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11 September 2015 Geometric multi-resolution analysis for dictionary learning
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Abstract
We present an efficient algorithm and theory for Geometric Multi-Resolution Analysis (GMRA), a procedure for dictionary learning. Sparse dictionary learning provides the necessary complexity reduction for the critical applications of compression, regression, and classification in high-dimensional data analysis. As such, it is a critical technique in data science and it is important to have techniques that admit both efficient implementation and strong theory for large classes of theoretical models. By construction, GMRA is computationally efficient and in this paper we describe how the GMRA correctly approximates a large class of plausible models (namely, the noisy manifolds).
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Mauro Maggioni, Stanislav Minsker, and Nate Strawn "Geometric multi-resolution analysis for dictionary learning", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95971C (11 September 2015); https://doi.org/10.1117/12.2189594
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