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As I know, k-svd is a dictionary learning algorithm(unfortunately I am not expert in k-svd) and svd is a way to decompose a matrix into 3 matrix, but is there any relation between k-svd and svd? I couldn't find the answer even when k=1.

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    $\begingroup$ Yes the k-SVD clustering algorithm uses this (singular) decomposition as a technique of minimizing differences (within the cluster.). $\endgroup$ – kolobokish Nov 8 '16 at 20:29
  • $\begingroup$ @kolobokish so k-SVD when k = 1 is not equal to svd, is it true? $\endgroup$ – user137927 Nov 8 '16 at 20:42
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    $\begingroup$ No. The k-SVD is a type of cluster analysis. It is a tool of data analyzing. SVD is a technique used for decomposition of matrix. Generally, as far as I understand, the latter is mathematical tool used in the algorithm of k-mean cluster analysis. $\endgroup$ – kolobokish Nov 8 '16 at 21:06

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