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Summary: Patch-to-Tensor Embedding
Guy Wolf Moshe Salhov Amir Averbuch
School of Computer Science
Tel Aviv University, Tel Aviv 69978, Israel
May 10, 2011
Abstract
A popular approach to deal with the "curse of dimensionality"
in relation with the analysis of high-dimensional datasets, is to as-
sume that points in these datasets lie on a low-dimensional manifold
immersed in a high-dimensional ambient space. Kernel methods op-
erate on this assumption and introduce the notion of local affinities
between data-points via the construction of a suitable kernel. Spectral
analysis of this kernel provides a global, preferably low-dimensional,
coordinate system that preserves the qualities of the manifold. In this
paper, we extend the scalar relations used in this framework to matrix
relations, which can encompass multidimensional similarities between
local neighborhoods of points on the manifold. We utilize the diffu-
sion maps method together with linear-projection operators between
tangent spaces of the manifold to construct a super-kernel that rep-
resents these relations. The properties of the presented super-kernels
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