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International Journal of Machine Learning and Cybernetics
Erschienen in: International Journal of Machine Learning and Cybernetics 5/2017

13.04.2016 | Original Article

k-Proximal plane clustering

verfasst von: Li-Ming Liu, Yan-Ru Guo, Zhen Wang, Zhi-Min Yang, Yuan-Hai Shao

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 5/2017

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Abstract

Instead of clustering data points to cluster center points in k-means, k-plane clustering (kPC) clusters data points to the center planes. However, kPC only concerns on within-cluster data points. In this paper, we propose a novel plane-based clustering, called k-proximal plane clustering (kPPC). In kPPC, each center plane is not only close to the objective data points but also far away from the others by solving several eigenvalue problems. The objective function of our kPPC comprises the information from between- and within-clusters data points. In addition, our kPPC is extended to nonlinear case by kernel trick. A determinative strategy using a Laplace graph to initialize data points is established in our kPPC. The experiments conducted on several artificial and benchmark datasets show that the performance of our kPPC is much better than both kPC and k-means.
Vorheriger Artikel Representation of graphs based on neighborhoods and soft sets
Nächster Artikel Lexicography minimum solution of fuzzy relation inequalities: applied to optimal control in P2P file sharing system

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Literatur
1.
Han J, Kamber M (2006) Data mining concepts and techniques. Morgan Kaufmann, San FranciscoMATH
2.
Wang Z, Shao Y, Bai L et al (2015) Twin support vector machine for clustering. IEEE Trans Neural Netw Learn Sys 26(10):2583–2588MathSciNetCrossRef
3.
Anderberg M (1973) Cluster analysis for applications. Academic Press, New YorkMATH
4.
Aldenderfer M, Blashfield R (1985) Cluster analysis. Sage Publications, Los AngelesMATH
5.
Andrews H (1972) Introduction to mathematical techniques in pattern recognition. Wiley, New YorkMATH
6.
Celeux G, Govaert G (1995) Gaussian parsimonious clustering models. Pattern Recognit 28(5):781–793CrossRef
7.
Jain A, Dubes R (1988) Algorithms for clustering data. Englewood Cliffs, NJMATH
8.
Fisher D (1987) Knowledge acquisition via incremental conceptual clustering. Mach Learn 2(2):139–172
9.
Hassoun M (1995) Fundamentals of artificial neural networks. MIT, CambridgeMATH
10.
Bradley P, Mangasarian O, Street W (1997) Clustering via concave minimization. Adv Neural Inf Process Syst 9:368–374
11.
Rao M (1987) Cluster analysis and mathematical programming. Am Stat Assoc 66(335):622–626MATHCrossRef
12.
Selim S, Ismail M (1984) K-means-type algorithms: a generalized convergence theorem and characterization of local optimality. IEEE Trans Pattern Anal Mach Intell PAMI 6(1):81–87MATHCrossRef
13.
Bezdek JC, Hathaway RJ, Sabin MJ, Tucker WT (1987) Convergence theory for fuzzy c-means: counterexamples and repairs. Syst Man Cybern IEEE Trans 17(5):873–877MATHCrossRef
14.
Mangasarian O, Wild E (2006) Multisurface proximal support vector classification via generalize eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRef
15.
16.
17.
Amaldi E, Coniglio S (2013) A distance-based point-reassignment heuristic for the k-hyperplane clustering problem. Eur J Oper Res 227(1):22–29MathSciNetMATHCrossRef
18.
Rahman MA, Islam MZ, Bossomaier T (2014) Denclust: a density based seed selection approach for k-means. Artif Intell Soft Comput 8468:784–795CrossRef
19.
Bezdek JC, Pal NR (1998) Some new indexes of cluster validity. Syst Man Cybernet Part B Cybern IEEE Trans 28(3):301–315CrossRef
20.
Li C, Kuo B, Chin T (2011) Lda-based clustering algorithm and its application to an unsupervised feature extraction. Fuzzy Syst IEEE Trans 19(1):152–163CrossRef
21.
Pang Y, Wang S, Yuan Y (2014) Learning regularized lda by clustering. Neural Netw Learn Syst IEEE Trans 25(12):2191–2201CrossRef
22.
Yang ZM, Guo YR, Li CN, Shao YH (2015) Local k-proximal plane clustering. Neural Comput Appl 26(1):199–211CrossRef
23.
Shao Y, Deng N, Chen W, Wang Z (2013) Improved generalized eigenvalue proximal support vector machine. IEEE Signal Process Lett 20(3):213–216CrossRef
24.
Shao Y, Zhang C, Wang X, Deng N (2011) Improvements on twin support vector machines. IEEE Trans Neural Netw 22(6):962–968CrossRef
25.
Shao Y, Chen W, Deng N (2014) Nonparallel hyperplane support vector machine for binary classification problems. Inf Sci 263:22–35MathSciNetMATHCrossRef
26.
Qi Z, Tian Y, Shi Y (2012) Twin support vector machine with universum data. Neural Netw 36:112–119MATHCrossRef
27.
Qi Z, Tian Y, Shi Y (2012) Robust twin support vector machine for pattern classification. Pattern Recognit 46(1):305–316MATHCrossRef
28.
Han J, Kamber M (2006) Data mining: concepts and techniques, 2nd edn. China Machine Press, BeijingMATH
29.
Ding C, He X (2004) K-means clustering via principal component analysis, in: Proceedings of the twenty-first international conference on machine learning, ACM, p 29
30.
Scarborough J (1958) Numerical mathematical analysis, 4th edn. Johns Hopkins Press, New YorkMATH
31.
Deng N, Tian Y, Zhang C (2013) Support vector machines: optimization based theory, algorithms, and extensions. CRC Press, Boca RatonMATH
32.
Naldi M, Campello R (2014) Evolutionary k-means for distributed datasets. Neurocomputing 127(3):30–42CrossRef
33.
Bradley P, Fayyad U (1998) Refining initial points for k-means clustering, in: Proceedings of the 15th international conference on machine learning (ICML98), pp. 91–99
34.
Fayyad U, Reina C, Bradley B (1998) Initialization of iterative refinement clustering algorithms In: Proc 14th Intl Conf on machine learning (ICML), pp. 194–198
35.
Shao Y-H, Bai L, Wang Z, Hua X-Y, Deng N-Y (2013) Proximal plane clustering via eigenvalues. Proc Comput Sci 17:41–47CrossRef
36.
37.
Hathaway RJ, Bezdek JC, Huband JM (2005) Kernelized non-euclidean relational c-means algorithms. Neural Parallel Sci Comput 13(3):305–326MathSciNetMATH
38.
Scholköpf B, Smola A (2002) Learning with kernels. MIT Press, Cambridge, MAMATH
39.
Shao Y, Deng N (2012) A coordinate descent margin based-twin support vector machine for classification. Neural Netw 25:114–121MATHCrossRef
40.
Qi Z, Tian Y, Shi Y (2012) Laplacian twin support vector machine for semi-supervised classification. Neural Netw 35:46–53MATHCrossRef
41.
Shao Y-H, Wang Z, Chen W-J, Deng N-Y (2013) A regularization for the projection twin support vector machine. Knowl Based Syst 37:203–210CrossRef
42.
43.
Derya B, Alp K (2007) ST-DBSCAN: an algorithm for clustering spatial–temporal data. Data Knowl Eng 60(1):208–221CrossRef
44.
Zhou A, Zhou S, Cao J, Fan Y, Hu Y (2000) Approaches for scaling DBSCAN algorithm to large spatial databases. J Comput Sci Technol 15(6):509–526MATHCrossRef
45.
46.
Halkidi M, Batistakis Y, Vazirgiannis M (2001) On clustering validation techniques. Intell Inf Syst J 17:107–145MATHCrossRef
47.
Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mac Learn Res 7(1):1–30MathSciNetMATH
48.
49.
Hollander M, Wolfe D, Chicken E (1973) Nonparametric statistical methods, 2nd edn. Wiley, New YorkMATH
50.
Wang Y, Jiang Y, Wu Y, Zhou Z (2011) Localized k-flats. In: Proceedings of the twenty-fifth AAAI conference on artificial intelligence, pp. 525–530
51.
Huang P, Zhang D (2010) Locality sensitive c-means clustering algorithms. Neurocomputing 73:2935–2943CrossRef
52.
Yang B, Chen S (2010) Sample-dependent graph construction with application to dimensionality reduction. Neurocomputing 74:301–314CrossRef
53.
Tian Y, Shi Y, Liu X (2012) Recent advances on support vector machines research. Technol Econ Dev Econ 18(1):5–33CrossRef
54.
Shao Y-H, Deng N-Y, Chen W-J (2013) A proximal classifier with consistency. Knowl Based Syst 49:171–178CrossRef
55.
Bezdek JC, Gunderson R, Ehrlich R, Meloy T (1978) On the extension of fuzzy k-means algorithms for detection of linear clusters. Decision and control including the 17th symposium on adaptive processes 17(1):1438–1443MATH
56.
Bezdek JC, Coray C, Gunderson R, Watson J (1981) Detection and characterization of cluster substructure i. linear structure: fuzzy c-lines. SIAM J Appl Math 40(2):339–357MathSciNetMATHCrossRef
57.
Bezdek JC, Coray C, Gunderson R, Watson J (1981) Detection and characterization of cluster substructure ii. fuzzy c-varieties and complex combinations thereof. SIAM J Appl Math 40(2):358–372MathSciNetMATHCrossRef
Metadaten
Titel
k-Proximal plane clustering
verfasst von
Li-Ming Liu
Yan-Ru Guo
Zhen Wang
Zhi-Min Yang
Yuan-Hai Shao
Publikationsdatum
13.04.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 5/2017
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-016-0526-y

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