Read e-book online Advances in Independent Component Analysis and Learning PDF

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 autonomous part research (ICA), this publication studies key advances within the idea and alertness of ICA, in addition to its effect on sign processing, development reputation, desktop studying, and information mining.

Examples of themes that have constructed from the advances of ICA, that are lined within the ebook 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 evaluation of advancements within the conception and functions of self sufficient part research, and its impact in very important components corresponding to statistical sign processing, trend popularity and deep learning.
  • A assorted set of software fields, starting from laptop imaginative and prescient to technology coverage data.
  • Contributions from top researchers within the field.

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Extra resources for Advances in Independent Component Analysis and Learning Machines

Example text

2(m−2)/2 m 2 j=1,j=n,j=i xj m/2 m/2 m is odd m is even 45 46 CHAPTER 1 The initial convergence rate of the FastICA algorithm for n = 2, . . , m and κn . 194) n=1 t 1 3 ≈ g(κ1 , . . 195) where g(κ1 , . . , κm ) ⎧ 2m−1 ⎪ ⎪ m/2 ⎪ ⎪ ⎨ (2π) = ⎪ ⎪ ⎪ 2m−1 ⎪ ⎩ (2π)m/2 m m n=1 i=1,i=n m m n=1 i=1,i=n bn1 0 dx1 · · · bnm 0 dxm √ bn1 0 dx1 · · · bnm 0 dxm √ (m−2)!! 2(m−2)/2 m 2 j=1,j=n,j=i xj 1+(bni )2 + m/2 m 2 j=1,j=n,j=i xj m is odd m is even. m/2 The errors have been introduced in both Eqs. 192). We first estimate the error in Eq.

33). 31 32 CHAPTER 1 The initial convergence rate of the FastICA algorithm To determine the local stability of Eq. 32) about the solutions defined in Eq. 33), define the perturbed coefficient values |ci | = ci,s + it where ci,s = |ci,s | in Eq. 33) and J is any valid subset of the elements of I . Because of the unit-norm constraint in Eq. 28), we only need to consider perturbations { i } that are tangent or orthogonal to cs , such that m cs,j j = 0. 102) j=1 Furthermore, assume that each | i | 1.

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.

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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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