### Abstract

This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from unknown continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between distributions). The maximum intracluster distance is assumed to be smaller than the minimum intercluster distance, and both values are assumed to be known. The goal is to group the data sequences together if their underlying generative distributions (which are unknown) belong to one cluster. Distribution distance metrics based k-medoids algorithms are proposed for known and unknown number of distribution clusters. Upper bounds on the error probability and convergence results in the large sample regime are also provided. It is shown that the error probability decays exponentially fast as the number of samples in each data sequence goes to infinity. The error exponent has a simple form regardless of the distance metric applied when certain conditions are satisfied. In particular, the error exponent is characterized when either the Kolmogrov-Smirnov distance or the maximum mean discrepancy are used as the distance metric. Simulation results are provided to validate the analysis.

Original language | English (US) |
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Article number | 8651294 |

Pages (from-to) | 2093-2106 |

Number of pages | 14 |

Journal | IEEE Transactions on Signal Processing |

Volume | 67 |

Issue number | 8 |

DOIs | |

State | Published - Apr 15 2019 |

### Keywords

- composite distributions
- error probability
- k-medoids clustering
- Kolmogorov-Smirnov distance
- maximum mean discrepancy
- unsupervised learning

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Signal Processing*,

*67*(8), 2093-2106. [8651294]. https://doi.org/10.1109/TSP.2019.2901370