What a histogram can really tell the classifier

摘要

This paper presents a simple and efficient clustering technique based on the partitioning of the data histogram. The clustering technique was developed in the context of a study of possible unsupervized classification procedures for multispectral earth imagery. The ultimate goal was on-board data compression, the algorithmic production of thematic maps.The incoming raw spectral data is first reduced to its two principal (Karhunen-Loêve) components, the histogram of which is then partitioned into natural classes on the sole weight of evidence of the global statistics of the imagery. During the course of the study, it became clear that some connection existed between the proposed philosophy and professor Thom's novel theory of “catastrophes”.(1) A simple metric is added to the histogram topology. The metric uses both Shannon's and Fisher's notions of self information. In the domain of definition of the histogram, zones corresponding to the natural classes become separated by a no man's land, an inter-class zone. Under the same formulation, the metric is “Euclidean” on the class zone, “non-Euclidean”, i.e. “Lorentz” on the inter-class zone. This methodology and the underlying philosophy were tested in practice, and encouraging results were obtained.