TR-2002-01
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
Mikhail Belkin; Partha Niyogi. 4 January, 2002.
Communicated by Partha Niyogi.
Abstract
One of the central problems in machine learning and pattern recognition is to develop
appropriate representations for complex data. We consider the problem of constructing
a representation for data lying on a low dimensional manifold embedded in a high
dimensional space. Drawing on the correspondence between the graph Laplacian, the
Laplace Beltrami operator on the manifold, and the connections to the heat equation,
we propose a geometrically motivated algorithm for representing the high dimensional
data. The algorithm provides a computationally efficient approach to non-linear
dimensionality reduction that has locality preserving properties and a natural
connection to clustering. Some potential applications and illustrative examples
are discussed.
Original Document
The original document is available in Postscript (uploaded 4 January, 2002 by
Partha Niyogi).
