Principal Ellipsoid Analysis (PEA): Efficient non-linear dimension reduction & clustering

• URL: http://arxiv.org/abs/2008.07110v2
• Date: Mon, 7 Sep 2020 03:23:24 GMT
• Title: Principal Ellipsoid Analysis (PEA): Efficient non-linear dimension reduction & clustering
• Authors: Debolina Paul, Saptarshi Chakraborty, Didong Li and David Dunson
• Abstract summary: This article focuses on improving upon PCA and k-means, by allowing nonlinear relations in the data and more flexible cluster shapes. The key contribution is a new framework for Principal Analysis (PEA), defining a simple and computationally efficient alternative to PCA. In a rich variety of real data clustering applications, PEA is shown to do as well as k-means for simple datasets, while dramatically improving performance in more complex settings.
• Score: 9.042239247913642
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination of simplicity, interpretability and computational efficiency. The focus of this article is on improving upon PCA and k-means, by allowing non-linear relations in the data and more flexible cluster shapes, without sacrificing the key advantages. The key contribution is a new framework for Principal Elliptical Analysis (PEA), defining a simple and computationally efficient alternative to PCA that fits the best elliptical approximation through the data. We provide theoretical guarantees on the proposed PEA algorithm using Vapnik-Chervonenkis (VC) theory to show strong consistency and uniform concentration bounds. Toy experiments illustrate the performance of PEA, and the ability to adapt to non-linear structure and complex cluster shapes. In a rich variety of real data clustering applications, PEA is shown to do as well as k-means for simple datasets, while dramatically improving performance in more complex settings.

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