階層型ニューラルネットによる非線形多変量データ解析に関する研究
Project/Area Number |
09680317
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Statistical science
|
Research Institution | Osaka Electronic-Communication University |
Principal Investigator |
TSUJITANI Masaaki Osaka Electro-Communi. Univ. Faculty of Inf. Sci. & Tech., 情報工学部, 教授 (90140475)
|
Project Period (FY) |
1997 – 1999
|
Project Status |
Completed (Fiscal Year 1999)
|
Budget Amount *help |
¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1998: ¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 1997: ¥500,000 (Direct Cost: ¥500,000)
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Keywords | Neural Network / Discriminant Analysis / AIC / CART / Kullback-Leibler Measure / 多変量解析 / ニューロ・コンピューティング / データマイニング / 情報量規準 / パターン認識 / ニューラルネット / 分割表 / 非線形解析 |
Research Abstract |
In application of feed-forward neural network models to regression and classification problems, we introduce the probabilistic interpretations of network outputs and construct the likelihood principle of the models. We first, present a feed-forward neural network model for a single binary output, which can be regarded as an extension of ordinal logistic regression models. With the arc-sine transformation for binary response, we provide the likelihood function of network models and the learning algorithm. It is proved that maximizing the likelihood function based on the arc-sine transformation results in minimizing the sum-of-squares error function in the neural network model. The proposed method is evaluated by comparison with ordinal logistic regression model through the index plots of the residuals. Non-linear discriminant analysis in classification problems is also investigated by using feed-forward neural networks with a single or multiple outputs. We derive the theorem of the relat
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ionship of two types of error function, i. e., the sum-of-squares error function and the Kullback-Leibler measure. Statistical inference based on the likelihood approach is then formulated in order to optimize a complex network model. AIC with the sum-of-squares, which is based on the assumption that the noise is normally distributed, has been used for selection of a best model among several competing models. We suggest an alternative information criterion based on the bootstrap method for determination of the appropriate number of hidden units. We also present the bootstrap estimates of the actual error rates because excess error estimation is important when the training sample is small relative to the number of parameters. It is shown that the proposed method has smaller error rates than those by Fisher's discriminant analysis and CART (Classification And Regression Trees). Complex network models do not always achieve good generalization due to the learning of the noise. We thus develop the pruning algorithm of the connection weights using the likelihood-ratio statistic in order to test the significance of the connection weights. We also use the likelihood-ratio statistic for selecting the best subset of predictor variables. From the point of dimensionality reduction, we finally study the relationship between discriminant analysis and fee-forward neural networks used for classification. By analogy with the technique for the canonical scores in the multi-dimensional canonical discriminant analysis, we derive the compression scores as the linear combination of predictor variables. It allows us to reduce the dimensions of the information due to graphical presentation of the data. Less
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Research Products
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