arXiv subjects

Andrew Jirasek

Publications and source records attributed to Andrew Jirasek.

5 recordsLinked to original sources

arXiv2026

Robust model-based clustering via mixtures of multivariate pseudo-Voigt distributions

We propose a multivariate extension of the pseudo-Voigt profile-a weighted convex combination of Gaussian and Cauchy distributions-within a finite mixture modeling framework for robust model-based clustering and outlier detection. To ensure parsimony and coherence within clusters, shared location and scale parameters are imposed between the Gaussian and Cauchy components. Parameter estimation is carried out via an Expectation Maximization algorithm, with latent variables facilitating efficient likelihood-based inference. The performance of the proposed model is evaluated through simulation studies and applications to real-world data. Comparisons with established robust models, including mixtures of contaminated normal distributions, are provided to illustrate the model's clustering accuracy and outlier detection capabilities. The framework is shown to be particularly effective for data characterized by heavy-tailed behavior.

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arXiv2026

Mixtures of spatial factor analyzers for tensor-variate data

A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. By leveraging the underlying coordinate system, the proposed framework incorporates a flexible, spline-based spatial decay covariance structure that prevents parameter inflation as dimensionality increases. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and applications to Raman spectroscopy and hyperspectral texture databases demonstrate their capacity to accurately infer and differentiate distinct spatial patterns.

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arXiv2026

Spatial Covariance Constraints for Gaussian Mixture Models

Although extensive research exists in spatial modeling, few studies have addressed finite mixture model-based clustering methods for spatial data. Finite mixture models, especially Gaussian mixture models, particularly suffer from high dimensionality due to the number of free covariance parameters. This study introduces a spatial covariance constraint for Gaussian mixture models that requires only four free parameters for each component, independent of dimensionality. Using a coordinate system, the spatially constrained Gaussian mixture model enables clustering of multi-way spatial data and inference of spatial patterns. The parameter estimation is conducted by combining the expectation-maximization (EM) algorithm with the generalized least squares (GLS) estimator. Simulation studies and applications to Raman spectroscopy data are provided to demonstrate the proposed model.

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arXiv2024

DEEPEAST technique to enhance power in two-sample tests via the same-attraction function

Data depth has emerged as an invaluable nonparametric measure for the ranking of multivariate samples. The main contribution of depth-based two-sample comparisons is the introduction of the Q statistic (Liu and Singh, 1993), a quality index. Unlike traditional methods, data depth does not require the assumption of normal distributions and adheres to four fundamental properties. Many existing two-sample homogeneity tests, which assess mean and/or scale changes in distributions often suffer from low statistical power or indeterminate asymptotic distributions. To overcome these challenges, we introduced a DEEPEAST (depth-explored same-attraction sample-to-sample central-outward ranking) technique for improving statistical power in two-sample tests via the same-attraction function. We proposed two novel and powerful depth-based test statistics: the sum test statistic and the product test statistic, which are rooted in Q statistics, share a "common attractor" and are applicable across all depth functions. We further proved the asymptotic distribution of these statistics for various depth functions. To assess the performance of power gain, we apply three depth functions: Mahalanobis depth (Liu and Singh, 1993), Spatial depth (Brown, 1958; Gower, 1974), and Projection depth (Liu, 1992). Through two-sample simulations, we have demonstrated that our sum and product statistics exhibit superior power performance, utilizing a strategic block permutation algorithm and compare favourably with popular methods in literature. Our tests are further validated through analysis on Raman spectral data, acquired from cellular and tissue samples, highlighting the effectiveness of the proposed tests highlighting the effective discrimination between health and cancerous samples.

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arXiv2021

Nonnegative Matrix Factorization with Group and Basis Restrictions

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices multiplied together ($\mathbf{X} \approx \mathbf{WH}$). These two matrices can be described as the latent factors, represented in the rows of $\mathbf{H}$, and the scores of the observations on these factors that are found in the rows of $\mathbf{W}$. This paper provides an extension of this method which allows one to specify prior knowledge of the data, including both group information and possible underlying factors. This is done by further decomposing the matrix, $\mathbf{H}$, into matrices $\mathbf{A}$ and $\mathbf{S}$ multiplied together. These matrices represent an 'auxiliary' matrix and a semi-constrained factor matrix respectively. This method and its updating criterion are proposed, followed by its application on both simulated and real world examples.

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