Sparse PCA: a Geometric Approach

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs) iteratively through deflation, we propose GeoSPCA, a novel algorithm to build all PCs at once while satisfying the orthogonality constraints which brings substantial benefits over deflation. This novel approach is based on the left eigenvalues of the covariance matrix which helps circumvent the non-convexity of …

algorithm benefits binary building components constraints covariance data explained focus linear matrix novel optimization solution support through variance