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Structured and Complex Data
Data with structure or complexities beyond the textbook require special treatment.
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time series FuncICA for Time Series Pattern Discovery
Nishant Mehta and Alexander Gray
SIAM International Conference on Data Mining (SDM) 2009

An Independent Component Analysis (ICA) for data where each point is a function, such as a time series. [pdf]

Abstract: We introduce FuncICA, a new independent component analysis method for pattern discovery in inherently functional data, such as time series data. FuncICA can be considered an analog to functional principal component analysis, where instead of extracting components to minimize L2 reconstruction error, we maximize independence of the components over the functional observations. We develop an algorithm for extracting independent component curves and offer a method for optimizing a smoothing parameter. Results for synthetic, gene expression, and event-related potential data indicate that FuncICA can recover well-known phenomena and improve classification accuracy, highlighting the utility of FuncICA for unsupervised learning in temporal data.

@Inproceedings{mehta2009funcica, Author = "Nishant Mehta and Alexander Gray", Title = "{FuncICA for Time Series Pattern Discovery}", Booktitle = "{SIAM International Conference on Data Mining (SDM)}, Year = "2009" }
See also

Kernels for Structured Data
We have developed new kernels for probability distributions, which can be used for structured data via modeling them using hidden Markov models, for example. [see webpage here]

In preparation

Fast Hidden Markov Model Learning
A new approach to learning HMMs, which is very efficient for massive time series.