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Dynamic Clustering Algorithms via Small-Variance Analysis of Markov Chain Mixture Models
Name
1707.08493.pdf
Description
Submitted version
Size
6.18 MB
Format
Adobe PDF
Checksum (MD5)
73e7783b356bccffeba1bdb43f06564f
Author(s)
Campbell, Trevor
Kulis, Brian
How, Jonathan
Date Issued
2019
Journal
IEEE Transactions on Pattern Analysis and Machine Intelligence
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
© 1979-2012 IEEE. Bayesian nonparametrics are a class of probabilistic models in which the model size is inferred from data. A recently developed methodology in this field is small-variance asymptotic analysis, a mathematical technique for deriving learning algorithms that capture much of the flexibility of Bayesian nonparametric inference algorithms, but are simpler to implement and less computationally expensive. Past work on small-variance analysis of Bayesian nonparametric inference algorithms has exclusively considered batch models trained on a single, static dataset, which are incapable of capturing time evolution in the latent structure of the data. This work presents a small-variance analysis of the maximum a posteriori filtering problem for a temporally varying mixture model with a Markov dependence structure, which captures temporally evolving clusters within a dataset. Two clustering algorithms result from the analysis: D-Means, an iterative clustering algorithm for linearly separable, spherical clusters; and SD-Means, a spectral clustering algorithm derived from a kernelized, relaxed version of the clustering problem. Empirical results from experiments demonstrate the advantages of using D-Means and SD-Means over contemporary clustering algorithms, in terms of both computational cost and clustering accuracy.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1109/TPAMI.2018.2833467
