A method for finding minimal sets of features adequately describing discrete information objects

Abstract

One of the classical Data Mining problems is the problem of classifying new objects on the basis of available information when the information associated with these objects does not allow identifying them unambiguously as elements of some set. In such cases using rough sets theory is often an effective solution. This theory operates with such concepts as "indiscernible" elements and relations. A rough set is characterized by lower and upper approximations for finding which the authors earlier suggested an original algebraic method. The given method uses only logic operations, which makes the process of searching logic rules very quick and efficient.The upper and lower approximations of a rough set allow describing elements of this set as completely as it is possible from the viewpoint of available information. In this connection it seems interesting and important to find irreducible sets of features describing a rough set with the same "precision" as with the help of a full set of features (so called reducts). This problem is quite difficult and complicated and at present it does not have good solutions. Our paper continues research carried out by the authors earlier and we suggest a method for finding reducts based on eliminating non-salient features in the reverse order of their importance. The suggested procedure allows us to avoid exhaustive searching by extracting a predefined number of most significant reducts. In this paper we consider arbitrary features taking on their values from finite sets.

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“…While this method of selecting features based on information gain or impurity rank, may result in including features that could be inter-correlated, this does not adversely affect the performance or the results in contrast to traditional statistical methods. This method may not provide the minimal feature set, which is very difficult to identify ( 59 ), but roughly identified sets such as ours work well in practice.…”

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“…in our series of papers [2][3][4][5] we try to give the rough set ideology a bit different perspective by avoiding the usage of the knowledge granularity concept. Whereas the classical rough set theory is based on the indiscernibility relation (which can be equivalence, tolerance or other types of relations), we do not use such a notion and try to consider uncertainty from a logic-algebraic viewpoint.…”