近年來臉部辨識系統與機器學習分類法兩者發展迅速，在這兩個領域上，各自都有一套常用的方法。本文與一般常見的影像辨識做法不同之處，在於先將臉部影像資料經處理轉換為數據形態並經過處理後，再使用相關的多變量分析與資料探勘方法，如多維線性主成分分析 (Multilinear principal component analysis, MPCA)、正規化區別分析 (Regularized discriminant analysis, RDA)，與隨機森林 (Random forest)等，找出在不同類別影像中較具辨識能力的因子。
人的五官與臉部特徵雖不盡相同，但部份唐氏症患者從外表就能判斷出其是否具有該疾病，這些變異我們有時可以從他們的五官看出；例如：五官比例、耳朵外觀、鼻子形狀、眼睛輪廓等等。本文探討如何利用臉部影像資料以及常用之機器學習方法來辨識唐氏症患者。我們根據一些唐氏症患者與一般非唐氏症患者之照片，在經過資料處理後找出具辨識能力之因子，並將其特徵點還原至圖片上，配合醫生的經驗法則來建立影像中唐氏症病徵的主要規則。

In recent years, both facial recognition system and machine learning are developed rapidly. In these two areas, each has many commonly used methods. In this work, we use a two-stage approach on images for classification. First, we transform the facial image data into multi-dimensional data form, and then apply appropriate multivariate analysis and data mining methods on it. Methodologies such as Multilinear principal component analysis (MPCA), Regularized Discriminant Analysis (RDA), Random Forest are adopted. We aim at finding factors that are important in identifying different types of images.

Although facial features are different for individuals, but most people with Down's syndrome can be discriminated from the outlooks whether he or she has the disease or not. These variations sometimes can be seen from their facial features. For example, the features such as facial proportion, ear appearance, nose shape and eye contour and so on, can help to determine if a person has the disease or not.

This thesis discusses how to use multivariate analysis and machine learning methods based on the facial image data to identify Down's syndrome patients. According to some of the sample images from those with Down's syndrome or not, we find the important areas on the facial image which are useful in discriminating Down's syndrome patients. In the end, after restoring the important areas of the facial image, it is expected that the above methodology is helpful as one of the main criteria for the doctors to identify the Down’s syndrome symptoms with high accuracies.

論文審定書…………………………………………………………………………………… i

誌謝…………………………………………………………………………………………… ii

摘要…………………………………………………………………………………………… iii

Abstract……………………………………………………………………………………… iv

1 前言………………………………………………………………………………………… 1

2 資料描述…………………………………………………………………………………… 1
2.1 資料蒐集方式………………………………………………………………………… 1
2.2 資料處理……………………………………………………………………………… 3

3 研究方法…………………………………………………………………………………… 4
3.1 因素分析……………………………………………………………………………… 4
3.1.1 多線性主成分估計法………………………………………………………… 5
3.1.2 因素轉軸……………………………………………………………………… 6
3.1.3 因素分數……………………………………………………………………… 6
3.2 機器學習：分類方法………………………………………………………………… 6
3.2.1 隨機森林……………………………………………………………………… 6
3.3 正規化區別分析……………………………………………………………………… 8
3.4 因素篩選……………………………………………………………………………… 8
3.5 評估與驗證…………………………………………………………………………… 8
3.6 交叉驗證……………………………………………………………………………… 9
3.7 因素負荷表示………………………………………………………………………… 9

4 研究結果…………………………………………………………………………………… 10
4.1 多線性主成分分析 (MPCA) 處理結果……………………………………………… 10
4.1.1 降維結果……………………………………………………………………… 10
4.1.2 重建影像……………………………………………………………………… 11
4.1.3 因素分數……………………………………………………………………… 11
4.2 結合影格數值化結果………………………………………………………………… 12
4.3 隨機森林 (Random Forest) 分類結果 …………………………………………… 13
4.3.1 基於多線性主成分分析分類結果…………………………………………… 13
4.3.2 基於合併影格數值化分類結果……………………………………………… 16
4.4 正規化區別分析 (Regularized Discriminant Analysis, RDA) 分類結果…… 19
4.4.1 基於多線性主成分分析分類結果…………………………………………… 19
4.4.2 基於合併影格數值化分類結果……………………………………………… 22
4.5 總比較………………………………………………………………………………… 25

5 討論與節語………………………………………………………………………………… 26

參考文獻……………………………………………………………………………………… 28

附錄…………………………………………………………………………………………… 29

A 臉部分析…………………………………………………………………………………… 29
A.1 全臉分析……………………………………………………………………………… 29

B 統計性質…………………………………………………………………………………… 32
B.1 多線性主成分分析統計性質………………………………………………………… 32
B.2 因素轉軸……………………………………………………………………………… 35
B.3 因素分數……………………………………………………………………………… 35
B.4 Wilk's Lambda 統計量……………………………………………………………… 36
B.4.1 Wilk's Lambda 準則檢定新增變數………………………………………… 36
B.5 正規化區別分析……………………………………………………………………… 37
B.6 隨機森林……………………………………………………………………………… 38

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Down syndrome from Wikipedia, http://en.wikipedia.org/wiki/Down syndrome
Machine learning from Wikipedia, http://en.wikipedia.org/wiki/Machine_learning
Random forest from Wikipedia, http://en.wikipedia.org/wiki/Random_forest