilot FBMC symbols, are also analyzed. The simulation results demonstrate significant improvements from the proposed approach for both mildly and highly frequency selective channels. Most notably, no error floors appear anymore over a quite wide range of SNR values.

cs.IT↗

arXiv2009

Preamble-Based Channel Estimation for CP-OFDM and OFDM/OQAM Systems: A Comparative Study

In this paper, preamble-based least squares (LS) channel estimation in OFDM systems of the QAM and offset QAM (OQAM) types is considered, in both the frequency and the time domains. The construction of optimal (in the mean squared error (MSE) sense) preambles is investigated, for both the cases of full (all tones carrying pilot symbols) and sparse (a subset of pilot tones, surrounded by nulls or data) preambles. The two OFDM systems are compared for the same transmit power, which, for cyclic prefix (CP) based OFDM/QAM, also includes the power spent for CP transmission. OFDM/OQAM, with a sparse preamble consisting of equipowered and equispaced pilots embedded in zeros, turns out to perform at least as well as CP-OFDM. Simulations results are presented that verify the analysis.

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