Geometrical Invariants Approach to Recognition the Structures in Time Series and Abstract Maps

The problem of recognition of geometrical objects in different types of data and signals is considered. The main tool in the proposed methodology is a new definition of a cluster based on the invariants of some transformations of space. The invariant properties are closely connected to the symmetry groups of objects. As an illustration, the classical symmetries of space such as continuous groups (Lie transformations) are considered. The particular case of spike recognition in neurophysiology is described in details. Preliminary investigations show the high potential power of method. The further prospects of the proposed method are discussed including the problem of perception and models of mentality.