## Multiple Alignment of Continuous Time Series

**Jennifer Listgarten,
Radford M. Neal,
Sam T. Roweis,
Andrew Emili
**
Multiple realizations of continuous-valued time series from a
stochastic process often contain systematic variations in rate and
amplitude. To leverage the information contained in such noisy
replicate sets, we need to align them in an appropriate way (for
example, to allow the data to be properly combined by adaptive
averaging). We present the Continuous Profile Model (CPM), a
generative model in which each observed time series is a non-uniformly
subsampled version of a single latent trace, to which local rescaling
and additive noise are applied. After unsupervised training, the
learned trace represents a canonical, high resolution fusion of all
the replicates. As well, an alignment in time and scale of each
observation to this trace can be found by inference in the model. We
apply CPM to successfully align speech signals from multiple speakers
and sets of Liquid Chromatography - Mass Spectrometry (LC-MS)
proteomic data.

In L. K. Saul, et al (editors),
*Advances in Neural Information Processing Systems 17*
(aka NIPS*2004), MIT Press, 8 pages:
postscript,
pdf.

Also available via the NIPS site