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An algorithm for clusterwise linear regression based on smoothing techniques. (English) Zbl 1311.90106
Summary: We propose an algorithm based on an incremental approach and smoothing techniques to solve clusterwise linear regression (CLR) problems. This algorithm incrementally divides the whole data set into groups which can be easily approximated by one linear regression function. A special procedure is introduced to generate an initial solution for solving global optimization problems at each iteration of the incremental algorithm. Such an approach allows one to find global or approximate global solutions to the CLR problems. The algorithm is tested using several data sets for regression analysis and compared with the multistart and incremental Späth algorithms.

MSC:
90C26 Nonconvex programming, global optimization
Software:
Algorithm 39; UCI-ml
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References:
[1] Preda, C; Saporta, G, Clusterwise PLS regression on a stochastic process, Comput. Stat. Data Anal., 49, 99-108, (2005) · Zbl 1429.62299
[2] Wedel, M; Kistemaker, C, Consumer benefit segmentation using clusterwise linear regression, Int. J. Res. Mark., 6, 45-59, (1989)
[3] Späth, H, Algorithm 39: clusterwise linear regression, Computing, 22, 367-373, (1979) · Zbl 0387.65028
[4] Späth, H, Algorithm 48: a fast algorithm for clusterwise linear regression, Computing, 29, 175-181, (1981) · Zbl 0485.65030
[5] Gaffney, S., Smyth, P.: Trajectory clustering using mixtures of regression models. In: Chaudhuri, S., Madigan, D. (eds.) Proceedings of the ACM Conference on Knowledge Discovery and Data Mining, pp. 63-72, New York (1999) · Zbl 1093.90023
[6] Zhang, B.: Regression clustering. In: Proceedings of the 3rd IEEE International Conference on Data Mining (ICDM03), pp. 451-458. IEEE Computer Society, Washington, DC (2003) · Zbl 1317.90242
[7] DeSarbo, WS; Cron, WL, A maximum likelihood methodology for clusterwise linear regression, J. Classif., 5, 249-282, (1988) · Zbl 0692.62052
[8] Carbonneau, RA; Caporossi, G; Hansen, P, Globally optimal clusterwise regression by mixed logical-quadratic programming, Eur. J. Oper. Res., 212, 213-222, (2011)
[9] Carbonneau, RA; Caporrossi, G; Hansen, P, Extensions to the repetitive branch-and-bound algorithm for globally-optimal clusterwise regression, Comput. Oper. Res., 39, 2748-2762, (2012) · Zbl 1251.90313
[10] DeSarbo, WS; Oliver, RL; Rangaswamy, A, A simulated annealing methodology for clusterwise linear regression, Psychometrika, 54, 707-736, (1989)
[11] Bagirov, AM; Ugon, J; Mirzayeva, H, Nonsmooth nonconvex optimization approach to clusterwise linear regression problems, Eur. J. Oper. Res., 229, 132-142, (2013) · Zbl 1317.90242
[12] Xavier, AE; Oliveira, AAFD, Optimal covering of plane domains by circles via hyperbolic smoothing, J. Glob. Optim., 31, 493-504, (2005) · Zbl 1093.90023
[13] Xavier, AE, The hyperbolic smoothing clustering method, Pattern Recogn., 43, 731-737, (2010) · Zbl 1187.68514
[14] Bagirov, AM; Al Nuiamat, A; Sultanova, N, Hyperbolic smoothing function method for minimax problems, Optimization, 62, 759-782, (2013) · Zbl 1282.65065
[15] Bache, K., Lichman, M.: UCI machine learning repository. School of Information and Computer Science, University of California, Irvine, CA (2013). http://archive.ics.uci.edu/ml · Zbl 0485.65030
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