Soft vector quantization and the EM algorithm

The relation between hard c-means (HCM), fuzzy c-means (FCM), fuzzy learning vector quantization (FLVQ), soft competition scheme (SCS) of Yair et al. (1992) and probabilistic Gaussian mixtures (GM) have been pointed out recently by Bezdek and Pal (1995). We extend this relation to their training, showing that learning rules by these models to estimate the cluster centers can be seen as approximations to the expectation–maximization (EM) method as applied to Gaussian mixtures. HCM and unsupervised, LVQ use 1-of-c type competition. In FCM and FLVQ, membership is the ¹2/(m ¹ 1)th power of the distance. In SCS and GM, Gaussian function is used. If the Gaussian membership function is used, the weighted within-groups sum of squared errors used as the fuzzy objective function corresponds to the maximum likelihood estimate in Gaussian mixtures with equal priors and covariances. The fuzzy clustering method named fuzzy c-means alternating optimization procedure (FCM-AO) proposed to optimize...

• Type: Journal
• Year: 1998
• Where: NN
• Authors: Ethem Alpaydin
• Keywords: Gaussian, Gaussian Mixtures, Neural Networks, NN 1998, Vector Quantization