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

使用 HEP 神经网络进行非线性因子分析及其在制药和医疗数据中的应用

• 批准号: 13672253
• 负责人: TAKAGI Tatsuya
• 金额: $ 1.02万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13672253/
• 关键词: metric pharmaceutical science; principal component analysis; independent component analysis; profiling analysis; nonlinear problem; nonlinear classification; factor analysis; Profiling Analysis; 非線形主成分分析; ニューラルネットワーク; 教師なし学習; Hebbian学習; コンピュータ

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.

为了进行独立成分分析，我们利用Oja等人提出的Hebbian学习方法对非线性因素分析算法进行了改进，并编写了相应的程序。这种方法与众所周知的误差反向传播学习方法完全不同，它使我们能够更有效地进行独立分量分析。虽然该学习方法是基于只使用一个激活函数的Oja方法，但我们使用多个激活函数作为follws:Wj(t+1)=Wj(t)+Exfj{x‘(t)Wj(t)}diag{sign(cj(t))}In加法，采用了输出值的方差最大时的权重系数。通过率算法如下：(1)以原始数据的主成分分数作为输入数据。(2)对数据进行标准化。(3)计算权系数Wj，并将其替换为由公式W‘(T)=W(T)/||W(T)||得到的W(T)。(4)使用上面的公式计算Cj(T)。(5)计算t次学习后第j次激活函数计算的Cj符号彼此不同的情况的比率r。(6)计算z的方差，得到t的最大值t(Max)。(7)迭代程序(3)-(6)，直到收敛为止。利用编码程序，利用GC-MS数据对没收的兴奋剂进行了轮廓分析。比较PCA、CATPCA、MDS、SOM、HNN和HEP这六种方法，只有HEP给出了合理的MAP。虽然其他五种方法不能对已知的四种方法合成的四个样品进行分级，但HEP可以区分已知的样品。这表明HEP方法作为一种因子分析方法可以给出合适的结果。

项目成果

Tatsuya TAKAGI: "Application of Computer Intensive Statistical Method to Chemistry and Pharmaceutical Sciences"Chemical Industry. Vol.53, No.4. 298-302 (2002)

Tatsuya TAKAGI：“计算机密集统计方法在化学和制药科学中的应用”化学工业。