Gradient descent with sparsification: an iterative algorithm for sparse recovery with restricted isometry property

We present an algorithm for finding an ssparse vector x that minimizes the squareerror y - x 2 where satisfies the restricted isometry property (RIP), with isometric constant 2s < 1/3. Our algorithm, called GraDeS (Gradient Descent with Sparsification) iteratively updates x as: x Hs x + 1 ? (y - x) where > 1 and Hs sets all but s largest magnitude coordinates to zero. GraDeS converges to the correct solution in constant number of iterations. The condition 2s < 1/3 is most general for which a near-linear time algorithm is known. In comparison, the best condition under which a polynomialtime algorithm is known, is 2s <

• Type: Conference
• Year: 2009
• Where: ICML
• Authors: Rahul Garg, Rohit Khandekar
• Keywords: Condition 2s, ICML 2009, Isometric Constant 2s, Machine Learning, Near-linear Time Algorithm