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

为了进行独立分量分析，我们采用Oja等人提出的Hebbian学习方法对非线性因子分析算法进行了改进，并编写了相应的程序。该方法与众所周知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分量分析。虽然学习方法是基于Oja的方法，只使用一个激活函数，但我们使用了几个激活函数：Wj(t+1)=Wj(t)+Exfj{x'(t)Wj(t)}diag{sign(cj(t))}，并采用输出值方差最大时的权重系数。整个算法如下：(1)使用原始数据的主成分分数作为输入数据。(2)数据标准化。(3)计算权重系数Wj，代之以W(t) =W(t)/||W(t)||得到的W(t)。(4) cj(t)由上式计算。(5)计算t次学习后，使用第j次激活函数计算的cj的符号不同的情况r的比例。然后，使用这些比率，计算主成分分数z。(6)计算z的方差后，得到t(max)，表示t的最大值。(7)迭代(3)-(6)过程，直到该值收敛。利用编码程序对没收的兴奋剂进行气相色谱-质谱分析。对比PCA、CATPCA、MDS、SOM、HNN和HEP 6种分析方法，只有HEP给出了合理的图谱。虽然其他5种方法不能对已知4种方法合成的4种样品进行分类，但HEP可以对已知样品进行区分。这表明HEP方法作为一种因子分析方法，可以得到较好的结果。

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.