Robust Nonparametric Nearest Neighbor Random Process Clustering

被引:3
|
作者
Tschannen, Michael [1 ]
Bolcskei, Helmut [1 ]
机构
[1] ETH, Dept Informat Technol & Elect Engn, CH-8092 Zurich, Switzerland
关键词
Clustering; stationary random processes; time series; nonparametric; k-means; nearest neighbors; TIME-SERIES; CLASSIFICATION; ALGORITHM;
D O I
10.1109/TSP.2017.2736513
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
We consider the problem of clustering noisy finitelength observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the L-1-distance between estimated power spectral densities (PSDs) as a measure of dissimilarity, are analyzed. The first one, termed nearest neighbor process clustering (NNPC), relies on partitioning the nearest neighbor graph of the observations via spectral clustering. The second algorithm, simply referred to as k-means, consists of a single k-means iteration with farthest point initialization and was considered before in the literature, albeit with a different dissimilarity measure. We prove that both algorithms succeed with high probability in the presence of noise and missing entries, and even when the generative process PSDs overlap significantly, all provided that the observation length is sufficiently large. Our results quantify the tradeoff between the overlap of the generative process PSDs, the observation length, the fraction of missing entries, and the noise variance. Finally, we provide extensive numerical results for synthetic and real data and find that NNPC outperforms state-of-the-art algorithms in human motion sequence clustering.
引用
收藏
页码:6009 / 6023
页数:15
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