Generating Normally Distributed Clusters by Means of a Self-organizing Growing Neural Network– An Application to Market Segmentation –
This paper presents a new growing neural network for
cluster analysis and market segmentation, which optimizes the size
and structure of clusters by iteratively checking them for multivariate
normality. We combine the recently published SGNN approach [8]
with the basic principle underlying the Gaussian-means algorithm
[13] and the Mardia test for multivariate normality [18, 19]. The new
approach distinguishes from existing ones by its holistic design and
its great autonomy regarding the clustering process as a whole. Its
performance is demonstrated by means of synthetic 2D data and by
real lifestyle survey data usable for market segmentation.
[1] Assael, H. (1993): Marketing - Principles and Strategy, 2nd ed., Dryden
Press, Fort Worth.
[2] Atukorale, A.; Suganthan, N. (2000): Hierarchical Overlapped Neural
Gas Network with Application to Pattern Classification, Neurocomputing,
Vol. 35, 165-176.
[3] Berry, M. (Ed.) (2003): Survey of Text Mining: Clustering, Classification,
and Retrieval, Springer, New York.
[4] Bock, T.; Uncles, M. (2002): A Taxonomy of Differences Between
Consumers for Market Segmentation, International Journal of Research
in Marketing, Vol. 19, 215-224.
[5] Boone, D.S.; Roehm, M. (2002): Evaluating the Appropriateness of
Market Segmentation Solutions Using Artificial Neural Networks and
the Membership Clustering Criterion, Marketing Letters, Vol. 13, No. 4,
317-333.
[6] Chu, S.-C.; Roddick, J.F.; Pan, J.-S. (2002): An Incremental Multi-
Centroid, Multi-run Sampling Scheme for k-Medoids-based Algorithms,
Knowledge Discovery and Management Laboratory, Technical Report
KDM-02-003, Flinders University of South Australia.
[7] Daszykowksi, M.; Walczak, B.; Massart, D.L. (2002): On the Optimal
Partitioning of Data with k-means, Growing k-means, Neural Gas, and
Growing Neural Gas, Journal of Chemical Information and Computer
Sciences, Vol. 42, 1378-1389.
[8] Decker, R. (2005): Market Basket Analysis by Means of a Growing
Neural Network, International Review of Retail, Distribution and Consumer
Research, Vol. 15, No. 2, 151-169.
[9] Decker, R.; Monien, K. (2003): Market Basket Analysis with Neural
Gas Networks and Self-organizing Maps, Journal of Targeting, Measurement
and Analysis for Marketing, Vol. 11, No. 4, 373-386.
[10] Dittenbach, M.; Rauber, A.; Merkl, D. (2002): Uncovering Hierarchical
Structure in Data Using the Growing Hierarchical Self-organizing Map,
Neurocomputing, Vol. 48, 199-216.
[11] Fritzke, B. (1995): A Growing Neural Gas Network Learns Topologies,
in: Tesauro, G.; Touretzky, D.S.; Leen, T.K. (Eds.): Advances in Neural
Information Processing Systems 7, MIT Press, 625-632.
[12] Glotsos, D.; Tohka, J.; Ravazoula, P.; Cavouras, D.; Nikiforidis, G.
(2005): Automated Diagnosis of Brain Tumours Astrocytomas Using
Probabilistic Neural Network Clustering and Support Vector Machines,
International Journal of Neural Systems, Vol. 15, No. 1-2, 1-11.
[13] Hamerly, G.; Elkan, C. (2003): Learning the k in k-means, Advances in
Neural Information Processing Systems, Vol. 17.
[14] Hoff, K.E.; Culver, T.; Keyser, J.; Lin, M.; Manocha, D. (1998): Fast
Computation of Generalized Voronoi Diagrams Using Graphics Hardware,
Department of Computer Science, University of North Carolina.
[15] Hruschka, H.; Natter, M. (1999): Comparing Performance of Feedforward
Neural Nets and K-means for Cluster-based Market Segmentation,
European Journal of Operational Research, Vol. 114, No. 2, 346-353.
[16] Kohonen, T. (2001): Self-Organizing Maps, 3rd ed., Springer, Berlin.
[17] Likert, R. (1932): A Technique for the Measurement of Attitudes, Archives
of Psychology, Vol. 140, 1-55.
[18] Mardia, K.V. (1970): Measures of Multivariate Skewness and Kurtosis
with Applications, Biometrika, Vol. 57, 519-530.
[19] Mardia, K.V. (1974): Applications of Some Measures of Multivariate
Skewness and Kurtosis for Testing Normality and Robustness Studies,
Sankhya: Indian Journal of Statistics, Vol. 36, Series B, 115-128.
[20] Marsland, S.; Shapiro, J.; Nehmzow, U. (2002): A Self-Organising
Network that Grows When Required, Neural Networks, Vol. 15, No. 8-
9, 1041-1058.
[21] Martinetz, T.; Schulten, K. (1991): A ÔÇÿNeural Gas- Network Learns
Topologies, in: Kohonen, T.; Maekisara, K.; Simula, O.; Kangas, J.
(Eds.): Artificial Neural Networks, North Holland, Amsterdam, 397-
402.
[22] Mecklin, C.J.; Mundfrom, D.J. (2004): An Appraisal and Bibliography
of Tests for Multivariate Normality, International Statistical Review,
Vol. 72, No. 1, 123-138.
[23] Ozbay, Y.; Ceylan, R.; Karlik, B. (2006): A Fuzzy Clustering Neural
Network Architecture for Classification of ECG Arrhythmias, Computers
in Biology & Medicine, Vol. 36, No. 4, 376-88.
[24] Papastefanou, G.; Schmidt, P.; Börsch-Supan, A.; L├╝dtke, H.; Oltersdorf,
U. (Eds.) (2001): Social Research with Consumer Panel-Data,
GESIS, Mannheim.
[25] Questier, F.; Guo, Q.; Walczak, B.; Massart, D.L.; Boucon, C.; de Jong,
S. (2002): The Neural-Gas Network for Classifying Analytical Data,
Chemometrics and Intelligent Laboratory Systems, Vol. 61, No. 1-2,
105-121.
[26] Sander, J.; Qin, X.; Lu, Z.; Niu, N.; Kovarsky, A. (1999): Automatic
Extraction of Clusters from Hierarchical Clustering Representations,
Working Paper, Department of Computing Science, University of Alberta
Edmonton.
[27] Schwager, S.J. (1985): Testing For Multivariate Normality, in: Kotz, S.;
Johnson, N.L. (Eds.): Encyclopedia of Statistical Sciences, Vol. 6, John
Wiley & Sons, New York, 122.
[28] Solomon, M.R.; Marshall, G.W.; Stuart, E.W. (2005): Marketing - Real
People, Real Choices, 4th ed., Prentice Hall, Upper Saddle River.
[29] Sugar, C.A.; James, G.M. (2003): Finding the Number of Clusters in a
Dataset: An Information-theoretic Approach, Journal of the American
Statistical Society, Vol. 98, No. 463, 750-762.
[30] Wagner, R.; Scholz, S.W.; Decker, R. (2005): The Number of Clusters
in Market Segmentation, in: Baier, D.; Decker, R.; Schmidt-Thieme, L.
(Eds.): Data Analysis and Decision Support, Springer, Berlin, 166-176.
[31] Wedel, M.; Kamakura, W. (2000): Market Segmentation: Conceptual
and Methodological Foundations, 2nd ed., Kluwer Academic Publishers,
Dordrecht.
[32] Wirth, N.; Dietrich, H. (2005): Management of Segmentation Projects,
Yearbook of Marketing and Consumer Research, Vol. 3, 22-36.
[1] Assael, H. (1993): Marketing - Principles and Strategy, 2nd ed., Dryden
Press, Fort Worth.
[2] Atukorale, A.; Suganthan, N. (2000): Hierarchical Overlapped Neural
Gas Network with Application to Pattern Classification, Neurocomputing,
Vol. 35, 165-176.
[3] Berry, M. (Ed.) (2003): Survey of Text Mining: Clustering, Classification,
and Retrieval, Springer, New York.
[4] Bock, T.; Uncles, M. (2002): A Taxonomy of Differences Between
Consumers for Market Segmentation, International Journal of Research
in Marketing, Vol. 19, 215-224.
[5] Boone, D.S.; Roehm, M. (2002): Evaluating the Appropriateness of
Market Segmentation Solutions Using Artificial Neural Networks and
the Membership Clustering Criterion, Marketing Letters, Vol. 13, No. 4,
317-333.
[6] Chu, S.-C.; Roddick, J.F.; Pan, J.-S. (2002): An Incremental Multi-
Centroid, Multi-run Sampling Scheme for k-Medoids-based Algorithms,
Knowledge Discovery and Management Laboratory, Technical Report
KDM-02-003, Flinders University of South Australia.
[7] Daszykowksi, M.; Walczak, B.; Massart, D.L. (2002): On the Optimal
Partitioning of Data with k-means, Growing k-means, Neural Gas, and
Growing Neural Gas, Journal of Chemical Information and Computer
Sciences, Vol. 42, 1378-1389.
[8] Decker, R. (2005): Market Basket Analysis by Means of a Growing
Neural Network, International Review of Retail, Distribution and Consumer
Research, Vol. 15, No. 2, 151-169.
[9] Decker, R.; Monien, K. (2003): Market Basket Analysis with Neural
Gas Networks and Self-organizing Maps, Journal of Targeting, Measurement
and Analysis for Marketing, Vol. 11, No. 4, 373-386.
[10] Dittenbach, M.; Rauber, A.; Merkl, D. (2002): Uncovering Hierarchical
Structure in Data Using the Growing Hierarchical Self-organizing Map,
Neurocomputing, Vol. 48, 199-216.
[11] Fritzke, B. (1995): A Growing Neural Gas Network Learns Topologies,
in: Tesauro, G.; Touretzky, D.S.; Leen, T.K. (Eds.): Advances in Neural
Information Processing Systems 7, MIT Press, 625-632.
[12] Glotsos, D.; Tohka, J.; Ravazoula, P.; Cavouras, D.; Nikiforidis, G.
(2005): Automated Diagnosis of Brain Tumours Astrocytomas Using
Probabilistic Neural Network Clustering and Support Vector Machines,
International Journal of Neural Systems, Vol. 15, No. 1-2, 1-11.
[13] Hamerly, G.; Elkan, C. (2003): Learning the k in k-means, Advances in
Neural Information Processing Systems, Vol. 17.
[14] Hoff, K.E.; Culver, T.; Keyser, J.; Lin, M.; Manocha, D. (1998): Fast
Computation of Generalized Voronoi Diagrams Using Graphics Hardware,
Department of Computer Science, University of North Carolina.
[15] Hruschka, H.; Natter, M. (1999): Comparing Performance of Feedforward
Neural Nets and K-means for Cluster-based Market Segmentation,
European Journal of Operational Research, Vol. 114, No. 2, 346-353.
[16] Kohonen, T. (2001): Self-Organizing Maps, 3rd ed., Springer, Berlin.
[17] Likert, R. (1932): A Technique for the Measurement of Attitudes, Archives
of Psychology, Vol. 140, 1-55.
[18] Mardia, K.V. (1970): Measures of Multivariate Skewness and Kurtosis
with Applications, Biometrika, Vol. 57, 519-530.
[19] Mardia, K.V. (1974): Applications of Some Measures of Multivariate
Skewness and Kurtosis for Testing Normality and Robustness Studies,
Sankhya: Indian Journal of Statistics, Vol. 36, Series B, 115-128.
[20] Marsland, S.; Shapiro, J.; Nehmzow, U. (2002): A Self-Organising
Network that Grows When Required, Neural Networks, Vol. 15, No. 8-
9, 1041-1058.
[21] Martinetz, T.; Schulten, K. (1991): A ÔÇÿNeural Gas- Network Learns
Topologies, in: Kohonen, T.; Maekisara, K.; Simula, O.; Kangas, J.
(Eds.): Artificial Neural Networks, North Holland, Amsterdam, 397-
402.
[22] Mecklin, C.J.; Mundfrom, D.J. (2004): An Appraisal and Bibliography
of Tests for Multivariate Normality, International Statistical Review,
Vol. 72, No. 1, 123-138.
[23] Ozbay, Y.; Ceylan, R.; Karlik, B. (2006): A Fuzzy Clustering Neural
Network Architecture for Classification of ECG Arrhythmias, Computers
in Biology & Medicine, Vol. 36, No. 4, 376-88.
[24] Papastefanou, G.; Schmidt, P.; Börsch-Supan, A.; L├╝dtke, H.; Oltersdorf,
U. (Eds.) (2001): Social Research with Consumer Panel-Data,
GESIS, Mannheim.
[25] Questier, F.; Guo, Q.; Walczak, B.; Massart, D.L.; Boucon, C.; de Jong,
S. (2002): The Neural-Gas Network for Classifying Analytical Data,
Chemometrics and Intelligent Laboratory Systems, Vol. 61, No. 1-2,
105-121.
[26] Sander, J.; Qin, X.; Lu, Z.; Niu, N.; Kovarsky, A. (1999): Automatic
Extraction of Clusters from Hierarchical Clustering Representations,
Working Paper, Department of Computing Science, University of Alberta
Edmonton.
[27] Schwager, S.J. (1985): Testing For Multivariate Normality, in: Kotz, S.;
Johnson, N.L. (Eds.): Encyclopedia of Statistical Sciences, Vol. 6, John
Wiley & Sons, New York, 122.
[28] Solomon, M.R.; Marshall, G.W.; Stuart, E.W. (2005): Marketing - Real
People, Real Choices, 4th ed., Prentice Hall, Upper Saddle River.
[29] Sugar, C.A.; James, G.M. (2003): Finding the Number of Clusters in a
Dataset: An Information-theoretic Approach, Journal of the American
Statistical Society, Vol. 98, No. 463, 750-762.
[30] Wagner, R.; Scholz, S.W.; Decker, R. (2005): The Number of Clusters
in Market Segmentation, in: Baier, D.; Decker, R.; Schmidt-Thieme, L.
(Eds.): Data Analysis and Decision Support, Springer, Berlin, 166-176.
[31] Wedel, M.; Kamakura, W. (2000): Market Segmentation: Conceptual
and Methodological Foundations, 2nd ed., Kluwer Academic Publishers,
Dordrecht.
[32] Wirth, N.; Dietrich, H. (2005): Management of Segmentation Projects,
Yearbook of Marketing and Consumer Research, Vol. 3, 22-36.
@article{"International Journal of Business, Human and Social Sciences:62884", author = "Reinhold Decker and Christian Holsing and Sascha Lerke", title = "Generating Normally Distributed Clusters by Means of a Self-organizing Growing Neural Network– An Application to Market Segmentation –", abstract = "This paper presents a new growing neural network for
cluster analysis and market segmentation, which optimizes the size
and structure of clusters by iteratively checking them for multivariate
normality. We combine the recently published SGNN approach [8]
with the basic principle underlying the Gaussian-means algorithm
[13] and the Mardia test for multivariate normality [18, 19]. The new
approach distinguishes from existing ones by its holistic design and
its great autonomy regarding the clustering process as a whole. Its
performance is demonstrated by means of synthetic 2D data and by
real lifestyle survey data usable for market segmentation.", keywords = "Artificial neural network, clustering, multivariatenormality, market segmentation, self-organization", volume = "2", number = "2", pages = "137-7", }
