貝氏架構下部分最小平方法

Abstract

本論文的目的在於建構一種分析法則，是一種以機率為基礎的多變數分析方法。此新的學習法則稱之貝氏架構下部份最小平方法，綜合了廣泛應用在生物訊號量測與分析的多變數方法中的部份最小平方法以及正則化的優點，並且導入貝氏分析的觀點，即使資料在有雜訊的情況下，可避免過度配適的現象，得到較好的估算結果。 在模擬數據分析部份，貝氏架構下部份最小平方法用來分析二種不同的波形，另外，也提出了一假設，我們考慮資料分佈為高斯分佈與一般分佈是否會造成整體分析效能的不同，利用正切函數來針對資料進行轉換，並以均方根誤差及相關係數來做為判定的標準說明貝氏架構下部份最小平方法可得到較好的結果。得到一具有雜訊消除的分析方法，並於未來將之應用於生醫訊號量測分析上。

The main purpose of this thesis is to develop a method of analyzing. It is the probability-based multivariate analysis method, names as Bayesian-based partial least squares (Bayesian-based PLS). It combines the advantages of PLS which is widely used method in biomedical spectroscopic analysis, regularization technique and the Bayesian analysis to provide an efficient procedure to avoid the circumstance of overfitting and attain better results when calibrating under noisy data. In the simulated experiments, Bayesian-based PLS is applied to analyze two different kinds of simulated waves. Besides, we also make an assumption to consider data with Gaussian distribution and uniform distribution. We examine these two cases to know which is better for analyzed results. The tangent function is used for transfer function. According to estimated standard of root mean square error and correlation coefficient, proving that Bayesian-based PLS has better analyzed performance. In the future, we will apply the proposed method which is able to reduce noise signal to Bio-signal measurement and analysis.