Real-Time Vector Quantization and Clustering Based on Ordinary Differential Equations

This brief presents a dynamical system approach to vector quantization or clustering based on ordinary differential equations with the potential for real-time implementation. Two examples of different pattern clusters demonstrate that the model can successfully quantize different types of input patterns. Furthermore, we analyze and study the stability of our dynamical system. By discovering the equilibrium points for certain input patterns and analyzing their stability, we have shown the quantizing behavior of the system with respect to its vigilance parameter. The proposed system is applied to two real-world problems, providing comparable results to the best reported findings. This validates the effectiveness of our proposed approach.

[1]  Mehdi R. Zargham,et al.  Operation of an associative memory , 1994, Pattern Recognit..

[2]  Assaf Gottlieb,et al.  Algorithm for data clustering in pattern recognition problems based on quantum mechanics. , 2001, Physical review letters.

[3]  Ethem Alpaydin,et al.  Combining multiple representations and classifiers for pen-based handwritten digit recognition , 1997, Proceedings of the Fourth International Conference on Document Analysis and Recognition.

[4]  Stephen Grossberg,et al.  Adaptive pattern classification and universal recoding: II. Feedback, expectation, olfaction, illusions , 1976, Biological Cybernetics.

[5]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[6]  Yuan-chin Ivan Chang,et al.  Synergy of Logistic Regression and Support Vector Machine in Multiple-Class Classification , 2004, IDEAL.

[7]  Asim Roy,et al.  Connectionism, Controllers, and a Brain Theory , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[8]  Emile Fiesler,et al.  High-order and multilayer perceptron initialization , 1997, IEEE Trans. Neural Networks.

[9]  F. Verhulst.  Nonlinear Differential Equations and Dynamical Systems , 1989 .

[10]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[11]  Nizar Bouguila,et al.  Count Data Modeling and Classification Using Finite Mixtures of Distributions , 2011, IEEE Transactions on Neural Networks.

[12]  David A. Wood,et al.  Adaptive competitive self-organizing associative memory , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[14]  James T. Kwok,et al.  Simplifying Mixture Models Through Function Approximation , 2006, IEEE Transactions on Neural Networks.

[15]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[16]  Raymond J. Mooney,et al.  Integrating constraints and metric learning in semi-supervised clustering , 2004, ICML.

[17]  Ethem Alpaydin,et al.  Combining Multiple Representations for Pen-based Handwritten Digit Recognition , 2001 .

[18]  Qunjing Wang,et al.  Further Development of Input-to-State Stabilizing Control for Dynamic Neural Network Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[19]  Stephen Grossberg,et al.  The ART of adaptive pattern recognition by a self-organizing neural network , 1988, Computer.