函數資料分析在高光譜影像資料之研究

Application of Functional Data Analysis to Hyperspectral Imaging

王洛騏(Lo-Chi Wang)

指導教授 ： 蔡政安

國立臺灣大學/共同教育中心/統計碩士學位學程/碩士(2021年)

https://doi.org/10.6342/NTU202101165

摘要

不同於每個像素由紅、綠、藍組成的三原色光模式 (RGB color model)，高光譜影像 (hyperspectral imaging, HSI) 在連續波長範圍內提供了更詳細的光譜資訊。而在分析HSI主要面臨的挑戰為其紀錄的光譜具有無限維的特徵空間，以及相對有限的樣本。直觀而言，可將HSI在每個像素的資料視為波長的函數，而函數主成分分析 (functional principal component analysis, FPCA) 能夠對此類型資料進行維度縮減。FPCA是主成分分析 (principal component analysis, PCA) 的延伸，即一種針對函數型資料的降維方法。從傳統的FPCA估計出的函數主成分 (functional principal components, FPCs) 是由可解釋多少函數資料的變異來進行排序，並無將反應變數納入考量。在本研究中，提出了兩種監督式判別方法 (支援向量機和隨機森林) 來對這些FPCs重新排名。而在降維後，便可利用機器學習演算法進行後續的統計分析。我們將透過三個實際資料應用、兩筆模擬資料，來評估提出的方法之可行性。

關鍵字

高光譜影像 ； 函數資料分析 ； 函數主成分分析 ； 支援向量機 ； 隨機森林

並列摘要

Unlike conventional imaging systems, in which each pixel consists of RGB color, hyperspectral imaging (HSI) technology provides detailed spectral information over a continuum of wavelength. The major challenges faced by an analysis of HSI are that the recorded spectra have an infinite-dimensional feature space and the relatively limited samples. A reasonable way to deal with such data is to consider them as functions of wavelength, and a natural solution is functional principal component analysis (FPCA). FPCA can be viewed as an extension of principal component analysis (PCA), i.e., a dimension reduction tool for the functional data. In the conventional FPCA, the leading functional principal components (FPCs) are ranked in the order of explained variation of the functional predictor. In this paper, we propose a new ranking strategy for the leading FPCs using two supervised discriminative methods, support vector machines and random forests algorithms. After the dimension reduction, we put extracted features into machine learning algorithms for statistical analyses. Three real hyperspectral datasets and two simulation studies are used to demonstrate the effectiveness of our proposed methods.

並列關鍵字

hyperspectral imaging ； functional data analysis ； functional principal component analysis ； support-vector machines ； random forests

參考文獻

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