We present a study of the statistical behavior of the dissimilarity measure, /spl Dscr//sub 5/ proposed previously (Desobry, F. and Davy, M., Proc. IEEE ICASSP, 2003), and which results from a machine learning-based quantile estimation approach, namely, a single-class support vector machine. This dissimilarity measure possesses the interesting property of being asymptotically equivalent to the Fisher ratio when dealing with radial Gaussian probability density functions. More generally, it can be efficiently applied to non-connected quantiles, and to noisy data sets, as outliers are taken into account by the SVM. A generalisation of /spl Dscr//sub 5/ is then proposed, which results in the design of a more general class of dissimilarity measures, also defined in feature space and with the same properties.
[1]
Paul Corazza,et al.
INTRODUCTION TO METRIC-PRESERVING FUNCTIONS
,
1999
.
[2]
M. Basseville.
Distance measures for signal processing and pattern recognition
,
1989
.
[3]
Richard O. Duda,et al.
Pattern classification and scene analysis
,
1974,
A Wiley-Interscience publication.
[4]
Alexander J. Smola,et al.
Learning with kernels
,
1998
.
[5]
Manuel Davy,et al.
Support vector-based online detection of abrupt changes
,
2003,
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..