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K-SVD : ウィキペディア英語版
K-SVD

In applied mathematics, K-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. K-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data. K-SVD can be found widely in use in applications such as image processing, audio processing, biology, and document analysis.
== Problem description ==
(詳細はsparsely, as a linear combination of these atoms; to represent y, the representation vector x should satisfy the exact condition y = Dx, or the approximate condition y \approx Dx, made precise by requiring that \|y - Dx\|_p \le \epsilon for some small value and some . The vector x \in \mathbb^ contains the representation coefficients of the signal y. Typically, the norm p is selected as , , or .
If n < K and D is a full-rank matrix, an infinite number of solutions are available for the representation problem, Hence, constraints should be set on the solution. Also, to ensure sparsity, the solution with the fewest number of nonzero coefficients is preferred. Thus, the sparsity representation is the solution of either
:
(P_0) \quad \min \limits _x \|x\|_0 \qquad \text y = Dx

or
:
(P_) \quad \min \limits _x \|x\|_0 \qquad \text \|y - Dx\|_2 \le \epsilon

where the \|x\|_0 counts the nonzero entries in the vector x. (See the zero "norm".)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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