Mathematics – Numerical Analysis
Scientific paper
2005-10-26
Mathematics
Numerical Analysis
Scientific paper
In many applications, it is of interest to approximate data, given by mxn 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 mxn matrix A. Each iteration involves the reading of O(k) of columns or rows of A. The complexity of our algorithm 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.
Friedland Shmuel
Kaveh Mostafa
Niknejad Amir
Zare Hossein
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