Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices
Top Cited Papers
- 23 January 2004
- proceedings article
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3, 2156-2162
- https://doi.org/10.1109/acc.2003.1243393
Abstract
We present a heuristic for minimizing the rank of a positive semidenite matrix over a convex set. We use the logarithm of the determinant as a smooth approx- imation for rank, and locally minimize this function to obtain a sequence of trace minimization problems. Using a technique that relates the rank of any general matrix to that of a corresponding positive semidenite one, we readily extend the proposed heuristic to handle general matrices. We then examine the vector case as a special case, where the heuristic reduces to a known iterative ‘1-norm minimization technique. As practical applications of the rank minimizationKeywords
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