2014/01/10 by Hemant Kumar Aggarwal, Aggarwal, Hemant Kumar, Angshul Majumdar +1
Engineering · Computer Science · #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.1401.2288
The Kaczmarz algorithm is popular for iteratively solving an overdetermined\nsystem of linear equations. The traditional Kaczmarz algorithm can approximate\nthe solution in few sweeps through the equations but a randomized version of\nthe Kaczmarz algorithm was shown to converge exponentially and independent of\nnumber of equations. Recently an algorithm for finding sparse solution to a\nlinear system of equations has been proposed based on weighted randomized\nKaczmarz algorithm. These algorithms solves single measurement vector problem;\nhowever there are applications were multiple-measurements are available. In\nthis work, the objective is to solve a multiple measurement vector problem with\ncommon sparse support by modifying the randomized Kaczmarz algorithm. We have\nalso modeled the problem of face recognition from video as the multiple\nmeasurement vector problem and solved using our proposed technique. We have\ncompared the proposed algorithm with state-of-art spectral projected gradient\nalgorithm for multiple measurement vectors on both real and synthetic datasets.\nThe Monte Carlo simulations confirms that our proposed algorithm have better\nrecovery and convergence rate than the MMV version of spectral projected\ngradient algorithm under fairness constraints.\n