Mathematics in Independent Component Analysis

112 Chapter 5. IEICE TF E87-A(9):2355-2363, 2004
THEIS and NAKAMURA: QUADRATIC INDEPENDENT COMPONENT ANALYSIS
−0.17 0.16 −0.25 0.08 0.16 −0.11 0.28 −0.10 0.19 −0.13 −0.24 0.23
−0.20 0.12 −0.27 0.27 0.19 −0.16 −0.17 0.16 −0.30 0.09 0.38 0.05
−0.19 0.17 0.18 −0.12 −0.24 0.24 −0.22 0.22 −0.24 0.22 0.24 −0.17
0.24 −0.09 0.25 −0.22 0.23 −0.15 0.19 −0.17 0.18 −0.16 0.21 −0.21
0.26 −0.20 0.33 −0.15 −0.28 0.15 −0.17 0.17 −0.17 0.16 −0.23 0.23
−0.24 0.23 0.23 −0.22 0.20 −0.20 −0.30 0.30 0.18 −0.16 −0.18 0.15
0.28 −0.24 −0.23 0.18 0.20 −0.20 −0.26 0.26 0.19 −0.19 −0.22 0.22
0.31 −0.30 0.26 −0.23 0.18 −0.13 0.15 −0.15 0.18 −0.18 −0.31 0.30
−0.23 0.17 −0.25 0.24 −0.27 0.26 0.25 −0.23 −0.19 0.17 0.11 −0.11
−0.08 0.06 −0.15 0.13 0.25 −0.24 0.28 −0.26 −0.23 0.20 −0.18 0.15
−0.22 0.19 −0.22 0.18 0.11 −0.09 0.28 −0.28
Fig. 9 Quadratic ICA of natural images. 3·10 5 sample pictures
of size 8 × 8 were used. Plotted are the recovered maximal filters
of i.e. rows of the eigenvalue matrices of the quadratic form coefficient
matrices (top figure). For each component the two largest
filters (with respect to the absolute eigenvalues) are shown (altogether
2 · 64). Above each image the corresponding eigenvalue
(multiplied with 10 3 ) is printed. In the bottom figure, the absolute
values of the 10 largest eigenvalues of each filter are shown.
Clearly, in most filters one or two eigenvalues are dominant.
’Nonlinearity and Nonequilibrium in Condensed Matter’
and the BMBF in the project ’ModKog’.
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