arXiv subjects

Una Radojičić

Publications and source records attributed to Una Radojičić.

7 recordsLinked to original sources

arXiv2026

Explainable Outlier Detection for Multivariate Functional Data

This work addresses the challenges of robust covariance estimation and interpretable outlier detection for multivariate functional data with separable covariance structure. We develop a method that simultaneously improves robustness and interpretability in this context by establishing a connection between stochastic processes with separable covariance structures and the corresponding matrix-variate distribution of their basis representations. Leveraging this connection, we employ the recently developed matrix-variate counterpart of the Minimum Covariance Determinant estimator (MMCD) in conjunction with a truncated multivariate functional Mahalanobis semi-distance to robustly estimate mean and covariance for multivariate functional data. For interpretable outlier detection, we generalize multivariate outlier explanations based on Shapley values to decompose overall multivariate functional outlyingness into time-coordinate-specific contributions. Importantly, we reduce the otherwise exponential computational complexity (relative to the number of components) to linear complexity, while retaining the key properties of the Shapley value. This integrated framework combines robust Mahalanobis distances, MMCD estimators, and Shapley value-based outlyingness decomposition to provide a robust and interpretable approach for analyzing multivariate functional data with separable covariance structures. The effectiveness of this approach is demonstrated through both theoretical analysis and practical applications, including simulations and real-world examples.

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arXiv2026

Testing Covariance Separability in High Dimensions

Separability is an important structural assumption often placed on the covariance when working with matrix-variate data, because it greatly simplifies both interpretation and computation of subsequent covariance-based statistical tasks. Yet testing the separability assumption is difficult in the high-dimensional regime. We propose to test separability by recasting the problem as a sphericity test after whitening the data using the separable maximum likelihood estimate of the covariance. The test is calibrated by Monte Carlo simulation, yielding finite-sample level control. Furthermore, we prove the test's high-dimensional consistency under dense alternatives. To reduce its reliance on distributional assumptions, we introduce an angular version of the test based on radial normalization after whitening. We demonstrate the practical utility, empirical power, and computational efficiency of the prop

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arXiv2026

Robust functional PCA for relative data

This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been limited focus on developing robust methods to effectively handle anomalous observations and large noise. To address this, we extend the Mahalanobis distance concept to Bayes spaces, proposing its regularized version that accounts for the constraints inherent in density data. Based on this extension, we introduce a new method, robust density principal component analysis (RDPCA), for more accurate estimation of functional principal components in the presence of outliers. The method's performance is validated through simulations and real-world applications, showing its ability to improve covariance estimation and principal component analysis compared to traditional methods.

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arXiv2024

Robust covariance estimation and explainable outlier detection for matrix-valued data

This work introduces the Matrix Minimum Covariance Determinant (MMCD) method, a novel robust location and covariance estimation procedure designed for data that are naturally represented in the form of a matrix. Unlike standard robust multivariate estimators, which would only be applicable after a vectorization of the matrix-variate samples leading to high-dimensional datasets, the MMCD estimators account for the matrix-variate data structure and consistently estimate the mean matrix, as well as the rowwise and columnwise covariance matrices in the class of matrix-variate elliptical distributions. Additionally, we show that the MMCD estimators are matrix affine equivariant and achieve a higher breakdown point than the maximal achievable one by any multivariate, affine equivariant location/covariance estimator when applied to the vectorized data. An efficient algorithm with convergence guarantees is proposed and implemented. As a result, robust Mahalanobis distances based on MMCD estimators offer a reliable tool for outlier detection. Additionally, we extend the concept of Shapley values for outlier explanation to the matrix-variate setting, enabling the decomposition of the squared Mahalanobis distances into contributions of the rows, columns, or individual cells of matrix-valued observations. Notably, both the theoretical guarantees and simulations show that the MMCD estimators outperform robust estimators based on vectorized observations, offering better computational efficiency and improved robustness. Moreover, real-world data examples demonstrate the practical relevance of the MMCD estimators and the resulting robust Shapley values.

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arXiv2023

Exploratory functional data analysis of multivariate densities for the identification of agricultural soil contamination by risk elements

Geochemical mapping of risk element concentrations in soils is performed in countries around the world. It results in large datasets of high analytical quality, which can be used to identify soils that violate individual legislative limits for safe food production. However, there is a lack of advanced data mining tools that would be suitable for sensitive exploratory data analysis of big data while respecting the natural variability of soil composition. To distinguish anthropogenic contamination from natural variation, the analysis of the entire data distributions for smaller sub-areas is key. In this article, we propose a new data mining method for geochemical mapping data based on functional data analysis of probability density functions in the framework of Bayes spaces after post-stratification of a big dataset to smaller districts. Proposed tools allow us to analyse the entire distribution, going beyond a superficial detection of extreme concentration anomalies. We illustrate the proposed methodology on a dataset gathered according to the Czech national legislation (1990--2009). Taking into account specific properties of probability density functions and recent results for orthogonal decomposition of multivariate densities enabled us to reveal real contamination patterns that were so far only suspected in Czech agricultural soils. We process the above Czech soil composition dataset by first compartmentalising it into spatial units, in particular the districts, and by subsequently clustering these districts according to diagnostic features of their uni- and multivariate distributions at high concentration ends. Comparison between compartments is key to the reliable distinction of diffuse contamination. In this work, we used soil contamination by Cu-bearing pesticides as an example for empirical testing of the proposed data mining approach.

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arXiv2023

Minimum regularized covariance trace estimator and outlier detection for functional data

In this paper, we propose the Minimum Regularized Covariance Trace (MRCT) estimator, a novel method for robust covariance estimation and functional outlier detection. The MRCT estimator employs a subset-based approach that prioritizes subsets exhibiting greater centrality based on the generalization of the Mahalanobis distance, resulting in a fast-MCD type algorithm. Notably, the MRCT estimator handles high-dimensional data sets without the need for preprocessing or dimension reduction techniques, due to the internal smoothening whose amount is determined by the regularization parameter $α> 0$. The selection of the regularization parameter $α$ is automated. The proposed method adapts seamlessly to sparsely observed data by working directly with the finite matrix of basis coefficients. An extensive simulation study demonstrates the efficacy of the MRCT estimator in terms of robust covariance estimation and automated outlier detection, emphasizing the balance between noise exclusion and signal preservation achieved through appropriate selection of $α$. The method converges fast in practice and performs favorably when compared to other functional outlier detection methods.

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arXiv2022

Numerical considerations and a new implementation for ICS

Invariant Coordinate Selection (ICS) is a multivariate data transformation and a dimension reduction method that can be useful in many different contexts. It can be used for outlier detection or cluster identification, and can be seen as an independent component or a non-Gaussian component analysis method. The usual implementation of ICS is based on a joint diagonalization of two scatter matrices, and may be numerically unstable in some ill-conditioned situations. We focus on one-step M-scatter matrices and propose a new implementation of ICS based on a pivoted QR factorization of the centered data set. This factorization avoids the direct computation of the scatter matrices and their inverse and brings numerical stability to the algorithm. Furthermore, the row and column pivoting leads to a rank revealing procedure that allows computation of ICS when the scatter matrices are not full rank. Several artificial and real data sets illustrate the interest of using the new implementation compared to the original one.

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