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Linearly-scalable Learning of Smooth Low-dimensional Patterns with Permutation-aided Entropic Dimension Reduction by Horenko, Illia; Pospisil, Lukas is a scholarly article available to read on EtoBox.

What is Linearly-scalable Learning of Smooth Low-dimensional Patterns with Permutation-aided Entropic Dimension Reduction about?

In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding monotonic orderings in low-dimensional data, whereas typical dimension reduction and feature extraction algorithms are not primarily designed for extracting smooth low-dimensional data patterns. We show that when selecting the Euclidean smoothness as a pattern quality criterium, both of these problems (finding the optimal 'crisp' data permutation and extracting the sparse set of permuted low-dimensional smooth patterns) can be efficiently solved numerically as one unsupervised entropy-regularized iterative optimization problem. We formulate and prove the conditions for monotonicity and convergence of this linearly-scalable (in dimension) numerical procedure, with the iteration cost scaling of $\mathcal{O}(DT^2)$, where $T$ is the size of the data statistics and $D$ is a feature space dimension. The efficacy of the proposed method is demonstrated through the examination of synthetic examples as well as a real-world application involving the identif

Author

Horenko, Illia; Pospisil, Lukas

Published

2023

Language

EN