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

1. 在Sugihara-May方法的基础上，提出了离散数据序列预测、回归和分类的非线性局部逼近方法。该近似模型能够通过Caprile-Girosi算法学习度量来测量输入向量之间的距离。2 .在厚生劳动省的协助下，建立了医药福利数据库，进行了检验护理需求认证适用性的数值实验。在青森广播公司的帮助下，建立了语音信号数据库。在住友金属工业株式会社的帮助下，建立了固体晶体中作为分子动力学模拟数值解的原子运动数据库。利用医学数据库对总护理时间和总护理时间进行预测的数值实验表明，用优化后的度量可以测量出患者和总护理时间之间的函数依赖关系的局部超曲面的非线性。这意味着决策规则的复杂性或复杂行为的潜在动态可以通过所提出的度量来估计。实验还表明，尽管局部超表面的非线性被粗粒度增强，但粗粒度化的客观变量可以提高近似的预测性能。该近似方法成功地应用于语音信号和数值原子行为，以再现时间序列数据背后的动力学。该度量可以作为与Vapnik-Chervonenkis维数相关联的指标来控制局部近似的泛化误差。澄清度规和VC维之间的数学关系有待于未来的研究。目前的工作可以说是为构建局部非线性近似技术的支持向量算法的变体提供了关键成分。少

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