Math @ Duke

Publications [#243818] of Mauro Maggioni
Papers Published
 Chen, G; Maggioni, M, Multiscale geometric wavelets for the analysis of point clouds,
2010 44th Annual Conference on Information Sciences and Systems, CISS 2010
(February, 2010) [doi]
(last updated on 2018/01/16)
Abstract: Data sets are often modeled as point clouds in RD, for D large. It is often assumed that the data has some interesting lowdimensional structure, for example that of addimensional manifold M, with d much smaller than D. When M is simply a linear subspace, one may exploit this assumption for encoding efficiently the data by projecting onto a dictionary of d vectors in RD (for example found by SVD), at a cost (d + n)D for n data points. When M is nonlinear, there are no "explicit" constructions of dictionaries that achieve a similar efficiency: typically one uses either random dictionaries, or dictionaries obtained by blackbox optimization. In this paper we construct datadependent multiscale dictionaries that aim at efficient encoding and manipulating of the data. Their construction is fast, and so are the algorithms to map data points to dictionary coefficients and vice versa. In addition, data points are guaranteed to have a sparse representation in terms of the dictionary. We think of dictionaries as the analogue of wavelets, but for approximating point clouds rather than functions. ©2010 IEEE.


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