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arXiv · 1206.1529

Sparse projections onto the simplex

Anastasios Kyrillidis·Stephen Becker·Volkan Cevher and·Christoph Koch
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Abstract

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints.

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Anastasios Kyrillidis, Stephen Becker, Volkan Cevher and, Christoph Koch. 2013-04-10. Sparse projections onto the simplex. https://arxiv.org/abs/1206.1529

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