Randomized Nonlinear Component Analysis

TL;DR

This paper introduces scalable randomized algorithms for nonlinear component analysis, extending PCA and CCA to large datasets with minimal performance loss, and demonstrates their effectiveness on real-world data.

Contribution

The paper presents novel randomized methods for nonlinear PCA and CCA that are computationally efficient and scalable to large datasets, extending to other multivariate analysis tools.

Findings

Algorithms perform comparably to state-of-the-art on real data

Significant computational savings achieved

Applicable to spectral clustering and LDA

Abstract

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real-world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.