Talk Abstract:

Dimensionality Reduction in Machine Learning and Multimedia Processing

Dimensionality reduction is a fundamental problem in statistical learning, exploratory data analysis, and scientific visualization. Methods in dimensionality reduction are also playing an increasingly important role in multimedia processing. I will review some traditional uses of dimensionality reduction for improving the front ends and statistical models of automatic speech recognition. I will then describe a new approach to dimensionality reduction, called locally linear embedding (LLE), that we are investigating for problems in speech, image, and language processing.

LLE is an unsupervised learning algorithm for discovering low dimensional representations of high dimensional data. LLE uses local symmetries and linear reconstructions to compute neighborhood preserving embeddings of multivariate data. The algorithm involves a simple eigenvector calculation, with no learning rates or local minima. Unlike classical methods, such as principal component analysis or linear discriminant analysis, LLE can discover highly nonlinear embeddings. I will illustrate the method on several nonlinear manifolds, including images of faces and documents of text.

(This is joint work with Sam Roweis of the Gatsby Computational Neuroscience Unit, University College of London.)

Mathematical Foundations of Speech Processing and Recognition

2000-2001 Program: Mathematics in Multimedia