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Mathematical Modeling and Stochastic Sensitivity Analysis for Data Mining

数据挖掘的数学建模和随机敏感性分析

基本信息

批准号：
11680435
负责人：
KODA Masato
金额：
$ 2.3万
依托单位：
University of Tsukuba
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

We have studied the mathematical modeling and stochastic sensitivity analysis techniques that are required to develop advanced machine-learning systems for data mining, and obtained the following results :1. A new stochastic learning algorithm for neural networks : Based on a functional derivative formulation of the gradient descent method in conjunction with stochastic sensitivity analysis techniques using variational approach, a novel stochastic learning algorithm using Gaussian white noise is developed for a class of discrete-time neural networks. Unlike the back-propagation algorithm, the proposed method does not require the synchronous transmission of information backward along connection weights. The proposed algorithm uses only ubiquitous noise inherent in the network and local signals, to achieve simple sequential updating of connection weights.2. Bootstrap re-sampling for unbalanced data in supervised leaning : A technical framework using bootstrap techniques is developed to assess the impact of re-sampling on the generalization ability of a supervised learning. Based on the bootstrap expression of the prediction error, the proposed method enables identification of the optimal re-sampling proportion for unbalanced data set. The analysis is also conducted to extend the proposed method to cross-validation.3. Applications to manufacturing scheduling and processes : Data mining techniques to assess the association or closeness of dispatching rules are studied in order to develop optimal manufacturing schedules. Minimum Description Length (MDL) criterion is also studied to discover unnatural patterns or events in manufacturing processes. The results we obtained clearly indicate that techniques of data mining will play an essential role in the production scheduling and statistical process control.

我们研究了开发先进的机器学习数据挖掘系统所需的数学建模和随机灵敏度分析技术，并取得了以下成果：1。一种新的神经网络随机学习算法：基于梯度下降法的泛函导数形式，结合变分法的随机灵敏度分析技术，提出了一类离散时间神经网络在高斯白色噪声下的随机学习算法。与反向传播算法不同，该方法不需要信息沿沿着连接权值反向同步传输。该算法仅利用网络中普遍存在的噪声和本地信号，实现简单的连接权值顺序更新.监督学习中不平衡数据的Bootstrap重采样：开发了一个使用Bootstrap技术的技术框架，以评估重采样对监督学习泛化能力的影响。基于预测误差的自举表达式，该方法能够识别不平衡数据集的最佳重采样比例。通过分析，将所提出的方法扩展到交叉验证。应用于制造调度和流程：数据挖掘技术，以评估关联或紧密的调度规则进行了研究，以制定最佳的制造进度。最小描述长度（MDL）标准也研究发现不自然的模式或事件在制造过程中。我们得到的结果清楚地表明，数据挖掘技术将在生产调度和统计过程控制中发挥至关重要的作用。