Non-Negative Sparse PCA: An Intelligible Exact Approach

Abstract

An iterative method for the computation of a non-negative sparse principal component basis is presented. The iterative nature of the proposed method enables online learning, useful for time-evolving data, such as stock price time series. This way, the computation of the covariance matrix is avoided whenever new data become available. Due to the non-negative constraints explicitly enforced, the extracted eigenvectors turn to be sparse without employing any sparsity controlling parameter. Accordingly, only one parameter has to be tuned, i.e., the learning rate. Also, the complexity of the method under study is approximately linear under plausible assumptions. To assess the method’s performance, comprehensive experimental evaluation is conducted on both image and financial data. The proposed method is thoroughly compared to state-of-the-art and yields promising experimental findings.