Formalization of 'natural' classification and systematics as fix-points ofpredictions

摘要

Nowadays there exist many approaches to classification andclustering; for instance one can mention those based on compactnessand various metrics on feature spaces, based on etalons, on distributionscomposition partitioning, etc. In contrast to these approaches, the taskof “natural” classification is to discover a classification as a law of naturethat satisfy some requirements promoted by naturalists. The sense ofthis law is in the compression of information by extracting the structureof natural objects. We propose a formalization of this law based on fix–points of probabilistic laws of special type.We prove that the probabilisticlaws we define solve the problem of statistical ambiguity and thus theyenable us to predict without contradictions and to provide consistentfix–points. These fix–points form a “natural” classification. Finally wepresent the results of a computer experiment on building and recognitionof classes of transcription factors binding sites.