A new proximity aware similarity metric for contiguous clustering for segmenting signals

There are various motivations to cluster a set of signals. The common time-series clustering problem is, (1) where the features over the signal time-span of the members, belonging to the same cluster, are same. In other words, the model generating them are same. The other problem could be (2) to divide every member of a multivariate signal into fragments within which individual signals exhibit similar features, which vary from one partition to other. The properties may differ from one signal to other, but the boundaries of the partitions are same. We propose an algorithm to solve problem (2). There are algorithms to divide a single time-series into K segments such that the generating parameters (like regression coefficients) are same for individual segments. It is a complex problem to find the optimum boundaries for K segments and modeling parameters for each segment, minimizing the error. In this work, our target is to segment signals based on features extracted at discrete points in time. Simple clustering algorithms assign same cluster labels based on some similarity measure between feature-vectors, irrespective of their contiguity. As a result, members of a cluster, in general, will be scattered over the time-span of the signal. Members of the same cluster will not be contiguous. To achieve individual clusters to be contiguous, neighboring samples are to be assigned to the same cluster with higher probability, than a sample at further distance, though with similar feature. In our algorithm, similarity measure includes contiguity information of samples from their original physical space. The algorithm consists of calculating the modified similarity metric, and two layers of clustering. The complexity is similar to simple clustering algorithm and therefore it is fast. We applied the algorithm for clustering multivariate EEG signals. The stability of the result over different samples verify the reliability of the algorithm.