Clustering construction on a multimodal probability model

In 2009, Yu et al. proposed a multimodal probability model (MPM) for clustering. This paper makes advanced clustering constructions on the MPM. We first reconstruct most existing clustering algorithms, such as the k-means, fuzzy c-means, possibilistic c-means, mean shift, classification maximum likelihood, and latent class methods, by establishing the relationships between these clustering algorithms and the MPM. Under our clustering construction, we find that the MPM can be seen as a basic probability model for most existing clustering algorithms. We then construct new clustering frameworks based on the MPM. One of the frameworks develops new penalized-type clustering algorithms. Another one induces entropy-type clustering algorithms, especially with sample-weighted clustering. Several numerical and real data sets are made for comparisons. These experimental results show that our clustering constructions based on the MPM can produce useful and effective clustering algorithms.