Adaptive PCA for Time-Varying Data

TL;DR

This paper introduces an online adaptive PCA algorithm capable of efficiently updating the eigenspace for sequential data, maintaining high accuracy with low computational cost in both deterministic and stochastic modes.

Contribution

The paper presents a novel one-step update rule for adaptive PCA that efficiently computes eigenspaces for time-varying data with proven convergence and low complexity.

Findings

High accuracy approximation of batch PCA eigenspaces

Efficient O(1) stochastic mode converges to deterministic results

Effective on diverse physical phenomena datasets

Abstract

In this paper, we present an online adaptive PCA algorithm that is able to compute the full dimensional eigenspace per new time-step of sequential data. The algorithm is based on a one-step update rule that considers all second order correlations between previous samples and the new time-step. Our algorithm has O(n) complexity per new time-step in its deterministic mode and O(1) complexity per new time-step in its stochastic mode. We test our algorithm on a number of time-varying datasets of different physical phenomena. Explained variance curves indicate that our technique provides an excellent approximation to the original eigenspace computed using standard PCA in batch mode. In addition, our experiments show that the stochastic mode, despite its much lower computational complexity, converges to the same eigenspace computed using the deterministic mode.