Which principal components are most sensitive to distributional changes?

Autor:	Tveten, Martin
Rok vydání:	2019
Předmět:	Mathematics - Statistics Theory Statistics - Machine Learning Statistics - Other Statistics
Druh dokumentu:	Working Paper
Popis:	PCA is often used in anomaly detection and statistical process control tasks. For bivariate data, we prove that the minor projection (the least varying projection) of the PCA-rotated data is the most sensitive to distributional changes, where sensitivity is defined by the Hellinger distance between distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, i.e., the change is sparse. Simulations indicate that the minor projections are the most sensitive for a large range of changes and pre-change settings in higher dimensions as well. This motivates using the minor projections for detecting sparse distributional changes in high-dimensional data. Comment: 11 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.06318 Zobrazit plný text záznamu View this record from Arxiv