Pinboard: bookmarks for shivak tagged 'embeddings'

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Dimension reduction by random hyperplane tesselations

"Given a subset K of the unit Euclidean sphere, we estimate the minimal number m = m(K) of hyperplanes that generate a uniform tessellation of K, in the sense that the fraction of the hyperplanes separating any pair x,y in K is nearly proportional to the Euclidean distance between x and y. Random hyperplanes prove to be almost ideal for this problem; they achieve the almost optimal bound m = O(w(K)^2) where w(K) is the Gaussian mean width of K."

tesselations dimension_reduction embeddings papers to_read
november 2011 by shivak

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Bourgain's discretization theorem

Up to a constant, in terms of distortion, embedding an entire Banach space into another is no harder than embedding an epsilon net.

embeddings functional_analysis metric_spaces papers
october 2011 by shivak

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Subspace embeddings for the L1-norm with applications

L1 dimension reduction??

to_view videos embeddings dimension_reduction
october 2011 by shivak

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Expander Graphs and Their Applications
graph_theory spectral_methods coding_theory embeddings surveys to_read filetype:pdf media:document
december 2010 by shivak

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New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property

Matrices satisfying RIP with random column signs operate as optimal low-distortion embeddings.

embeddings incoherence papers
september 2010 by shivak

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Tight embedding of subspaces of $L_p$ in $\ell_p^n$ for even $p$

"We obtain a tight estimate on the dimension of $\ell_p^n$, $p$ an even integer, needed to almost isometrically contain all $k$-dimensional subspaces of $L_p$."

embeddings papers
september 2010 by shivak

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A metric notion of dimension and its applications to learning

The doubling dimension.

metric_spaces capacity_control learning_theory embeddings have_viewed
august 2010 by shivak

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15-859(J) Metric Embeddings, Fall 2003

"In recent years, the study of distance-preserving embeddings has given a powerful tool to algorithm designers. This course will study various aspects of embedding of metric spaces into "simpler" ones."

embeddings metric_spaces algorithms courses cmu gupta anupam ravi r
june 2010 by shivak

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