| Taxonomy
methods
give the way to create the initial classification of the given multitude
m of objects. That classification S = <s1, s2, ...sl, ...sk> may
be fixed in the data table, gathering together in separate layers all ml
strings (objects), contained in one l-th taxon.
For the shortest representation of the main content of such table one may write, e.g. the average meaning and dispersion of object properties for each taxon. It is possible to keep one or more typical representatives (‘precedents’) from each taxon. It is also possible to describe the borders, separating taxons from each other, in the properties space. Any of these descriptions represents itself the generalised pattern of each class. If after that appears the new object q, not participated in taxonomy, and it is necessary to ascribe it to one of the existing k classes, then it is necessary to analyse q object properties and recognise the pattern of the sl class, most similar to the given object. Such procedure have received the name of «pattern recognition» in the data analysis literature. Usually the algorithm input is supplied by «training set» in a from of a data table, containing m objects (à1, à2, ...ài, ...àm), described by properties Õ = (õ1, õ2, ...õj, ...õn). Then there is the «aim» property Y, which shows the belonging of each object to one or another pattern. The recognition process includes two main steps – «learning» and «control». At the first stage the algorithm must discover the regularity between values of «describing» properties X and value of «aim» property Y. This regularity is expressed in a form of «decision rule», providing the making of decision about belonging of any object q, according to its properties, to one of the k existing classes at the «control» stage. Ideally every pattern must be represented by full analytic description of the distribution of all existing in nature objects of this pattern («general set»), instead of learning set of limited volume. For the simplest variants of this ideal case, the mathematical statistics literature describes the strict and elegant methods of creation of the decision rules [1,2]. Practically all real recognition problems differ from such ideal case in the most important property: the knowledge about the general set of objects to be investigated is absent. This gap in knowledge is filled by one or another heuristic hypothesis. The most well-known is the hypothesis of compactness. During the last time the hypothesis of l-compactness was started to be applied. Their main meaning is that the objects of the one properly organised pattern are revealed in the space of their properties into points, geometrically closed to each other, forming «compact» clots. If the learning set is large, then it possible to rely upon the models, i.e. to approximate these clots by distributions of some type and to use then the strict statistic methods. In the opposite case the only thing that can be done is to rely upon the precedents, i.e. on the properties of concrete objects from the learning set. When the statistic models are used as a support, the decision rules may have the simple shape of a plane or second-order surface, separating the property space into k non-intersecting areas. The object q to be recognised is considered as belonging to the pattern, to which area it gets. Sometimes the pattern area is limited by the closed simple-shaped figure (hyper-parallelepiped or hyper-sphere). This software includes algorithm RASP, based on this approach [3]. Algorithm «Splitting Standards» used if separating surface is complicate. If the number of objects to be recognised is high, then it is necessary to apply «PORA» or «MPV» algorithms. In the case of simultaneous recognition of few objects it is reasonable to construct the decision rule directly in the recognition process, using the information from learning and control sets simultaneously. Such decision rule will be more stable to interference, arising from the non-representativeness of the learning set. «Taxonomic Solving Functions» (TRF) algorithm is based on this approach. There are algorithms, creating the decision rules with simultaneous selection of informative properties. Such are "DW" and "ASQUIS" algorithms [4]. 1. Wald A. Statistical Decision Functions. New-York, John Wiley and Sons, 1950. 2. Anderson T.V. Introduction to multidimensional statistic analysis, 1963 3. Zagoruiko N.G. Pattern Recognition Methods and it Applications. Published by "Soviet Radio", M., 1972. 4. Zagoruiko N.G., Elkina V.N., Lbov G.S., Emelianov S.V. A package of the applied programs OTEKS. M.: Finance and Statistics, 1986. - 160 p. |