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Published on Jun 18, 2016
Title: A Framework for Sparse PCA
Abstract: Principal component analysis (PCA) is one of the most popular tools for identifying structure and extracting interpretable information from datasets. In this talk, I will discuss constrained variants of PCA such as Sparse or Nonnegative PCA that are computationally harder, but offer higher data interpretability. I will describe a framework for solving quadratic optimization problems --such as PCA-- under sparsity or other combinatorial constraints. Our method can surprisingly solve such problems exactly when the involved quadratic form matrix is positive semidefinite and low rank. Of course, real datasets are not low-rank, but they can frequently be well approximated by low-rank matrices. For several datasets, we obtain excellent empirical performance and provable upper bounds that guarantee that our objective is close to the unknown optimum.