Download PDF by Ella Bingham, Samuel Kaski, Jorma Laaksonen, Jouko Lampinen: Advances in Independent Component Analysis and Learning

By Ella Bingham, Samuel Kaski, Jorma Laaksonen, Jouko Lampinen

ISBN-10: 0128028068

ISBN-13: 9780128028063

In honour of Professor Erkki Oja, one of many pioneers of self reliant part research (ICA), this e-book reports key advances within the concept and alertness of ICA, in addition to its impression on sign processing, development attractiveness, computer studying, and information mining.

Examples of themes that have constructed from the advances of ICA, that are lined within the e-book are:

  • A unifying probabilistic version for PCA and ICA
  • Optimization equipment for matrix decompositions
  • Insights into the FastICA algorithm
  • Unsupervised deep studying
  • Machine imaginative and prescient and snapshot retrieval
  • A assessment of advancements within the idea and purposes of self sufficient part research, and its impact in very important components comparable to statistical sign processing, development attractiveness and deep learning.
  • A diversified set of program fields, starting from computing device imaginative and prescient to technology coverage data.
  • Contributions from prime researchers within the field.

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Additional info for Advances in Independent Component Analysis and Learning Machines

Sample text

6 Numerical evaluations 0 Theory [Eq. 3 Evolutions of inter-channel interference from predictions and simulations for mixtures of three uniformly-distributed independent sources. computed from Eq. 60). As can be seen, the “(1/3)rd Rule” is accurate in describing the initial convergence performance of the FastICA algorithm in this case. Note that the averaged value of E{ICIt } reaches a limiting value due to finite data block size of N = 10,000 in the algorithm, and thus there is no additional faster-than-linear convergence regime observed in practice.

75) reduced to the expression in Eq. 72) for the three-dimensional case. 2. 31 times larger than the maximum ICI in the two-source case with κ1 = κ2 . Again, these results support the “(1/3)rd Rule” described earlier. 5 GENERAL m-SOURCE CASE We now provide an analysis of the average ICI of the FastICA algorithm for general m-source mixtures assuming arbitrary kurtosis values. 78) where p = 2(3t ) and q = 3t − 1. The following theorem provides a bounded expression for the average ICI in this case.

Of ICIt is highly skewed toward zero, indicating fast convergence of the ICI. Moreover, if limu→1− p0 (u) = 0, then convergence is clearly faster than linear. 3 The average value of the ICI Our attention now turns to the average ICI of the FastICA algorithm, denoted as E{ICIt }, for a two-source mixture with equal-kurtosis sources. From our previous derivations, it is clear that we require a distribution for the initial value of θt , denoted as θ0 , to obtain an exact result. f. of ICIt observed in the previous subsection, however, suggests that we may be able to obtain a relationship between p0 (u) and E{ICIt } in more general circumstances.

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Advances in Independent Component Analysis and Learning Machines by Ella Bingham, Samuel Kaski, Jorma Laaksonen, Jouko Lampinen


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