Visual Data Mining Based on Partial Similarity Concepts

General Concept Of Similarity

Observing the surrounding world as an extremely sophisticated variety of objects, relationships between them and processes we try to put order on it for making it more comprehensible. One of ways to reach this is establishment of similarities between objects or processes which make it possible to apply some statements about individual objets or processes to the members of their similarity classes. This way of action is not only a human discovery. A wild animal first-time testing an apple and finding it good fixes in its mind a pattern of similar size, form, color and scent objects. In its later experiences the pattern may be corrected by exclusion the small size and dark-green color objects which finally leads to a fixation in the mind a pattern (a concept) of “good for being eaten” objects. Establishment of similarity concepts and detection of similarities in individual cases in many living beings is thus a capability of fundamental importance. Non less important seems explaining what, in general, does the similarity mean.

Strong similarity. In the forthcoming, the notion object will be assigned to any formal representative (geometrical point, vector, string of symbols, etc.) of a real or abstract being, characterizing its features and identifying it among other beings. Similarity is a property of a class C of objects that in the simplest case can be described by a formal similarity relation [Rasiowa H., Sikorski R., 1968]:

• 1⁰ reciprocal (each object a is similar to itself),

• 2⁰ symmetrical (if object a is similar to object b then b is similar to a), and

• 3⁰ transitive (if a is similar to b and b is similar to c then a is similar to c).