Fast Monte-Carlo Low Rank Approximations for Matrices

S. Friedland, A. Niknejad, M. Kaveh, H. Zare
2006 IEEE/SMC International Conference on System of Systems Engineering  
In many applications, it is of interest to approximate data, given by m × n matrix A, by a matrix B of at most rank k, which is much smaller than m and n. The best approximation is given by singular value decomposition, which is too time consuming for very large m and n. We present here a Monte Carlo algorithm for iteratively computing a k-rank approximation to the data consisting of m×n matrix A. Each iteration involves the reading of O(k) of columns or rows of A. The complexity of our
more » ... m is O(kmn). Our algorithm, distinguished from other known algorithms, guarantees that each iteration is a better k-rank approximation than the previous iteration. We believe that this algorithm will have many applications in data mining, data storage and data analysis.
doi:10.1109/sysose.2006.1652299 dblp:conf/sysose/FriedlandNKZ06 fatcat:fghybfja7bcmlmeaylzvcu6vx4