This thesis studies on key technologies of ranking-based subspace learning. The ranking problem has drawn much attention in the machine learning and information retrieval communities, due to its significant theory interests and potential applications. The main contributions of this thesis are summarized as follows: We propose a feature selection method for age estimation, which aims to preserve the local manifold structure and the ordinal pattern of facial images. Face aging is a typical temporal progression, and facial images should have ordinal pattern in aging feature space. From the geometric perspective, facial image is usually sampled from a low dimensional manifold embedded in original high dimensional image space. To achieve our goal, we first define the energy of preserving the locality and the energy of keeping ordinal information for each feature, respectively. we also define the redundant locality information and ordinal information between features, respectively. Based on the above definition, we formulate this issue as an optimization problem. Because labeling facial aging images is a hard work in practice, we also extend the proposed method for semi-supervised learning. We propose an ordinal distance metric learning (DML) algorithms for ranking. In previous work, most DML methods were proposed for the classification and clustering tasks. In our work, we focus on designing new DML algorithms for ranking tasks. We first present a linear DML model for image ranking, which aims at preserving the local geometry of the target neighbors and the ordinal information of data groups with different rank levels simultaneously. Since real-world image data is often endowed with nonlinear structure, we further develop a kernel-based DML algorithm called KDMLR for ranking. Finally, to further improve the ranking performance, we derive a multiple-kernel DML approach to describe complex nonlinear properties by multiple image features, which learns multiple distance functions sequentially by multiple-kernel embedding. We propose a global feature transformation method for ranking, which aims at preserving the global structure and the ordinal information of data simultaneously. To this end, we first define two matrices, which work in the row direction and column direction respectively. The two matrices aim at leveraging the global structure of the data set and ordinal information of the observations. By maximizing the corresponding objective f...
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