2006
DOI: 10.1007/11871637_33
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The Discrete Basis Problem

Abstract: Matrix decomposition methods represent a data matrix as a product of two smaller matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. If the original data is binary, the interpretation of the basis vectors is hard. We describe a matrix decomposition formulation, the Discrete Basis … Show more

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Cited by 94 publications
(165 citation statements)
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References 15 publications
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“…When the L 1 -metric is 0, the two matrices are identical. Other metrics (and distances) can also be used - [15] discusses some alternatives and their implications.…”
Section: Definition 2 (Boolean Matrix Multiplication) a Boolean Matrmentioning
confidence: 99%
See 2 more Smart Citations
“…When the L 1 -metric is 0, the two matrices are identical. Other metrics (and distances) can also be used - [15] discusses some alternatives and their implications.…”
Section: Definition 2 (Boolean Matrix Multiplication) a Boolean Matrmentioning
confidence: 99%
“…We now give some additional definitions from Miettinen [15] pertaining to Boolean matrix multiplication.…”
Section: Definition 1 (Rbac)mentioning
confidence: 99%
See 1 more Smart Citation
“…However, when the original matrix X is binary, the eigen-images could contain negative values. In this case, the interpretation of the images is difficult, and important characteristics of data may not be captured well [13], [14], [24].…”
Section: Regularized Singular Value Decompositionmentioning
confidence: 99%
“…Some research has been done in designing dimension reduction methods specifically for binary data [7, 22, 24]. Similar to PCA and SVD, these methods focus on finding a set of new features that approximate the original data, but do not consider the problem of finding multiple sets of interacting features.…”
Section: Related Workmentioning
confidence: 99%