Elliptical basis function (EBF) networks are introduced as a new nonpa
rametric method of estimating probability density functions for proces
s data. Unlike Parzen window density estimators that use identical hyp
erspherical basis functions, the EBF method uses elliptical basis func
tions adapted to the local character of the data. This technique overc
omes the spikiness problem associated with Parzen windows, where in hi
gh dimension, they can fail to produce smooth probability density esti
mates. The EBF estimator produces valid density functions that converg
e to the underlying distribution of the data in the limit of an infini
te number of training examples. A technique based on statistical cross
validation is introduced for evaluating different density estimators.
The criterion is a measure of how well the density estimator estimate
s the density of data not used in the training. The EBF density estima
tion method and the evaluation technique are demonstrated using severa
l examples of fault diagnosis.