GPclust

Clustering time series using Gaussian processes and variational Bayes.

User guide and tutorials are available via the included notebooks.

Currently implemented models are

• MOG - Mixture of Gaussians
• MOHGP - Mixtures of Hierarchical Gaussian processes
• OMGP - Overlapping mixtures of Gaussian processes

Citation

The underlying algorithm is based on the 2012 NIPS paper:

http://books.nips.cc/papers/files/nips25/NIPS2012_1314.pdf

@article{hensman2012fast,
  title={Fast variational inference in the conjugate exponential family},
  author={Hensman, James and Rattray, Magnus and Lawrence, Neil D},
  journal={Advances in Neural Information Processing Systems},
  year={2012}
}

The code also implements clustering of Hierachical Gaussian Processes using that inference framework, detailed in the two following works:

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6802369

@article{hensman2014fast,
  author={Hensman, J. and Rattray, M. and Lawrence, N.},
  journal={Pattern Analysis and Machine Intelligence, IEEE Transactions on},
  title={Fast nonparametric clustering of structured time-series},
  year={2014},
  volume={PP},
  number={99},
  keywords={Biological system modeling;Computational modeling;Data models;Gaussian processes;Optimization;Time series analysis},
  doi={10.1109/TPAMI.2014.2318711},
  ISSN={0162-8828}
}

http://www.biomedcentral.com/1471-2105/14/252

@article{hensman2013hierarchical,
  title={Hierarchical Bayesian modelling of gene expression time series across irregularly sampled replicates and clusters},
  author={Hensman, James and Lawrence, Neil D and Rattray, Magnus},
  journal={BMC bioinformatics},
  volume={14},
  number={1},
  pages={1--12},
  year={2013},
  publisher={BioMed Central}
}

Additionally Overlapping Mixtures of Gaussian Processes model is implemented (using the variational methods described in the above), which was published in this paper:

@article{Lazaro-Gredilla2012,
  title = {{Overlapping Mixtures of Gaussian Processes for the data association problem}},
  author = {L{\'{a}}zaro-Gredilla, Miguel and {Van Vaerenbergh}, Steven and Lawrence, Neil D.},
  doi = {10.1016/j.patcog.2011.10.004},
  journal = {Pattern Recognition},
  month = {apr},
  number = {4},
  pages = {1386--1395},
  url = {},
  volume = {45},
  year = {2012}
}

Dependencies

This work depends on the GPy project, as well as the numpy/scipy stack. matplotlib is optional for plotting.

I've tested the demos with GPy v0.8, but it should work with later versions also.

Contributors

• James Hensman
• Valentine Svensson
• Max Zwiessele