Sparse Principal Component Analysis via Variable Projection

TL;DR

This paper introduces a robust, scalable, and efficient sparse principal component analysis (SPCA) algorithm formulated as a value-function optimization, capable of handling large-scale data and corrupted inputs with superior performance.

Contribution

The paper presents a novel formulation of SPCA as a value-function optimization problem, enabling robustness, scalability, and the use of randomized methods for big data applications.

Findings

Demonstrates exceptional computational efficiency.

Achieves meaningful sparse components despite corrupted data.

Validates approach on synthetic and real-world datasets.

Abstract

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. We demonstrate a robust and scalable SPCA algorithm by formulating it as a value-function optimization problem. This viewpoint leads to a flexible and computationally efficient algorithm. Further, we can leverage randomized methods from linear algebra to extend the approach to the large-scale (big data) setting. Our proposed innovation also allows for a robust SPCA formulation which obtains meaningful sparse principal components in spite of grossly corrupted input data. The proposed algorithms are demonstrated using both synthetic and real world data, and show exceptional computational efficiency and diagnostic performance.