Dictionary learning yi ma

for vectors on a sphere maximizing, L4 is minimizing L0

why the objective in Dict learning is only maximizing L4

There is no reconstruction error term in Dict learning bcoz when we assumed that U (D x D) is orthonormal then $U^{T}U=U{U}^T=I_D$ so reconstruction error would be $|x-U{U}^{T}x|=|x-x|$ hence only sparsity term

sae vs classic dict learning

PPCA

for a given matrix A, find matrix orthogonal matrix Q such that frobenium dist to A is minimum

used in MSP solve dictionary learning(orthogonal case, complete dictionary)