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On the Initialisation of Sammon's Nonlinear Mapping Boaz Lerner*, Hugo Guterman#, Mayer Aladjem#, Its'hak Dinstein#
 

Summary: On the Initialisation of Sammon's Nonlinear Mapping
Boaz Lerner*, Hugo Guterman#, Mayer Aladjem#, Its'hak Dinstein#
*University of Cambridge Computer Laboratory, New Museums Site, Cambridge CB2 3QG, UK
#Department of Electrical and Computer Engineering, Ben-Gurion University, Beer-Sheva 84105, Israel
(Published in Pattern Analysis & Applications 3(1), 2000)
Abstract
The initialisation of a neural network implementation of Sammon's mapping, either randomly or
based on the principal components (PCs) of the sample covariance matrix, is experimentally
investigated. When PCs are employed, fewer experiments are needed and the network configuration
can be set precisely without trial-and-error experimentation. Tested on five real-world databases, it
is shown that very few PCs are required to achieve a shorter training period, lower mapping error
and higher classification accuracy, compared with those based on random initialisation.
Keywords- classification, data projection, initialisation, Sammon's mapping, neural networks, principal component analysis (PCA)
1. Introduction
Sammon's nonlinear mapping [1] is a projection method for analysing multivariate data. The
method attempts to preserve the inherent structure of the data when the patterns are projected from
a higher-dimensional space to a lower-dimensional space by maintaining the distances between
patterns under projection. Denote the distances between pattern Xi and pattern Xj in the input space
and their projections Yi and Yj in the projected space as dij
* and dij, respectively. Employing

  

Source: Aladjem, Mayer - Department of Electrical and Computer Engineering, Ben-Gurion University

 

Collections: Computer Technologies and Information Sciences