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Abstract:
We suggest a nonparametric framework for unsupervised learning
of projection models in terms of density estimation on quantized
sample spaces. The objective is not to optimally reconstruct the
data
but instead the quantizer is chosen to optimally reconstruct the
density of the data. For the resulting
quantizing density estimator
(QDE) we present a general method for parameter estimation and
model selection. We show how projection sets which correspond to
traditional unsupervised methods like vector quantization or PCA
appear in the new framework. For a principal component quantizer
we present results on synthetic and real-world data, which show
that the QDE can improve the generalization of the kernel density
estimator although its estimate is based on significantly
lower-dimensional projection indices of the data.
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