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This paper introduces an elemental building block which combines Dictionary Learning and Dimension Reduction (DRDL). We show how this foundational element can be used to iteratively construct a Hierarchical Sparse Representation (HSR) of a sensory stream. We compare our approach to existing models showing the generality of our simple prescription. We then… (More)

We study Dictionary Learning (aka sparse coding). By geometrically interpreting an exact formulation of Dictionary Learning, we identify related problems and draw formal relationships among them. Dictionary Learning is viewed as the minimum generating set of a subspace arrangement. This formulation leads to a new family of dictionary learning algorithms.… (More)

Given a hypergraph H with m hyperedges and a set Q of m pinning subspaces, i.e. globally fixed subspaces in Euclidean space R d , a pinned subspace-incidence system is the pair (H, Q), with the constraint that each pinning subspace in Q is contained in the subspace spanned by the point realizations in R d of vertices of the corresponding hyperedge of H.… (More)

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