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.

我们利用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，以进行独立成分分析，并编写了程序。这种方法与众所周知的误差反向传播学习方法完全不同，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仅使用一个激活函数的 Oja 方法，但我们使用了多个激活函数，如下所示：Wj(t+1)=Wj(t)+Exfj{x'(t)Wj(t)}diag {sign(cj(t))}此外，采用输出值的方差最大化时的权重系数。整个算法如下：（1）将原始数据的主成分得分作为输入数据。（2）对数据进行标准化。（3）计算权重系数Wj，并替换为得到的W（t）由方程，W'(t)=W(t)/||W(t)||。 (4) cj(t) 使用上面的方程计算。 (5) 案例的比例 r其中 cj 的符号是使用第 j 个计算得出的经过t次学习计算后，激活函数彼此不同。然后，使用这些比率计算主成分得分 z。(6) 计算 z 的方差后，获得表示 t 最大值的 t(max)。(7) 过程 (3) - (6), 迭代直至值收敛。使用编码程序，我们通过GC-MS数据对没收的兴奋剂药物进行了轮廓分析。比较 PCA、CATPCA、MDS、SOM、HNN 和 HEP 六种分析方法，只有 HEP 给出了合理的图。尽管其他五种方法无法对由四种已知程序合成的四种样品进行分类，但HEP可以区分已知样品。这表明HEP方法作为一种因素分析能够给出合适的结果。

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。