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When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?
Non-Negative Matrix Factorization Parts
2015/8/21
We interpret non-negative matrix factorization geometrically, as the
problem of finding a simplicial cone which contains a cloud of data
points and which is contained in the positive orthant.
Matrix Factorization for an SO(2) Spinning Top and Related Problems
Matrix Factorization SO(2) Spinning Top Related Problems
2010/11/1
We study the matrix factorization problem associated with an SO(2) spinning top by using the algebro-geometric approach. We derive the explicit expressions in terms of Riemann theta functions and dis...
An Elementary Proof of the Polynomial Matrix Spectral Factorization Theorem
the Polynomial Matrix Spectral Factorization Theorem
2010/11/22
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and lin...
Factorization formulas for higher depth determinants of the Laplacian on the n-sphere
depth determinants the Laplacian on the n-sphere
2010/11/19
We explicitly give factorization formulas for higher depth determinants, which are defined via derivatives of the spectral zeta function at non-positive integer points, of Laplacians on the n-sphere i...