Unsupervised feature selection using Bayesian Tucker decomposition

arXiv stat.ML / 4/17/2026

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Key Points

The paper introduces Bayesian Tucker decomposition (BTuD), modeling the residual as Gaussian in a way analogous to linear regression.
It presents an algorithm for BTuD and notes that conventional higher-order orthogonal iteration can also produce compatible Tucker decompositions.
Using BTuD, the authors demonstrate unsupervised feature selection on multiple synthetic benchmarks and on structured systems like globally coupled maps.
The approach is also tested on gene expression data profiles, suggesting broad applicability beyond toy problems.
The authors argue their method is promising and expects alignment with previously proposed tensor-decomposition-based unsupervised feature selection (e.g., TD-based methods).

Abstract

In this paper, we proposed Bayesian Tucker decomposition (BTuD) in which residual is supposed to obey Gaussian distribution analogous to linear regression. Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. Using the proposed BTuD, we can perform unsupervised feature selection successfully applied to various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles. Thus we can conclude that our newly proposed unsupervised feature selection method is promising. In addition to this, BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed and successfully applied to a wide range of problems.