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Locality Regularized Reconstruction: Structured Sparsity and Delaunay Triangulations
May 3, 2024, 4:52 a.m. | Marshall Mueller, James M. Murphy, Abiy Tasissa
cs.LG updates on arXiv.org arxiv.org
Abstract: Linear representation learning is widely studied due to its conceptual simplicity and empirical utility in tasks such as compression, classification, and feature extraction. Given a set of points $[\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_n] = \mathbf{X} \in \mathbb{R}^{d \times n}$ and a vector $\mathbf{y} \in \mathbb{R}^d$, the goal is to find coefficients $\mathbf{w} \in \mathbb{R}^n$ so that $\mathbf{X} \mathbf{w} \approx \mathbf{y}$, subject to some desired structure on $\mathbf{w}$. In this work we seek $\mathbf{w}$ that forms a …
abstract arxiv classification compression cs.lg eess.sp extraction feature feature extraction linear math.oc representation representation learning set simplicity sparsity stat.ml tasks type utility vector
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