  We consider the problem of clustering noisy finite-length 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 (KM),
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.
