Linear Dimensionality Reduction

Alain Franc

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arXiv · 2209.13597

Linear Dimensionality Reduction

Alain Franc

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Abstract

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part of statistical learning, or as dimensionality reduction with a geometric flavor. Both approaches are tightly linked: it is easier to learn patterns from data in low dimensional spaces than in high-dimensional spaces. It is shown how a diversity of methods and tools boil down to a single core methods, PCA with SVD, such that the efforts to optimize codes for analyzing massive data sets like distributed memory and task-based programming or to improve the efficiency of the algorithms like Randomised SVD can focus on this shared core method, and benefit to all methods.

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Alain Franc. 2022-09-27. Linear Dimensionality Reduction. https://arxiv.org/abs/2209.13597

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