TY - GEN

T1 - Spatial representation of dissimilarity data via lower-complexity linear and nonlinear mappings

AU - Pekalska, EM

AU - Duin, RPW

N1 - ISSN 0302-9743, phpub 26

PY - 2002

Y1 - 2002

N2 - Dissimilarity representations are of interest when it is hard to define well-discriminating features for the raw measurements. For an exploration of such data, the techniques of multidimensional scaling (MDS) can be used. Given a symmetric dissimilarity matrix, they find a lower-dimensional configuration such that the distances are preserved. Here, Sammon nonlinear mapping is considered. In general, this iterative method must be recomputed when new examples are introduced, but its complexity is quadratic in the number of objects in each iteration step.
A simple modification to the nonlinear MDS, allowing for a significant reduction in complexity, is therefore considered, as well as a linear projection of the dissimilarity data. Now, generalization to new data can be achieved, which makes it suitable for solving classification problems. The linear and nonlinear mappings are then used in the setting of data visualization and classification. Our experiments show that the nonlinear mapping can be preferable for data inspection, while for discrimination purposes, a linear mapping can be recommended. Moreover, for the spatial lower-dimensional representation, a more global, linear classifier can be built, which outperforms the local nearest neighbor rule, traditionally applied to dissimilarities.

AB - Dissimilarity representations are of interest when it is hard to define well-discriminating features for the raw measurements. For an exploration of such data, the techniques of multidimensional scaling (MDS) can be used. Given a symmetric dissimilarity matrix, they find a lower-dimensional configuration such that the distances are preserved. Here, Sammon nonlinear mapping is considered. In general, this iterative method must be recomputed when new examples are introduced, but its complexity is quadratic in the number of objects in each iteration step.
A simple modification to the nonlinear MDS, allowing for a significant reduction in complexity, is therefore considered, as well as a linear projection of the dissimilarity data. Now, generalization to new data can be achieved, which makes it suitable for solving classification problems. The linear and nonlinear mappings are then used in the setting of data visualization and classification. Our experiments show that the nonlinear mapping can be preferable for data inspection, while for discrimination purposes, a linear mapping can be recommended. Moreover, for the spatial lower-dimensional representation, a more global, linear classifier can be built, which outperforms the local nearest neighbor rule, traditionally applied to dissimilarities.

KW - conference contrib. refereed

KW - ZX CWTS JFIS < 1.00

UR - http://link.springer.de/link/service/series/0558/bibs/2396/23960488.htm

M3 - Conference contribution

SN - 3-540-44011-9

SP - 470

EP - 478

BT - Structural, Syntactic, and Statistical Pattern Recognition, Proceedings

A2 - Caelli, T

A2 - Amin, A

A2 - Duin, RPW

A2 - Kamel, M

A2 - de Ridder, D

PB - Springer

CY - Berlin

T2 - Joint IAPR International Workshops SSPR'02 and SPR'02 (Windsor, Canada)

Y2 - 6 August 2002 through 9 August 2002

ER -