By William D. Penny, Richard M. Everson, Stephen J. Roberts (auth.), Mark Girolami BSc (Hons), BA, MSc, PhD, CEng, MIEE, MIMechE (eds.)

Independent part research (ICA) is a quick constructing quarter of severe learn curiosity. Following on from Self-Organising Neural Networks: self sustaining part research and Blind sign Separation, this ebook experiences the numerous advancements of the prior year.

It covers subject matters similar to using hidden Markov equipment, the independence assumption, and topographic ICA, and comprises instructional chapters on Bayesian and variational methods. It additionally offers the most recent methods to ICA difficulties, together with an research into sure "hard difficulties" for the first actual time.

Comprising contributions from the main revered and cutting edge researchers within the box, this quantity can be of curiosity to scholars and researchers in laptop technological know-how and electric engineering; examine and improvement group of workers in disciplines resembling statistical modelling and information research; bio-informatic employees; and physicists and chemists requiring novel info research methods.

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**Extra resources for Advances in Independent Component Analysis**

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The next two traces show partitionings from an HMICA model; the top one using GAR sources and the bottom one using GE sources. The dashed vertical line indicates a cue telling the subject when to begin hand movement. 5. We also applied the HMICA model to EEG data recorded whilst a subject performed a motor imagery task; the subject was instructed to imagine opening and closing his hand in response to an external cue. 9 shows the EEG data and the resulting partitioning from two HMlCA models. This again demonstrates that the HMlCA model can partition time series into meaningful stationary regimes and that GAR source models may often be more appropriate than GE source models.

5. The almost complete overlap of true and estimated probability contours shows that Rand f3 are estimated very accurately. This accuracy is due to the correct partitioning of the data into the two separate epochs; application of the Viterbi algorithm led to 100% of samples being correctly classified. Experimentation with initialisation of the state transition matrix showed that convergence was typically achieved in five to ten EM iterations with DB ranging from 10 to 400 samples. Convergence was even possible with DB as low as three, after 10 to 20 EM iterations.

1 Hidden Markov ICA 13 and N = 200 samples were generated in this way. The quality of the unmixing was measured by the unmixing error E - . 30) IIWVII where W is our estimated unmixing matrix and P is a permutation matrix [9]. The variance of the source noise was then set so as to achieve a certain Signal-to-Noise Ratio (SNR), which was the same for both sources. 1 shows the unmixing errors for the two methods over a range of SNRs. 1. Comparison of GE and GAR source models. Unmixing errors, E, for Generalised Exponential (GE) and Generalised Autoregressive (GAR) source models on mUltiple sine wave sources.