Nonlinear Factor Analysis using HEP Neural Network and Its Application to Pharmaceutical and Medical Data

为了进行独立成分分析，我们改进了Oja等人提出的Hebbian学习方法的非线性因子分析算法，并编写了相应的程序，该方法与著名的误差反向传播学习方法完全不同，使我们能够更有效地进行独立成分分析。虽然该学习方法基于仅使用一个激活函数的Oja方法，但是我们使用如下的几个激活函数：Wj（t+1）=Wj（t）+Exfj{x ′（t）Wj（t）}diag{sign（cj（t））}此外，采用了输出值的方差最大化时的权重系数。该算法的基本思想是：（1）以原始数据的主成分得分作为输入数据。(2)数据是标准化的。(3)计算权重系数Wj，并将其替换为通过等式W ′（t）=W（t）/W（t）获得的W（t）。||W（t）||. (4)cj（t）使用上述等式计算。(5)计算在t次学习之后使用第j个激活函数计算的cj的符号彼此不同的情况的比率r。然后，使用比率，计算主成分得分z。(6)在计算z的方差之后，获得指示t的最大值的t（max）。(7)利用所编制的程序，对收缴兴奋剂的GC-MS数据进行了定性分析。比较了主成分分析（PCA）、CATPCA、MDS、SOM、HNN和HEP等6种方法的优劣，只有HEP方法的图谱比较合理。虽然其他五种方法不能对四种已知方法合成的样品进行分类，但HEP可以区分已知样品。这表明，HEP方法作为一种因子分析方法，能够给出较好的结果。

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.