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Oscillatory neural networks with chaotic dynamics in application to cluster analysis


E. N. Benderskaya, S. V. Zhukova

The development of up to date cluster analysis techniques that respond to requirements on real-time processing with high quality results of pattern recognition solutions still stands to be actual as the variety and velocity of data increased greatly since last decade. One of promising trends in pattern recognition belongs to application of oscillatory neural networks with chaotic dynamics (OCNN). This class of neural networks attracts ones attention because of similarity to biological prototype (human brain) that consists in self-organized generalization of knowledge by means of inner synchronization emerging between highly unstable elements. Under main focus in this paper are the opportunities of OCNN application to general clustering problem solution when there is no a priori information about number and topology of clusters. The phenomenology of oscillatory clusters formation for the first time was discovered by K. Kaneko when he modeled multidimensional difference equations. Chaotic globally coupled maps with homogeneous weak linkage generated abstract oscillatory clusters. The heterogeneous mean field assignment by means of triangulation metric allows inner synchronization tuning of chaotic neurons in order to obtain clustering solution without an expert opinion. The proposed method to reveal fragmentary synchronization (typical for OCNN) predetermined correct interpretations of chaotic oscillatory dynamics under the condition when there is no coincidence between instant states of neurons that belong to the same cluster neither by amplitude, nor by phase or fixed phase lag. The role of chaos in fragmentary synchronization emergence was investigated. The substitution of logistic map to more simple transfer functions like sinus, logistic map with parameter  = 1.3, circle map with parameters К = 3, Ω = 0.2 brings to coherent dynamics of all neurons that corresponds to negative clustering results (all objects are recognized to be in one cluster). On the opposite application of other well-known chaotic maps (Baker’s map, tent map, Gauss map, circle map with parameters К = 0.32 , Ω = 0.2) as transfer functions give evidence to the existence of OCNN set applica-ble to cluster analysis. To demonstrate the advantages of new clustering method based on oscillatory neural network with chaotic dynamics the comparative analysis with 42 hierarchical clustering techniques and iterative k – means is given. Classical clustering techniques are based on inner (Euclidean, square Euclidean, Mahalanobis, Chebyshev, Minkovski, cityblock, cosine) and between clusters (single linkage, complete linkage, average linkage, centroid linkage, median linkage, weighted linkage) distance metrics. The advantages of OCNN clustering method were demonstrated on fundamental clustering problems suite: all test input datasets were clustered by one unified way with no mistakes. OCNN embedding into automatic pattern recognition systems is considered to be possible after development of clustering technique hardware implementation.

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