Abstract:Soft subspace clustering algorithm frequently falls into local optimum during searching clustering center point. A fuzzy clustering algorithm is proposed based on the framework of soft subspace clustering, and it integrates quantum-behaved particle swarm optimization (QPSO) algorithm into gradient descent method to optimize the objective function in soft subspace clustering. By the characteristic of searching global optimum in the QPSO algorithm, global optimal center points are solved in the subspace, and then by the high convergence speed of the gradient descent method, fuzzy weights and membership degree matrices of sample points can be obtained. Finally, the optimal clustering results of sample points are obtained. Experiment is carried out on UCI dataset and the results demonstrate the improvement in accuracy as well as the stability of the clustering results of the proposed method.
[1] PARSONS L, HAQUE E, LIU H. Subspace Clustering for High Dimensional Data: A Review. ACM SIGKDD Explorations Newsle-tter, 2004, 6(1): 90-105. [2] Wu X D, KUMAR V, QUINLAN J R, et al. Top 10 Algorithms in Data Mining. Knowledge and Information Systems, 2008, 14(1): 1-37. [3] AGRAWAL R, GEHRKE J, GUNOPULOS D, et al. Automatic Subspace Clustering of High Dimensional Data for Data Mining Applications. ACM SIGMOD Record, 1998, 27(2): 94-105. [4] SOICHER L H. On Cliques in Edge-Regular Graphs. Journal of Algebra, 2015, 421: 260-267. [5] KURI-MORALES A, ALDANA-BOBADILLA E. Finding Irregularly Shaped Clusters Based on Entropy // Proc of the 10th Industrial Conference on Advances in Data Mining Applications and Theoretical Aspects. Berlin, Germany: Springer-Verlag, 2010: 57-70. [6] AGGARWAL C C, WOLF J L, YU P S, et al. Fast Algorithms for Projected Clustering. ACM SIGMOD Record, 1999, 28(2): 61-72. [7] YANG J, WANG W, WANG H X, et al. δ-Clusters: Capturing Subspace Correlation in a Large Data Set // Proc of the 18th International Conference on Data Engineering. San Jose, USA: IEEE, 2002: 517-528. [8] CHAN E Y, CHING W K, NG M K, et al. An Optimization Algorithm for Clustering Using Weighted Dissimilarity Measures. Pattern Recognition, 2004, 37(5): 943-952. [9] JING L P, NG M K, XU J, et al. Subspace Clustering of Text Documents with Feature Weighting K-means Algorithm // Proc of the 9th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining. Berlin, Germany: Springer-Verlag, 2005: 802-812. [10] GAN G J, WU J H, YANG Z J. A Fuzzy Subspace Algorithm for Clustering High Dimensional Data // Proc of the 2nd International Conference on Advanced Data Mining and Applications. Berlin, Germany: Springer-Verlag, 2006: 271-278. [11] JING L P, NG M K, HUANG J Z. An Entropy Weighting k-means Algorithm for Subspace Clustering of High-Dimensional Sparse Data. IEEE Trans on Knowledge and Data Engineering, 2007, 19(8): 1026-1041. [12] DENG Z H, CHOI K S, CHUNG F L, et al. Enhanced Soft Subspace Clustering Integrating Within-Cluster and Between-Cluster Information. Pattern Recognition, 2010, 43(3): 767-781. [13] WANG J, WANG S T, CHUNG F L, et al. Fuzzy Partition Based Soft Subspace Clustering and Its Applications in High Dimensional Data. Information Sciences, 2013, 246: 133-154. [14] XIA H, ZHUANG J, YU D H. Novel Soft Subspace Clustering with Multi-objective Evolutionary approach for High-Dimensional Data. Pattern Recognition, 2013, 46(9): 2562-2575. [15] ZHU L, CAO L B, YANG J, et al. Evolving Soft Subspace Clus-tering. Applied Soft Computing, 2014, 14(B): 210-228. [16] WANG J, DENG Z H, JIANG Y Z, et al. Multiple-Kernel Based Soft Subspace Fuzzy Clustering // Proc of the IEEE International Conference on Fuzzy Systems. Beijing, China: IEEE, 2014: 186-193. [17] CARBONERA J L, ABEL M. An Entropy-Based Subspace Clus-tering Algorithm for Categorical Data // Proc of the 26th IEEE International Conference on Tools with Artificial Intelligence. Limassol, Cyprus: IEEE, 2014: 272-277. [18] WANG L J, HAO Z F, CAI R C, et al. Enhanced Soft Subspace Clustering through Hybrid Dissimilarity. Journal of Intelligent & Fuzzy Systems, 2015, 29(4): 1395-1405. [19] MERINO S, MARTNEZ J, GUZMN F. Metadomotic Optimization Using Genetic Algorithms. Applied Mathematics and Computation, 2015, 267: 170-178. [20] El-SAID S A. Image Quantization Using Improved Artificial Fish Swarm Algorithm. Soft Computing, 2015, 19(9): 2667-2679. [21] SPERANSKII D V. Ant Colony Optimization Algorithms for Digital Device Diagnostics. Automatic Control and Computer Sciences, 2015, 49(2): 82-87. [22] BARBIERI R, BARBIERI N, DE LIMA K F. Some Applications of the PSO for Optimization of Acoustic Filters. Applied Acoustics, 2015, 89: 62-70. [23] SUN J, FENG B, XU W B. Particle Swarm Optimization with Particles Having Quantum Behavior // Proc of the Congress on Evolutionary Computation. Portland, USA: IEEE, 2004, I: 325-331. [24] HRDLE W K, SPOKOINY V, PANOV V, et al. Basics of Modern Mathematical Statistics. Berlin, Germany: Springer-Verlag, 2014.