COMPLEX DATA CLUSTERING: FROM NEURAL NETWORK ARCHITECTURE TO THEORY AND APPLICATIONS OF NONLINEAR DYNAMICS OF PATTERN RECOGNITION

This work at the Laboratory for Industrial and Applied Mathematics on the theoretical foundation and applications of projected clustering of high dimensional and big data has been supported by a number of programs and funding agencies including the Canada Research Chairs program, the Natural Sciences and Engineering Research Council of Canada (discovery grant, collaborative research development program), the Mitacs globalink program, the Mitacs accelerate program, the Fields-Mitacs summer research program, the Canada Foundation for Innovation and the Ontario Innovation Trust. A few industrial partners have also been involved, these partners include the Generation 5 Mathematical Technologies Inc. and the InferSystems Corporation. Corresponding author.

[1]  Jianhong Wu,et al.  Subspace clustering for high dimensional categorical data , 2004, SKDD.

[2]  Hiroyuki Honda,et al.  New cancer diagnosis modeling using boosting and projective adaptive resonance theory with improved reliable index , 2007 .

[3]  Xiaohua Jia,et al.  Characterizing Information Diffusion in Online Social Networks with Linear Diffusive Model , 2013, 2013 IEEE 33rd International Conference on Distributed Computing Systems.

[4]  Roman Krakovsky,et al.  Clustering of text documents by projective dimension of subspaces using part neural network , 2012, 2012 7th IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI).

[5]  Iryna Sivak,et al.  An Epidemiological Approach to Information Propagation in the Digg Online Social Network , 2013 .

[6]  Guojun Gan,et al.  Data Clustering: Theory, Algorithms, and Applications (ASA-SIAM Series on Statistics and Applied Probability) , 2007 .

[7]  Bernd Tibken,et al.  Differential Equations with State-Dependent Delays , 2001 .

[8]  James R. Williamson,et al.  Gaussian ARTMAP: A Neural Network for Fast Incremental Learning of Noisy Multidimensional Maps , 1996, Neural Networks.

[9]  Zijiang Yang,et al.  A Fuzzy Subspace Algorithm for Clustering High Dimensional Data , 2006, ADMA.

[10]  Jianhong Wu,et al.  A convergence theorem for the fuzzy subspace clustering (FSC) algorithm , 2008, Pattern Recognit..

[11]  Qingwen Hu,et al.  Global Continua of Rapidly Oscillating Periodic Solutions of State-Dependent Delay Differential Equations , 2010 .

[12]  J. Wu,et al.  A genetic fuzzy k-Modes algorithm for clustering categorical data , 2009, Expert Syst. Appl..

[13]  Stephen Grossberg,et al.  ARTMAP: supervised real-time learning and classification of nonstationary data by a self-organizing neural network , 1991, [1991 Proceedings] IEEE Conference on Neural Networks for Ocean Engineering.

[14]  Jianhong Wu,et al.  Performance limitations from delay in human and mechanical motor control , 2008, Biological Cybernetics.

[15]  Hiroyuki Honda,et al.  Cancer diagnosis marker extraction for soft tissue sarcomas based on gene expression profiling data by using projective adaptive resonance theory (PART) filtering method , 2006, BMC Bioinformatics.

[16]  Stephen Grossberg,et al.  ART 3: Hierarchical search using chemical transmitters in self-organizing pattern recognition architectures , 1990, Neural Networks.

[17]  Dimitrios Gunopulos,et al.  Automatic subspace clustering of high dimensional data for data mining applications , 1998, SIGMOD '98.

[18]  Jianhong Wu,et al.  Fifty years later: a neurodynamic explanation of Fitts' law , 2006, Journal of The Royal Society Interface.

[19]  Stephen Grossberg,et al.  Fuzzy ARTMAP: A neural network architecture for incremental supervised learning of analog multidimensional maps , 1992, IEEE Trans. Neural Networks.

[20]  S. Grossberg,et al.  ART 2: self-organization of stable category recognition codes for analog input patterns. , 1987, Applied optics.

[21]  Kenneth R. Meyer.  from a Dynamical Systems Point of View , 2016 .

[22]  Yongqiang Cao,et al.  Neural networks for clustering: theory, architecture, algorithm and neural dynamics , 2003 .

[23]  Stephen Grossberg,et al.  A massively parallel architecture for a self-organizing neural pattern recognition machine , 1988, Comput. Vis. Graph. Image Process..

[24]  Zijiang Yang,et al.  A Genetic k-Modes Algorithm for Clustering Categorical Data , 2005, ADMA.

[25]  Piet Van Mieghem,et al.  Digging in the Digg Social News Website , 2011, IEEE Transactions on Multimedia.

[26]  Jianhong Wu,et al.  Projective ART for clustering data sets in high dimensional spaces , 2002, Neural Networks.

[27]  Lihong Huang,et al.  Projective ART with buffers for the high dimensional space clustering and an application to discover stock associations , 2009, Neurocomputing.

[28]  Jianhong Wu,et al.  Clustering neural spike trains with transient responses , 2008, 2008 47th IEEE Conference on Decision and Control.

[29]  GanGuojun,et al.  Subspace clustering for high dimensional categorical data , 2004 .

[30]  S. Grossberg,et al.  Neural Dynamics of Category Learning and Recognition: Attention, Memory Consolidation, and Amnesia , 1987 .

[31]  C. Malsburg.  Self-organization of orientation sensitive cells in the striate cortex , 2004, Kybernetik.

[32]  S. Grossberg,et al.  Adaptive pattern classification and universal recoding: I. Parallel development and coding of neural feature detectors , 1976, Biological Cybernetics.

[33]  Philip S. Yu,et al.  Fast algorithms for projected clustering , 1999, SIGMOD '99.

[34]  Qingwen Hu,et al.  Global Hopf bifurcation for differential equations with state-dependent delay , 2010 .

[35]  I. Scott MacKenzie,et al.  Speed-accuracy trade-off in planned arm movements with delayed feedback , 2006, Neural Networks.

[36]  Jianhong Wu,et al.  Estimates of Periods and Global Continua of Periodic Solutions for State-Dependent Delay Equations , 2012, SIAM J. Math. Anal..

[37]  Rung Ching Chen,et al.  Automating construction of a domain ontology using a projective adaptive resonance theory neural network and Bayesian network , 2008, Expert Syst. J. Knowl. Eng..

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

[39]  Jianhong Wu,et al.  Projective Clustering Using Neural Networks with Adaptive Delay and Signal Transmission Loss , 2011, Neural Computation.

[40]  Jianhong Wu,et al.  Dynamics of projective adaptive resonance theory model: the foundation of PART algorithm , 2004, IEEE Transactions on Neural Networks.

[41]  I. Scott MacKenzie,et al.  Estimation of psychomotor delay from the Fitts’ law coefficients , 2009, Biological Cybernetics.

[42]  Hiroyuki Honda,et al.  Construction of robust prognostic predictors by using projective adaptive resonance theory as a gene filtering method , 2005, Bioinform..

[43]  Stephen Grossberg,et al.  Fuzzy ART: Fast stable learning and categorization of analog patterns by an adaptive resonance system , 1991, Neural Networks.