This study has proposed and investigated a novel input variable selection method for nonlinear modelling based on principle component analysis (PCA) and cluster analysis. The proposed approach was applied to daily rainfall-runoff modelling of the Brue catchment of the United Kingdom using wavelet based hybrid forms of two nonlinear models, Artificial Neural Networks (ANNs) and Local Linear Regression (LLR), to identify meaningful wavelet decomposed sub-series. The homogenous group formation capability of cluster analysis and redundancy assessment capability of PCA were applied effectively in this study to solve input selection uncertainties associated with wavelet based hybrid models. Though this concept has been represented in the selection of effective wavelet decomposed subseries in runoff modelling, the application has gotten wider implications in time series modelling with highly redundant and large input space. The study revealed the weakness of conventional forms of cross-correlation analysis and also suggested that input selection could be improved by making sufficient natural clusters (equal to the desired number of input data series) of input space and restricting the search within each cluster according to silhouette or correlation value. The study also highlighted the higher modelling capability of ANN over traditional LLR models in rainfall-runoff modelling of the Brue catchment.

中文翻译：

---

PCA和聚类方法在混合径流模型输入选择中的应用

本研究提出并研究了一种基于主成分分析 (PCA) 和聚类分析的非线性建模新输入变量选择方法。使用基于小波的两种非线性模型、人工神经网络 (ANN) 和局部线性回归 (LLR) 的混合形式，将所提出的方法应用于英国 Brue 集水区的每日降雨径流建模，以识别有意义的小波分解子系列。本研究有效地应用了聚类分析的同质组形成能力和PCA的冗余评估能力，解决了基于小波混合模型的输入选择不确定性问题。虽然这个概念已经在径流建模中有效小波分解子序列的选择中得到体现，该应用程序在具有高度冗余和大输入空间的时间序列建模中得到了更广泛的影响。该研究揭示了传统形式的互相关分析的弱点，并建议通过制作足够的输入空间的自然集群（等于所需的输入数据系列数量）并根据以下条件限制每个集群内的搜索来改进输入选择轮廓或相关值。该研究还强调了 ANN 在 Brue 流域的降雨径流建模中比传统 LLR 模型具有更高的建模能力。该研究揭示了传统形式的互相关分析的弱点，并建议通过制作足够的输入空间的自然集群（等于所需的输入数据系列数量）并根据以下条件限制每个集群内的搜索来改进输入选择轮廓或相关值。该研究还强调了 ANN 在 Brue 流域的降雨径流建模中比传统 LLR 模型具有更高的建模能力。该研究揭示了传统形式的互相关分析的弱点，并建议通过制作足够的输入空间的自然集群（等于所需的输入数据系列数量）并根据以下条件限制每个集群内的搜索来改进输入选择轮廓或相关值。该研究还强调了 ANN 在 Brue 流域的降雨径流建模中比传统 LLR 模型具有更高的建模能力。