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 sufficient part research (ICA), this booklet studies key advances within the thought and alertness of ICA, in addition to its effect on sign processing, development attractiveness, laptop studying, and information mining.

Examples of themes that have built from the advances of ICA, that are coated within the publication 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 overview of advancements within the idea and functions of self sustaining part research, and its effect in very important components similar to statistical sign processing, trend attractiveness and deep learning.
  • A assorted set of program fields, starting from desktop imaginative and prescient to technology coverage data.
  • Contributions from best researchers within the field.

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Extra info for Advances in Independent Component Analysis and Learning Machines

Sample text

F. f. of the inter-channel interference for mixtures of two uniformly-distributed independent sources. d. Unif(− 3, 3) sources with a block size of N = 10,000. As can be seen, the theoretical expressions accurately match the histograms from the simulation results. f. rapidly converges to that in Eq. 49), again showing a (1/3)t decrease almost everywhere except near the origin (not depicted). 7 CONCLUSION In this chapter, we have analyzed the average initial convergence rate of the FastICA algorithm for the case of a cubic nonlinearity as applied to noiseless linear mixtures of independent sources.

17). Given that we have an exact expression for E{ICIt } under a particular initial condition, it is interesting to see how accurate the approximate expression for the ICI in Eq. 53) is. For a uniformly distributed look direction for w0 or c0 in angular space, it is straightforward to show by setting u = 1 in Eq. 122) that K = 1/π , such that Eq. 53) predicts an average ICI at iteration t of approximately E{ICIt } ≈ 1 π 1 3 t . 60) Numerical evaluation of Eq. 60) indicates that it is quite accurate in predicting the value of E{ICIt } in Eq.

2 PRELIMINARIES Our analysis of the average value of the ICI for the FastICA algorithm is performed in a coefficient-stochastic setting, in which 1. the number of measurements used to compute the averages in Eq. 18) is infinite, so that the evolutionary behavior described by the update in Eq. 30) is an accurate description of the FastICA algorithm given an initial combined system coefficient vector c0 ; and 2. the initial vector c0 possesses some distribution on the unit hypersphere, and thus the average performance of the algorithm depends on how this initial condition affects the evolution of the ICI performance measure in Eq.

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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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