Compressed Sensing: Sparse PCA and a Compressed Sensing Search Engine

Following up on their paper entitled Full Regularization Path for Sparse Principal Component Analysis, Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui have produced a new paper where they describe a greedy algorithm to perform their Sparse PCA analysis (as opposed to their previous approach using semidefinite programming). The new paper is: Optimal Solutions for Sparse Principal Component Analysis
the abstract reads:

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all target numbers of non zero coefficients, with total complexity O(n^3), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n^3) per pattern. We discuss applications in subset selection and sparse recovery and show on artificial examples and biological data that our algorithm does provide globally optimal solutions in many cases.

The code PathSPCA: A fast greedy algorithm for sparse PCA can be found here.

I have set up a search capability on the right side of this blog that uses the new capability for Google search to search through this page and ALL the sites I am linking to. Since I am making an effort at linking to all the researchers involved in Compressed Sensing, searching though this interface enables searching through most websites relevant to this subject.

Photo Credit: NASA, The Earth and the Moon as seen from Galileo en route to Jupiter.