Unsupervised nonparametric density estimation: A neural network approach
Edmondo Trentin, Antonino Freno · 2009
One major problem in pattern recognition is estimating probability density functions. Unfortunately, parametric techniques rely on an arbitrary assumption on the form of the underlying, unknown density function. On the other hand, nonparametric techniques, such as the popular kn-nearest neighbor (not to be confused with the k-nearest neighbor classification algorithm), allow to remove such an assumption. Albeit effective, the kn-nearest neighbor is affected by a number of limitations. Artificial neural networks are, in principle, an alternative family of nonparametric models. So far, artificial neural networks have been extensively used to estimate probabilities (e.g., class-posterior probabilities). However, they have not been exploited to estimate instead probability density functions. This paper introduces a simple, neural-based algorithm for unsupervised, nonparametric estimation of multivariate densities, relying on the kn-nearest neighbor technique. This approach overcomes the limitations of kn-nearest neighbor, possibly improving the estimation accuracy of the resulting pdf models. An experimental investigation of the algorithm behavior is offered, exploiting random samples drawn from a mixture of Fisher-Tippett density functions.