VARIANTS OF THE MCA EXIN NEURON - Neural-based Orthogonal Data Fitting: The EXIN Neural Networks - page 96

Table 3.3 Line fitting with Gaussian noise and strong outliers

2

σ NMCA EXIN ε w NOJA + ε w

0 . 1 0 . 0229 0 . 0253

0 . 2 0 . 0328 0 . 0393

0 . 3 0 . 0347 0 . 0465

0 . 4 0 . 0379 0 . 0500

0 . 5 0 . 0590 0 . 0880

Figure 3.4 Plot of NMCA EXIN weights in a very noisy environment with strong outliers.

this fact is explained by the type of approximation of NOJA + . Figure 3.4 shows
the plot of the NMCA EXIN weights for σ

2

= 0 . 5 for one of the 10 experiments

with this level of noise.

3.3 EXTENSIONS OF THE NEURAL MCA

In this section the neural analysis for MCA is extended to minor subspace analysis
(MSA), principal components analysis (PCA), and principal subspace analysis
(PSA).
Let R be the N × N autocorrelation matrix input data, with eigenvalues
0 ≤ λ N ≤ λ N − 1 ≤···≤ λ 1 and corresponding orthonormal eigenvectors

z N , z N − 1 , ... , z 1 . The following definitions are given: