A Fuzzy Clustering Algorithm Based on Fuzzy Distance Norms for Asynchronously Sampled Data

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 can not be directly applied to asynchronously sampled observations, of which the feature vectors have different number of elements. The traditional approach to this problem 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. And using the ideas, 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 based on fuzzy distance norms between asynchronous observations. Through some examples, it was shown that the F2CM algorithm gave much superior result than the traditional approaches.