Optimal multidimensional quantization for pattern recognition
Mingzhou Joe Song, Robert M. Haralick · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2002
In non-parametric pattern recognition, the probability density function is approximated by means of many parameters, each one for a density value in a small hyper-rectangular volume of the space. The hyper-rectangles are determined by appropriately quantizing the range of each variable. Optimal quantization determines a compact and efficient representation of the probability density of data by optimizing a global quantizer performance measure. The measure used here is a weighted combination of average log likelihood, entropy and correct classification probability. In multi-dimensions, we study a grid based quantization technique. Smoothing is an important aspect of optimal quantization because it affects the generalization ability of the quantized density estimates. We use a fast generalized k nearest neighbor smoothing algorithm. We illustrate the effectiveness of optimal quantization on a set of not very well separated Gaussian mixture models, as compared to the expectation maximization (EM) algorithm. Optimal quantization produces better results than the EM algorithm. The reason is that the convergence of the EM algorithm to the true parameters for not well separated mixture models can be extremely slow.