Scale Estimation for Kernel-Based Classification

This paper considers kernel density estimation for unsupervised data classification. A new methodology is proposed for finding the kernel scale using Bayesian statistics. K- nearest neighbourhoods are sampled by considering K as a random variable. The variance of each if-nearest neighbourhood is calculated and its probability density is fitted with a Gamma distribution. The estimated Gamma distribution is used to calculate the kernel scale. The proposed methodology is applied in three different machine learning algorithms: scale space, mean shift and quantum clustering. Quantum clustering employs the Shrodinger partial differential equation and uses the analogy between particles with their electro-magnetic field and data samples with their corresponding probability density function (pdf). The classification relies on the mode detection and the consequent data assignment in the resulting pdf. The proposed algorithm is applied for the classification of modulated signals and of topography extracted from radar images of terrain.