While the Direct optimization of the dictionary learning problem Toolbox is here, the paper featuring the technique is here: Direct Optimization of the Dictionary Learning Problem by Alain Rakotomamonjy, The abstract reads:

A novel way of solving the dictionary learning problem is proposed in this paper. It is based on a so-called direct optimization as it avoids the usual technique which consists in alternatively optimizing the coefﬁcients of a sparse decomposition and in optimizing dictionary atoms. The algorithm we advocate simply performs a joint proximal gradient descent step over the dictionary atoms and the coefﬁcient matrix. As such, we have denoted the algorithm as a one-step block-coordinate proximal gradient descent and we have shown that it can be applied to a broader class of non-convex optimization problems than the dictionary learning one. After having derived the algorithm, we also provided in-depth discussions on how the stepsizes of the proximal gradient descent have been chosen. In addition, we uncover the connection between our direct approach and the alternating optimization method for dictionary learning. The main advantage of our novel algorithm is that, as suggested by our simulation study, it is far more efﬁcient than alternating optimization algorithms.

Image Credit: NASA/JPL-Caltech. This image was taken by Rear Hazcam: Right A (RHAZ_RIGHT_A) onboard NASA's Mars rover Curiosity on Sol 0 (2012-08-06 06:03:27 UTC) .

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