Estimation of degrees of nonlinearity of the dynamics underlying complex behavior and its applications

复杂行为背后的动力学非线性程度估计及其应用

基本信息

批准号：
12834002
负责人：
MIYANO Takaya
金额：
$ 1.34万
依托单位：
Hirosaki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12834002/
关键词：
nonlinear systems complex systems local approximation time series analysis classification support vector algorithm

项目摘要

1. Nonlinear local approximation method for time series prediction, regression and classification of discrete sequences of data is developed based on the Sugihara-May method. The approximation model is capable of learning the metric to measure the distance between input vectors with the Caprile-Girosi algorithm.2. A data base of medicine and welfare is constructed with aid of the Ministry of Health, Welfare and Labor for numerical experiment of examining applicability to nursing care needs certification.3. A data base of speech signals is constructed with aid of the Aomori Radio and Broadcast Corporation.4. A data base of atomic motion in solid crystals as numerical solutions of molecular dynamics simulation is constructed with aid of Sumitomo Metal Industries, Ltd.5. From numerical experiments of predicting total care time and total nursing time with the medical data base, it is shown that the nonlinearity of local hyper surface representing the functional dependence between situation … More s of patients and the total nursing care time can be measured in terms of the optimized metric. This implies that the complexity of the decision rule or the underlying dynamics of complex behavior can be estimated by the metric proposed. The experiment also exhibits that coarse-graining of objective variables may improve the predictive performance of the approximate, although the nonlinearity of the local hyper surface is enhanced by the coarse-graining.6. The approximating method is successfully applied to speech signals and numerical atomic behavior to reproduce the dynamics underlying the time series data.7. The proposed metric could be utilized as an index associated with the Vapnik-Chervonenkis dimension to control the generalization error of local approximates. Clarifying the mathematical relationship between the metric and the VC (dimension is remained to be investigated in the future. The present work may be able to be said to providing a key ingredient for building a variation of the support vector algorithm for local nonlinear approximation techniques. Less

1。基于sugihara-may方法开发时间序列预测的非线性局部近似方法，数据序列的回归和分类。近似模型能够学习度量标准，以测量使用caprile-girosi algorithm.2的输入向量之间的距离。医学和福利的数据库是借助卫生部，福利和劳动部进行数字实验来构建的，以检查护理需求认证的适用性3。语音信号的数据库是在Aomori Radio and Broadcast Corporation的帮助下构建的。4。固体晶体中原子运动的数据库，作为分子动力学模拟的数值解，借助于Sumitomo Metal Industries，Ltd.5。从医疗数据库预测总护理时间和总护理时间的数值实验，可以表明，局部超表面的非线性代表情况之间的功能依赖性……更多的患者和总护士护理时间可以根据优化的度量来衡量。这意味着决策规则的复杂性或复杂行为的基本动态可以由提出的度量估算。该实验还表明，客观变量的粗粒度可以改善近似值的预测性能，尽管局部超级表面的非线性通过粗粒度增强了。6。近似方法成功地应用于语音信号和数字原子行为，以重现时间序列数据基础的动力学7。所提出的度量可以用作与Vapnik-Chervonenkis维度相关的索引，以控制局部近似值的概括误差。澄清度量与风险投资之间的数学关系（将来仍研究维度。目前的工作可能可以说是为构建支持向量算法的变体的关键成分，以减少局部非线性近似技术。较少的。