Title

Accelerated Learning Of Generalized Sammon Mappings

Abstract

The Sammon Mapping (SM) has established itself as a valuable tool in dimensionality reduction, manifold learning, exploratory data analysis and, particularly, in data visualization. The SM is capable of projecting high-dimensional data into a low-dimensional space, so that they can be visualized and interpreted. This is accomplished by representing inter-sample dissimilarities in the original space by Euclidean inter-sample distances in the projection space. Recently, Kernel Sammon Mapping (KSM) has been shown to subsume the SM and a few other related extensions to SM. Both of the aforementioned models feature a set of linear weights that are estimated via Iterative Majorization (IM). While IM is significantly faster than other standard gradient-based methods, tackling data sets of larger than moderate sizes becomes a challenging learning task, as IM's convergence significantly slows down with increasing data set cardinality. In this paper we derive two improved training algorithms based on Successive Over-Relaxation (SOR) and Parallel Tangents (PARTAN) acceleration, that, while still being first-order methods, exhibit faster convergence than IM. Both algorithms are relatively easy to understand, straightforward to implement and, performance-wise, are as robust as IM. We also present comparative results that illustrate their computational advantages on a set of benchmark problems. © 2011 IEEE.

Publication Date

10-24-2011

Publication Title

Proceedings of the International Joint Conference on Neural Networks

Number of Pages

2952-2960

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/IJCNN.2011.6033609

Socpus ID

80054774756 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/80054774756

This document is currently not available here.

Share

COinS