A Fuzzy Clustering Algorithm For Asynchronously Sampled Data

Clustering is the assignment of objects into groups (called clusters) so that objects from the same cluster are more similar to each other than objects from different clusters. Often similarity is assessed according to a distance measure. Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics.The clustering problem of asynchronously sampled data was considered. Conventional clustering algorithms, such as the k-means algorithms, the fuzzy c-means algorithms, the Gutstafson-Kessel algorithm, etc., all require that each observation contains the same number of features. These algorithms cannot be directly applied to asynchronously sampled observations, of which the feature vectors have different number of elements. The traditional approach is to first interpolate the asynchronously sampled observations into synchronous observations, and then cluster the observations with the above mentioned algorithms. But this approach gives poor result. In this paper, we introduced the concepts of the fuzzy neighborhood and the fuzzy distance norms of asynchronously sampled observations. Based on the concepts, we revised the standard FCM algorithm to allow it directly cluster asynchronously sampled data. We call the new algorithm the F2CM algorithm because it is a fuzzy c-means clustering algorithm base on fuzzy distance norms between asynchronous observations. The paper also revised various performance indices for the F2CM algorithm. Through some examples, it was shown that the F2CM algorithm obtained much superior result than the traditional approaches did.