Computational experiences with the exchange method. Applied to four commonly used partitioning cluster analysis criteria. (English) Zbl 0353.65004
References:
| [1] | Anderberg, M. R., (Cluster Analysis for Applications (1973), Academic Press: Academic Press New York) · Zbl 0299.62029 |
| [2] | Armour, G. C.; Buffa, E. S., A heuristic algorithm and simulation approach to relative location of facilities, Management Sci., 9, 294-309 (1963) |
| [3] | Bijnen, E. J., (Cluster Analysis, Survey and Evaluation of Techniques (1973), Tilburg Univ. Press: Tilburg Univ. Press Tilburg) · Zbl 0293.92001 |
| [4] | Bock, H. H., (Automatische Klassifikation (1974), Vandenhoeck & Ruprecht: Vandenhoeck & Ruprecht Göttingen) · Zbl 0279.62013 |
| [5] | Burkard, R. E., Heuristische Verfahren zur Lösung quadratischer Zuordnungsprobleme, Z. Operations Res., 19, 183-193 (1975) · Zbl 0311.90054 |
| [6] | Cooper, L., Location-allocation problems, Operations Res., 11, 331-343 (1963) · Zbl 0113.14201 |
| [7] | Cooper, L., Heuristic methods for location-allocation problems, SIAM Rev., 6, 37-63 (1964) · Zbl 0956.90014 |
| [8] | Domschke, W., Modelle und Verfahren zur Bestimmung betrieblicher und innerbetrieblicher Standorte — Ein Überblick, Z. Operations Res., 19(B), 13-41 (1975) · Zbl 0311.90017 |
| [9] | Duda, O.; Hart, P. E., (Pattern Classification and Scene Analysis (1973), Wiley: Wiley New York) · Zbl 0277.68056 |
| [10] | Duran, B. S.; Odell, P. L., (Cluster Analysis — A Survey (1974), Springer: Springer Berlin) · Zbl 0291.62069 |
| [11] | Everitt, B., (Cluster Analysis (1974), Heinemann: Heinemann London) |
| [12] | Francis, R. L.; White, J. A., (Facility Layout and Location (1974), Prentice Hall: Prentice Hall Englewood Cliffs, N.J.) |
| [13] | Friedmann, H. P.; Rugin, J., On some invariant criteria for grouping data, J. Am. Statist. Assoc., 62, 1159-1178 (1967) |
| [14] | Fukunaga, K.; Koonth, W. L.G., A criterion and an algorithm for grouping data, IEEE Trans. Computers, 19, 917-923 (1970) · Zbl 0206.48002 |
| [15] | Ilanan, M., On Steiner’s problem with rectilinear distance, SIAM J. Appl. Math., 14, 255-265 (1966) · Zbl 0151.33205 |
| [16] | L. Hannsson, Remark on algorithm 266-pseudo-random-generator, Collected Algorithms of the Communications of the ACM.; L. Hannsson, Remark on algorithm 266-pseudo-random-generator, Collected Algorithms of the Communications of the ACM. |
| [17] | Howard, R. N., Classifying a population into homogeneous groups, (Lawrence, J. R., Operational Research and Social Sciences (1966), Tavistock: Tavistock London) |
| [18] | Jensen, R. E., A dynamic programming algorithm for cluster analysis, J. Operations Res. Soc. Am., 7, 1034-1057 (1969) · Zbl 0183.49103 |
| [19] | Kiehne, R., (Innerbetriebliche Standortplanung und Raumordnung (1969), Gabler: Gabler Wiesbaden) |
| [20] | Koonth, W. L.G.; Narenda, P. M.; Fukunaga, K., A branch and bound clustering algorithm, IEEE Trans. Computers, 24, 908-915 (1975) · Zbl 0308.68039 |
| [21] | Kuenne, R. E.; Soland, R. M., Exact and approximate solutions to the multisource Weber problem, Math. Programming, 3, 193-209 (1972) · Zbl 0245.90021 |
| [22] | Kuhn, H. W., A note on Fermat’s problem, Math. Programming, 4, 98-107 (1973) · Zbl 0255.90063 |
| [23] | MacQueen, J., Some methods for classification and analysis of multivariate observations, (5th Berkeley Symp. Math., Stat. Prob., 1 (1967)), 281-297 · Zbl 0214.46201 |
| [24] | Maranzana, F. E., On the location of supply points to minimize transportation costs, IBM Systems J., 129-136 (1963) |
| [25] | Marriot, F. H.C., Practical problems in a method of cluster analysis, Biometrics, 27, 501-514 (1971) |
| [26] | McRae, D. J., MIKCA: A Fortran IV iterative K-means cluster analysis program, Behav. Sci., 16, 423-424 (1971) |
| [27] | Morrison, D. G., Measurement problems in cluster analysis, Management Sci., 13, 775-780 (1967) |
| [28] | Rao, M. R., Cluster analysis and mathematical programming, J. Am. Statist. Assoc., 66, 622-626 (1971) · Zbl 0238.90042 |
| [29] | Scott, A. J.; Simons, M. J., Clustering methods based on likelihood ratio criteria, Biometrics, 27, 387-397 (1971) |
| [30] | Späth, H., Algorithmen für multivariable Ausgleichsmodelle (1974), Oldenbourg: Oldenbourg München · Zbl 0327.65016 |
| [31] | Späth, H., (Cluster-Analyse-Algorithmen zur Objektklassifikation und Datenreduktion (1975), Oldenbourg: Oldenbourg München) · Zbl 0308.62044 |
| [32] | Späth, H., Algorithm: \(L_1\) cluster analysis, Computing, 16, 379-387 (1976) · Zbl 0322.65008 |
| [33] | Späth, H., Numerische Erfahrungen zu heuritischen Lösungsverfaliren beim Varianzkriterium in der Cluster-Analyse, Z. Angew. Informatik (1976), to appear |
| [34] | Soarks, D. N., Euclidean cluster analysis, Appl. Statist., 22, 126-130 (1973) |
| [35] | Streim, H., Heuristische Lösungsverfahren — Versuch einer Begriffsklärung, Z. Operations Res., 19, 143-162 (1975) · Zbl 0311.90040 |
| [36] | Vergin, R. C.; Rogers, J. D., An algorithm and computational procedure for locating ecouimic facilities, Management Sci., 13(B), 240-254 (1967) |
| [37] | Vinod, H. D., Integer programming and the theory of grouping, J. Am. Statist. Assoc., 64, 506-519 (1969) · Zbl 0272.90050 |
| [38] | Weiszfeld, K., Sur le point pour lequel la somme des distances de n points données est minimum, Tohoku Math. J., 43, 335-386 (1937) · Zbl 0017.18007 |
| [39] | Wesolowsky, G. O.; Love, R. F., The optimal location of new facilities using rectangular distances, Operations Res., 19, 124-130 (1971) · Zbl 0216.54102 |
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