以最小平方法訓練叢聚權重模型

Abstract

本論文是以叢聚權重模型為基礎, 其模型可以視為一個優良的函數逼近模型. 藉由估計輸入-輸出資料的機率密度來達成. 叢聚權重模型是以期望-最大化 (EM) 演算法來進行訓練. 在本論文中, 最小平方法 (LMS) 被用來更進一步將叢聚權重模型的訓練結果再度訓練, 且可視為一種互補的訓練方法. 因為期望-最大化演算法和最小平方法的目標函數並不相同, 因此兩者的極小值並不會相同. 最小平方法的訓練結果可以用來初始叢聚權重模型的參數, 因此提供了一個可以避免陷入區域極小值的問題. 本論文包含時間序列的預測, 颱風路徑預測以Lyapunov指數的估測實驗.

This thesis is based on Cluster-Weighted Modeling (CWM), which can be viewed as a novel uni-versal function approximator based on input-output joint density estimation. CWM is trained by Expectation-Maximization (EM) algorithm. In this thesis Least-Mean-Square (LMS) is ap- plied to further train the model parameters and it can be viewed as a complementary training method for CWM. Due to different objective functions of EM and LMS, the local minimum should not be the same for the two objective functions. The training result of LMS learning can be used to reinitialize CWM’s model parameters which provides an approach to mitigate local minimum problems. Experiments of time-series prediction, hurricane track prediction and Lyapunov exponents estimation are presented in this thesis.