Two derivations of Principal Component Analysis on datasets of distributions

• URL: http://arxiv.org/abs/2306.13503v1
• Date: Fri, 23 Jun 2023 14:00:14 GMT
• Title: Two derivations of Principal Component Analysis on datasets of distributions
• Authors: Vlad Niculae
• Abstract summary: We formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions. Just like the usual PCA on points can be equivalently derived via a variance-maximization principle and via a minimization of reconstruction error, we derive a closed-form solution for distributional PCA.
• Score: 15.635370717421017
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived via a variance-maximization principle and via a minimization of reconstruction error, we derive a closed-form solution for distributional PCA from both of these perspectives.

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