Generalized Spectral Bounds for Sparse LDA
We present a discrete spectral framework for the sparse or cardinality-constrained solution of a generalized Rayleigh quotient. This NPhard combinatorial optimization problem is central to supervised learning tasks such as sparse LDA, feature selection and relevance ranking for classication. We derive a new generalized form of the Inclusion Principle for variational eigenvalue bounds, leading to exact and optimal sparse linear discriminants using branch-and-bound search. An ecient greedy (approximate) technique is also presented. The generalization performance of our sparse LDA algorithms is demonstrated with real-world UCI ML benchmarks and compared to a leading SVM-based gene selection algorithm for cancer classification.