Integration and generalization of LVQ and c-means clustering (Invited Paper)

James C. Bezdek

doi:10.1117/12.131608

1 November 1992 Integration and generalization of LVQ and c-means clustering (Invited Paper)

James C. Bezdek

Proceedings Volume 1826, Intelligent Robots and Computer Vision XI: Biological, Neural Net, and 3D Methods; (1992) https://doi.org/10.1117/12.131608
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

This paper discusses the relationship between the sequential hard c-means (SHCM), learning vector quantization (LVQ), and fuzzy c-means (FCM) clustering algorithms. LVQ and SHCM suffer from several major problems. For example, they depend heavily on initialization. If the initial values of the cluster centers are outside the convex hull of the input data, such algorithms, even if they terminate, may not produce meaningful results in terms of prototypes for cluster representation. This is due in part to the fact that they update only the winning prototype for every input vector. We also discuss the impact and interaction of these two families with Kohonen's self-organizing feature mapping (SOFM), which is not a clustering method, but which often lends itself to clustering algorithms. Then we present two generalizations of LVQ that are explicitly designed as clustering algorithms: we refer to these algorithms as generalized LVQ equals GLVQ; and fuzzy LVQ equals FLVQ. Learning rules are derived to optimize an objective function whose goal is to produce 'good clusters'. GLVQ/FLVQ (may) update every node in the clustering net for each input vector. We use Anderson's IRIS data to compare the performance of GLVQ/FLVQ with a standard version of LVQ. Experiments show that the final centroids produced by GLVQ are independent of node initialization and learning coefficients. Neither GLVQ nor FLVQ depends upon a choice for the update neighborhood or learning rate distribution--these are taken care of automatically.

Citation Download Citation

James C. Bezdek "Integration and generalization of LVQ and c-means clustering (Invited Paper)", Proc. SPIE 1826, Intelligent Robots and Computer Vision XI: Biological, Neural Net, and 3D Methods, (1 November 1992); https://doi.org/10.1117/12.131608

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