Abstract:Low dimensional embeddings of manifold data have gained popularity in the last decade. However, a systematic analysis of low-distortionmanifold embeddings has not received much attention. The leading technical result in the area so far has been the 'random projections' result,which states that a scaled orthogonal linear projection of an n-dimensional compact manifold onto a random subspace of dimensionO(n/eps^2) can preserve all geodesic distances up to a factor of (1 +/- eps) with high probability.

Given the smooth nonlinear structure of manifolds, one hopes that some generic nonlinear embedding can achieve improved results.Inspired by Nash's embedding work in Riemannian geometry (1954), we present an algorithm that, given access to a sample of sizeabout O(1/eps^n), embeds the underlying n-dimensional manifold in just O(n) dimensions and preserves all geodesic distancesup to a factor of (1 +/- eps).

Link to the paper: cseweb.ucsd.edu/~naverma/manifold/nash_jmlr.pdf

Bio: Dr. Nakul Verma is a research specialist at Janelia Research Campus HHMI, a center for conducting fundamental research in basic sciences, where he is developing novel statistical techniques to help biologists quantitatively analyze behavioral phenotypes in model organisms and better understand the underlying neuroscience and genetic principles. His interests include high dimensional data analysis and exploiting intrinsic structure in data to design e�ective learning algorithms. Previously, Dr. Verma worked at Amazon as a research scientist developing risk assessment models for real-time fraud detection. Dr. Verma received his PhD in Computer Science from UC San Diego specializing in Machine Learning.

Speaker:

Nakul VermaResearch specialist, Janelia Research Campus HHMI

SEMINAR

Date: Fri., May 22, 2015Time: 1:00pmLocation: 6115 Gates Building

Distance Preserving Embeddings ofRiemannian Manifolds From Samples