Lowdimensional Additive Overlapping Clustering
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
To reveal the structure underlying two-way two-mode object by variable data, Mirkin (1987) has proposed an additive overlapping clustering model. This model implies an overlapping clustering of the objects and a reconstruction of the data, with the reconstructed variable profile of an object being a summation of the variable profiles of the clusters it belongs to. Grasping the additive (overlapping) clustering structure of object by variable data may, however, be seriously hampered in case the data include a very large number of variables. To deal with this problem, we propose a new model that simultaneously clusters the objects in overlapping clusters and reduces the variable space; as such, the model implies that the cluster profiles and, hence, the reconstructed data profiles are constrained to lie in a lowdimensional space. An alternating least squares (ALS) algorithm to fit the new model to a given data set will be presented, along with a simulation study and an illustrative example that makes use of empirical data.
- ANDERSON, T. (1951), “Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions,” The Annals of Mathematical Statistics 22, 327–351. CrossRef
- ARABIE, P., and HUBERT, L. (1994), “Cluster Analysis in Marketing Research,” in Handbook of Marketing Research, ed. R. Bagozzi, Oxford: Blackwell, pp. 160–189.
- BERKOWITZ, L. (1989), “Frustration-aggression Hypothesis: Examination and Reformulation,” Psychological Bulletin 106, 59–73. CrossRef
- BOCK, H.-H. (1987), “On the interface Between Cluster Analysis, Principal Component Analysis and Multidimensional Scaling,” in Multivariate Statistical Modeling and Data Analysis: Proceedings of the Advanced Symposium on Multivariate Modeling and Data Analysis May 15–16, 1986, eds. H. Bozdogan and A. Gupta, Dordrecht, The Netherlands: Reidel Publishing Company, pp. 17–34.
- CARROLL, J. D., and CHATURVEDI, A. (1995), “A General Approach to Clustering and Multidimensional Scaling of Two-way, Three-way or Higher-way Data,” in Geometric Representations of Perceptual Phenomena: Papers in honor of Tarow Indow on his 70th birthday, eds. D. R. Luce, M. D’Zmura, D. Hoffman, G. J. Iverson, and K. A. Romney, Mahwah, New Jersey: Lawrence Erlbaum Associates, pp. 295–318.
- CATTELL, R. B. (1966), “TheMeaning and Strategic Use of Factor Analysis,” in Handbook of Multivariate Experimental Psychology, ed. R. B. Cattell, Chicago: Rand McNally, pp. 174–243.
- CEULEMANS, E., and KIERS, H. A. L. (2006), “Selecting Among Three-mode Principal Component Models of Different Types and Complexities: A Numerical Convex Hull Based Method,” British Journal of Mathematical and Statistical Psychology 59, 133–150. CrossRef
- CEULEMANS, E., TIMMERMAN, M. E., and KIERS, H. A. L. (2011), “The CHull Procedure for Selecting Among Multilevel Component Solutions,” Chemometrics and Intelligent Laboratory Systems 106, 12–20. CrossRef
- CEULEMANS, E., and VAN MECHELEN, I. (2005), “Hierarchical Classes Models for Three-way Three-mode Binary Data: Interrelations and Model Selection,” Psychometrika 70, 461–480. CrossRef
- CEULEMANS, E., and VAN MECHELEN, I. (2004), “Tucker2 Hierarchical Classes Analysis,” Psychometrika 69, 375–399. CrossRef
- CEULEMANS, E., VAN MECHELEN, I., and LEENEN, I. (2007), “The Local Minima Problem in Hierarchical Classes Analysis: An Evaluation of a Simulated Annealing Algorithm and Various Multistart Procedures,” Psychometrika 72, 377–391. CrossRef
- CEULEMANS, E., VAN MECHELEN, I., and LEENEN, I. (2003), “Tucker3 Hierarchical Classes Analysis,” Psychometrika 68, 413–433. CrossRef
- CHANG, W.-C. (1983), “On Using Principal Components Before Separating a Mixture of Two Multivariate Normal Distributions,” Applied Statistics 32, 267–275. CrossRef
- CHATURVEDI, A., and CARROLL, J. D. (1994), “An Alternating Combinatorial Optimization Approach to Fitting the INDCLUS and Generalized INDCLUS Models,” Journal of Classification 11, 155–170. CrossRef
- COHEN, J., and COHEN, P. (1983), Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (2nd ed.), Hillsdale, NJ: Erlbaum.
- DEPRIL, D., VAN MECHELEN, I., and MIRKIN, B. G. (2008), “Algorithms for Additive Clustering of Rectangular Data Tables,” Computational Statistics and Data Analysis 52, 4923–4938. CrossRef
- DE SOETE, G., and CARROLL, J. D. (1994), “K-means Clustering an a Low-dimensional Euclidean Space,” in New Approaches in Classification and Data Analysis, eds. E. Diday, Y. Lechevallier, M. Schader, P. Bertrand, and B. Burtschy, Berlin, Germany: Springer-Verlag, pp. 212–219.
- EVERITT, B. (1977), “Cluster Analysis,” in The Analysis of Survey Data, Vol. 1: Exploring Data Structures, eds. C. A. O’Muircheartaig and C. Payne, London: Wiley, pp. 63–88.
- HUBERT, L. J., ARABIE, P., and HESSON-MCINNES, M. (1992), “Multidimensional Scaling in the City-block Metric - A Combinatorial Approach,” Journal of Classification 9, 211–236. CrossRef
- KRZANOWSKI,W. (1979), “Between-groups Comparison of Principal Components,” Journal of the American Statistical Association 74, 703–707. CrossRef
- KUPPENS, P., and VAN MECHELEN, I. (2007), “Determinants of the Anger Appraisals of Threatened Self-esteem, Other-blame, and Frustration,” Cognition and Emotion 21, 56–77. CrossRef
- KUPPENS, P., VANMECHELEN, I., and SMITS, D. J.M. (2003), “The Appraisal Basis of Anger: Specificity, Necessity and Sufficiency of Components,” Emotion 3, 254–269. CrossRef
- LEE, D. D., and SEUNG, S. H. (2001), “Algorithms for Non-negativeMatrix Factorization,” Advances in Neural Information Processing Systems 13, 556–562.
- LEE, D. D., and SEUNG, S. H. (1999), “Learning the Parts of Objects by Non-negative Matrix Factorization,” Nature 401, 788–791. CrossRef
- MIRKIN, B. G. (1987), “Method of Principal Cluster Analysis,” Automation and Remote Control 48, 1379–1386.
- ROCCI, R., and VICHI,M. (2005), “Three-mode Component Analysis with Crisp or Fuzzy Partition of Units,” Psychometrika 70, 715–736. CrossRef
- SCHEPERS, J., CEULEMANS, E., and VAN MECHELEN, I. (2008), “Selecting Among Multi-mode Partitioning Models of Different Complexities: A Comparison of Four Model Selection Criteria,” Journal of Classification 25, 67–85. CrossRef
- SHEPARD, R. N., and ARABIE, P. (1979), “Additive Clustering Representations of Similarities as Combinations of Discrete Overlapping Properties,” Psychological Review 86, 87–123. CrossRef
- SPIELBERGER, C. D., JOHNSON, E. H., RUSSELL, S. F., CRANE, J. C., JACOBS, G. A., and WORDEN, T. J. (1985), “The Experience and Expression of Anger: Construction and Validation of an Anger Expression Scale,” in Anger and Hostility in Cardiovascular and Behavioral Disorders, eds. M. A. Chesney and R. H. Rosenman, New York: Hemisphere, pp. 5–30.
- STEINLEY, D. (2003), “Local Optima in K-means Clustering: What You Don’t Know May Hurt You,” Psychological Methods 8, 294–304. CrossRef
- STEINLEY, D., and BRUSCO, M. J. (2007), “Intializing K-means Batch Clustering: A Critical Evaluation of Several Techniques,” Journal of Classification 24, 99–121. CrossRef
- STOICA, P., and VIBERG, M. (1996), “Maximum Likelihood Parameter and Rank Estimation in Reduced-Rank Multivariate Linear Regressions,” IEEE Transactions on Signal Processing 44, 3096–3078.
- TRYON, R. C., and BAILY, D. E. (1970), Cluster Analysis, New York: McGraw-Hill.
- VICHI, M., and KIERS, H. A. L. (2001), “FactorialK-means Analysis for Two-Way Data,” Computational Statistics and Data Analysis 37, 49–64. CrossRef
- VICHI, M., ROCCI, R., and KIERS, H. A. L. (2007), “Simultaneous Component and Clustering Models for Three-Way Data: Within and Between Approaches,” Journal of Classification 24, 71–98. CrossRef
- WILDERJANS, T. F., CEULEMANS, E., and KUPPENS, P. (2012), “Clusterwise HICLAS: A Generic Modeling Strategy to Trace Similarities and Differences in Multi-Block Binary Data,” Behavior Research Methods, 44, 532–545. CrossRef
- WILDERJANS, T. F., CEULEMANS, E., and MEERS, K. (in press), “CHull: A Generic Convex Hull Based Model Selection Method,” Behavior Research Methods.
- WILDERJANS, T. F., CEULEMANS, E., and VAN MECHELEN, I. (in press), “The SIMCLAS Model: Simultaneous Analysis of Coupled Binary Data Matrices with Noise Heterogeneity Between and Within Data Blocks,” Psychometrika.
- WILDERJANS, T. F., CEULEMANS, E., VAN MECHELEN, I., and DEPRIL, D. (2011), “ADPROCLUS: A Graphical User Interface for Fitting Additive Profile Clustering Models to Object by Variable Data Matrices,” Behavior Research Methods 43, 56–65. CrossRef
- Lowdimensional Additive Overlapping Clustering
Journal of Classification
Volume 29, Issue 3 , pp 297-320
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Additive overlapping clustering
- Dimensional reduction
- Alternating least squares algorithm
- Two-way two-mode data
- Object by variable data
- Industry Sectors