The model of generalized partially horizontal collaborative fuzzy C-means

Horizontal collaborative clustering is such a clustering method that carries clustering on a pattern set described in one feature space with collaborative introducing outer clustering information obtained by clustering the same pattern set but described in some other different feature spaces. For the sake of privacy-preserving, the outer clustering information is usually provided by the outer partition matrixes instead of the data sets themselves. In order to implement the horizontal collaborative clustering, horizontal collaborative fuzzy C-Means (HC-FCM) was proposed by W. Pedrycz. In HC-FCM, the outer partition matrixes are incorporated with the objective function of standard FCM. The processing manner of HC-FCM emphasizes on the use of total collaborative clustering information provided by the outer partition matrixes, thus HC-FCM can be called completely horizontal collaborative fuzzy c-means (CHC-FCM). But in reality, on many occasions of collaborative clustering, we may be interested only in the cluster information provided by some special patterns, say the patterns with distinct membership relation for example. To deal with such kind of clustering problems, our previous work gave the partially horizontal collaborative fuzzy c-means (PHC-FCM) which deals with such horizontal collaborative clustering as there is only one outer partition matrix. In this paper, we will present the generalized partially horizontal collaborative fuzzy c-means (GPHC-FCM) where the clustering is supervised by some groups of labeled patterns selected in terms of the corresponding outer partition matrixes.