"決定一個適當的距離函數是圖形識別與機器學習的一個基本問題。在這個兩年計劃裡我們將要發展一個針對由人臉影像估計人的年齡的應用設計之距離學習演算法。這兩年的研究主題包含: 第一年，我們將要發展一個使用提升法之距離學習法並將其應用於由人臉影像估計人的年齡。尤其，我們將應用我們最近發展出來的使用提升法與假說邊緣虧損函數之距離學習法。由於這個方法是使用提升法與假說邊緣虧損函數，其對估計人的年齡應用的效果非常值得期待。 由於人臉年齡特徵常是高維度資料，距離學習演算法必須考量樣本不足問題。在文獻裡Perturbation LDA(P-LDA, Zheng et al. 2009)納入考量類別中心的擾動來改寫Fisher's discriminant analysis (FDA)的公式，並導出此擾動項與調控參數間的關係。但是，我們發現P-LDA的推導過程有瑕疵，此瑕疵將限制P-LDA之調控技巧於其他的線性區別分析。在第二年，我們將首先納入類別中心的擾動來重新推導FDA的公式並指出P-LDA的公式瑕疵。然後，藉由新的公式，我們將提出一個摺疊法估計出來的調控參數。最後，我們將推廣此法至其他線性區別分析(例如graph embedding)於樣本不足問題。""Determining a proper distance is one of the fundamental problems in pattern recognition and machine learning. In this two-year project, we shall focus on developing algorithms of metric learning for estimating human age via face images. The topics of this two-year project are as follows. In the first year, we shall develop a boosting algorithm of metric learning for human age estimation. In particular, we shall adopt our recently developed boosting algorithm for supervised metric learning, which is based on a novel hypothesis-margin-based loss function. Since the algorithms to be developed are based on the boosting technique and a loss function for the nearest-neighbor classification, positive effect of the learned distance-metric on the human age estimation problem could be expected. Due to aging-related facial features are often high-dimensional data, we should take the undersampled problem into account. In the literature, Perturbation LDA (Zheng et al. 2009), which is referred as to P-LDA, reformulates Fisher's discriminant analysis, referred as to FDA, to include the perturbation in class centers. P-LDA has shown that proper regularization parameters can be derived according to the perturbation in class center. However, we have found that the way for deriving P-LDA has a theoretical fault. This fault may limit the applicability of the regularization technique for P-LDA to other algorithms of linear discriminant analysis. In the second year, first, we shall re-derive FDA with considering the perturbation in class centers, and indicate the theoretical fault of P-LDA. Second, we shall propose a jackknife estimate of the regularization parameter. Last, we shall show this jackknife estimate can be applied to other algorithms of LDA, such as graph embedding, on the undersampled problem."
Distance metric learning
Face-image-based age estimation