Isometric Projection

Contractively Complemented Subspaces of Pre-symmetric Spaces

In 1965, Ron Douglas proved that if X is a closed subspace of an L-space and X is isometric to another L-space, then X is the range of a contractive projection on the containing L-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 onto X. In 1993 Kirchberg proved that if a s...

A Quasi-isometric Embedding Algorithm

The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.

Ela Isometric Tight Frames

A d × n matrix, n ≥ d, whose columns have equal length and whose rows are orthonormal is constructed. This is equivalent to finding an isometric tight frame of n vectors in R d (or C d), or writing the d × d identity matrix I = d n n i=1 P i , where the P i are rank 1 orthogonal projections. The simple inductive procedure given shows that there are many such isometric tight frames.

Isometric Projection by Deng Cai , Xiaofei He , and

Recently the problem of dimensionality reduction has received a lot of interests in many fields of information processing, including data mining, information retrieval, and pattern recognition. We consider the case where data is sampled from a low dimensional manifold which is embedded in high dimensional Euclidean space. The most popular manifold learning algorithms include Locally Linear Embe...

Isometric Embedding of Riemannian Manifolds