主 题: Randomized Algorithms in Dimensionality Reduction
报告人: Prof. Jianzhong Wang (Sam Houston State University)
时 间: 2011-06-03 14：00-15：00
地 点: 理科一号楼1114（数学所活动）
Dimensionality reduction (DR) is a useful tool in machine learning
and compressive sensing. In data processing, when dimensions of the data
are very high, we meet the so-called curse of dimensionality so that most existent
data processing system cannot deal with them. The role of dimensionality
reduction it to transform high-dimensional data to low-dimensional ones.
The geometric (or spectral) approach to DR is based on manifold learning, in
which a high-dimensional data is modeled as a sample set on a low-dimensional
manifold. Then a DR kernel is constructed to characterize the geometry of
the underlying manifold. Therefore, DR is realized by the spectral decomposition
of the kernel. Many existent DR methods, such as Isomaps, Maximum
Variance Unfolding (MVU), Locally Linear Embedding (LLE), Local Tangent
Space Alignment (LTSA), Hessian Locally Linear Embedding (HLLE), Laplacian
Eigenmaps (Leigs), and Di usion Maps (Dmaps), adopt this approach.
However, these methods are limited by the cardinality of the sample set. In this
presentation, we introduce randomized algorithms to deal with the large-size
high-dimensional data. Random project and randomized Nystrom extension
are applied to signi cantly reduce the size of the kernel so that the randomized
fast algorithms are developed.