Column subset selection is NP-complete
نویسنده
چکیده
Let M be a real r × c matrix and let k be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity M − SA, where A can be an arbitrary k × c matrix, and S runs over all r × k submatrices of M. This problem and its applications in numerical linear algebra are being discussed for several decades, but its algorithmic complexity remained an open issue. We show that CSSP is NP-complete.
منابع مشابه
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Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing QR, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains a...
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Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing QR, which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains a...
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عنوان ژورنال:
- CoRR
دوره abs/1701.02764 شماره
صفحات -
تاریخ انتشار 2017