What is the particular reason for which we use sparse matrix X in dictionary learning equation Y=DX where Y is the signal matrix, D is dictionary and X is the coefficient matrix?

  • $\begingroup$ Since the dictionary is sparse. $\endgroup$ – Yuval Filmus Mar 10 at 18:21
  • $\begingroup$ @YuvalFilmus No, the dictionary is not sparse. But the X matrix is sparse. $\endgroup$ – Adex Mar 10 at 18:25
  • $\begingroup$ Right, the dictionary used in a particular document is sparse, and we can use it to our advantage. $\endgroup$ – Yuval Filmus Mar 10 at 18:26
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    $\begingroup$ Using sparsity, you can recover the dictionary from fewer samples. $\endgroup$ – Yuval Filmus Mar 10 at 18:51
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    $\begingroup$ You can look up sparse dictionary learning and compressed sensing on Wikipedia. $\endgroup$ – Yuval Filmus Mar 10 at 18:53

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