Abstract
When using topographic maps for clustering purposes, which is now being considered in the data mining community, it is crucial that the maps are free of topological defects. Otherwise, a contiguous cluster could become split into separate clusters. We introduce a new algorithm for monitoring the degree of topology preservation of kernel-based maps during learning. The algorithm is applied to a real-world example concerned with the identification of 3 musical instruments and the notes played by them, in an unsupervised manner, by means of a hierarchical clustering analysis, starting from the music signal's spectrogram.
Similar content being viewed by others
References
H. Ritter, T. Martinetz, and K. Schulten, Neural Computation and Self-Organizing Maps: An Introduction, Reading, MA: Addison-Wesley, 1992.
T. Kohonen, Self-Organizing Maps, Heidelberg: Springer, 1995.
M.M. Van Hulle, Faithful Representations and Topographic Maps: From Distortion-to Information-Based Self-Organization, New York: Wiley, 2000.
G.J. Deboeck and T. Kohonen, Visual Explorations in Finance with Self-Organizing Maps, Heidelberg: Springer, 1998.
M. Cottrell, P. Gaubert, P. Letremy, and P. Rousset, “Analyzing and Representing Multidimensional Quantitative and Qualitative Data: Demographic Study of the Rhône Valley. The Domestic Consumption of the Canadian Families,” in Kohonen Maps, Proc. WSOM99, Helsinki, E. Oja and S. Kaski (Eds.), 1999, pp. 1-14.
K. Lagus and S. Kaski, “Keyword Selection Method for Characterizing Text Document Maps,” in Proc. ICANN99, 9th Int. Conf. on Artificial Neural Networks, IEE: London, vol. 1, 1999, pp. 371-376.
T. Kohonen, “Self-Organized Formation of Topologically Correct Feature Maps,” Biol. Cybern., vol. 43, 1982, pp. 59-69.
T. Kohonen, Self-Organization and Associative Memory, Heidelberg: Springer, 1984.
M. Cottrell and J.C. Fort, “Etude d'un processus d'auto-organization,” Ann. Inst. Henri Poincaré, vol. 23, 1987, pp. 1-20.
E. Erwin, K. Obermayer, and K. Schulten, “Self-Organizing Maps: Ordering, Convergence Properties and Energy Functions,” Biol. Cybern., vol. 67, 1992, pp. 47-55.
T. Geszti, Physical Models of Neural Networks, Singapore: World Scientific Press, 1990.
H. Ritter, “Asymptotic Level Density for a Class of Vector Quantization Processes,” IEEE Trans. Neural Networks, vol. 2,no. 1, 1991, pp. 173-175.
D.R. Dersch and P. Tavan, “Asymptotic Level Density in Topological Feature Maps,” IEEE Trans. Neural Networks, vol. 6, 1995, pp. 230-236.
H.-U. Bauer and K.R. Pawelzik, “Quantifying the Neighborhood Preservation of Self-Organizing Feature Maps,” IEEE Trans. Neural Networks, vol. 3, 1992, pp. 570-579.
T. Villmann, R. Der, M. Herrmann, and T.M. Martinetz, “Topology Preservation in Self-Organizing Feature Maps: Exact Definition and Measurement,” IEEE Trans. Neural Networks, vol. 8,no 2, 1997, pp. 256-266.
T. Graepel, M. Burger, and K. Obermayer, “Phase Transitions in Stochastic Self-Organizing Maps,” Physical Rev. E, vol. 56,no. 4, 1997, pp. 3876-3890.
J. Sum, C.-S. Leung, L.-W. Chan, and L. Xu, “Yet Another Algorithm which can Generate Topography Map,” IEEE Trans. Neural Networks, vol. 8,no. 5, 1997, pp. 1204-1207.
C.M. Bishop, M. Svensén, and C.K.I. Williams, “GTM: The Generative Topographic Mapping,” Neural Computat., vol. 10, 1998, pp. 215-234.
M.M. Van Hulle, “Kernel-Based Equiprobabilistic Topographic Map Formation,” Neural Computat., vol. 10,no. 7, 1998, pp. 1847-1871.
J.J. Koenderink, “Simultaneous Order in Nervous Nets from A Functional Standpoint,” Biol. Cybern., vol. 50, 1984, pp. 35-41.
V.T. Ruoppila, T. Sorsa, and H.N. Koivo, “Recursive Least-Squares Approach to Self-Organizing Maps,” in Proc. IEEE Int. Conf. on Neural Networks, San Francisco, 1993, pp. 1480-1485.
T. Hastie and W. Stuetzle, “Principal Curves,” J. Am. Statist. Assoc., vol. 84, 1989, pp. 502-516.
S.P. Luttrell, “Derivation of a Class of Training Algorithms,” IEEE Trans. Neural Networks, vol. 1, 1990, pp. 229-232.
B.W. Silverman, Density Estimation for Statistics and Data Analysis, London: Chapman and Hall, 1992.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Van Hulle, M.M., Gautama, T. Monitoring the Formation of Kernel-Based Topographic Maps with Application to Hierarchical Clustering of Music Signals. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 32, 119–134 (2002). https://doi.org/10.1023/A:1016323603757
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1016323603757