| Research Abstract |
We improved the algorithm for nonlinear factor analysis using Hebbian learning method proposed by Oja et al in order to carry out independent component analysis, and wrote a program for it. This method, which is completely different from well-known error backpropagation learning method, enables us to carry out independent component analysis more effectively. Although the learning method is based on the Oja's method that uses only one activation function, we use several activation functions as follws:
Wj(t+1)=Wj(t)+Exfj{x'(t)Wj(t)}diag{sign(cj(t))}
In addition, weight coefficients at the time when the variance of output values is maximized are adopted. The throughout algorithm is as folloes:
(1) Principal component scores of raw data are used as input data.
(2) The data are standardized.
(3) Weight coefficients, Wj, are calculated, and are replaced by W(t) obtained by the equation, W'(t)=W(t)/||W(t)||.
(4) cj(t) are calculated using the equation above.
(5) The ratio of the cases, r, of which the signs of cj calculated using the j th activation function are different with each other after t times learnings is calculated. Then, using the ratios, principal component scores, z, are calculated.
(6) After calculating the variances of z, t(max), which indicates the maximum value of t, is obtained.
(7) The procedure, (3) - (6), is iterated untill the value is converged.
Using the coded program, we carried out the profiling analysis of confiscated stimulant drugs by GC-MS data. Comparing the six methods for the profiling, PCA, CATPCA, MDS, SOM, HNN, and HEP, only HEP gave a resonable map. Although other five methods could not calssify the four samples which were synthesized by four known procedures, HEP could distinguish the known samples. This indicates that HEP method can give appropriate results as a sort of factor analysis.
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