k-means Approach to the Karhunen-Loeve Transform

TL;DR

This paper introduces a unified approach that generalizes PCA and k-means by approximating data with multiple affine subspaces, offering improved results for certain data exploration tasks.

Contribution

It proposes a novel method combining PCA and k-means into a single framework using affine subspaces, enhancing data approximation capabilities.

Findings

Method outperforms classical PCA and k-means in specific data exploration scenarios.

Provides a flexible approach adaptable to different data structures.

Demonstrates improved data approximation accuracy.

Abstract

We present a simultaneous generalization of the well-known Karhunen-Loeve (PCA) and k-means algorithms. The basic idea lies in approximating the data with k affine subspaces of a given dimension n. In the case n=0 we obtain the classical k-means, while for k=1 we obtain PCA algorithm. We show that for some data exploration problems this method gives better result then either of the classical approaches.