Numerical methods for ordinary differential equations on matrix manifolds
Journal of Computational and Applied Mathematics
A continuous weighted low-rank approximation for collaborative filtering problems
ICAPR'05 Proceedings of the Third international conference on Advances in Pattern Recognition - Volume Part I
Subtractive clustering for seeding non-negative matrix factorizations
Information Sciences: an International Journal
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In various applications, data in multidimensional space are normalized to unit length. This paper considers the problem of best fitting given points on the m-dimensional unit sphere Sm-1 by k-dimensional great circles with k much less than m. The task is cast as an algebraically constrained low-rank matrix approximation problem. Using the fidelity of the low-rank approximation to the original data as the cost function, this paper offers an analytic expression of the projected gradient which, on one hand, furnishes the first order optimality condition and, on the other hand, can be used as a numerical means for solving this problem.