منابع مشابه
Relative-Error CUR Matrix Decompositions
Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features of the input data. In this paper, we propose and study matrix approximations that are explicitly express...
متن کاملCUR matrix decompositions for improved data analysis.
Principal components analysis and, more generally, the Singular Value Decomposition are fundamental data analysis tools that express a data matrix in terms of a sequence of orthogonal or uncorrelated vectors of decreasing importance. Unfortunately, being linear combinations of up to all the data points, these vectors are notoriously difficult to interpret in terms of the data and processes gene...
متن کاملEfficient algorithms for cur and interpolative matrix decompositions
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. For certain applications, further acceleration can be attained by incorporating techniques based on randomize...
متن کاملar X iv : 0 70 8 . 36 96 v 1 [ cs . D S ] 2 7 A ug 2 00 7 Relative - Error CUR Matrix Decompositions ∗
Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of “components.” Typically, these components are linear combinations of the rows and columns of the matrix, and are thus difficult to interpret in terms of the original features of the input data. In this paper, we propose and study matrix approximations that are explicitly express...
متن کاملCUR Decompositions, Similarity Matrices, and Subspace Clustering
A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces U = M ⋃ i=1 Si. The similarity matrices thus constructed give the exact clustering in the noise-free case. A simple adaptation of the technique also allows clus...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2008
ISSN: 0895-4798,1095-7162
DOI: 10.1137/07070471x