In this paper, we propose a uniÞed framework for improved structure estimation and feature selection. Most existing graph-based feature selection methods utilise a static representation of the structure of the available data based on the Laplacian matrix of a simple graph. Here on the other hand, we perform data structure learning and feature selection simultaneously. To improve the estimation of the manifold representing the structure of the selected features, we use a higher order description of the neighbourhood structures present in the available data using hypergraph learning. This allows those features which participate in the most signiÞcant higher order relations to be selected, and the remainder discarded, through a sparsiÞcation process. We formulate a single objective function to capture and regularise the hypergraph weight estimation and feature selection processes. Finally, we present an optimization algorithm to recover the hyper graph weights and a sparse set of feature selection indicators. This process offers a number of advantages. First, by adjusting the hypergraph weights, we preserve high-order neighborhood relations reßected in theoriginaldata,whichcannot be modeled by a simple graph. Moreover, our objective function captures the global discriminative structure of the features in the data. Comprehensive experiments on 9 benchmark data sets show that our method achieves statistically signiÞcant improvement over state-of-art feature selection methods, supporting the effectiveness of the proposed method.

Recently Sparse Representation (or coding) based Classification (SRC) has gained great success in face recognition. In SRC, the testing image is expected to be best represented as a sparse linear combination of training images from the same class, and the representation fidelity is measured by the`2-norm or`1-norm of the coding residual. However, SRC emphasizes the sparsity too much and overlooks the spatial information during local feature encoding process which has been demonstrated to be critical in real-world face recognition problems. Besides, some work considers the spatial information but overlooks the different discriminative ability in different face regions. In this paper, we propose to weight spatial locations based on their discriminative abilities in sparse coding for robust face recognition. Specifically, we learn the weights at face locations according to the information entropy in each face region, so as to highlight locations in face images that are important for classification. Furthermore, in order to construct a robust weights to fully exploit structure information of each face region, we employed external data to learn the weights, which can cover all possible face image variants of different persons, so the robustness of obtained weights can be guaranteed. Finally, we consider the group structure of training images (i.e. those from the same subject) and added an`2 ,1-norm (group Lasso) constraint upon the formulation, which enforcing the sparsity at the group level. Extensive experiments on three benchmark face datasets demonstrate that our proposed method is much more robust and effective than baseline methods in dealing with face occlusion, corruption, lighting and expression changes, etc.

Graph based methods have played an important role in machine learning due to their ability to encode the similarity relationships among data. A commonly used criterion in graph based feature selection methods is to select the features which best preserve the data similarity or a manifold structure derived from the entire feature set. However, these methods separate the processes of learning the feature similarity graph and feature ranking. In practice, the ideal feature similarity graph is difficult to define in advance. Because one needs to assign appropriate values for parameters such as the neighborhood size or the heat kernel parameter involved in graph construction, the process is conducted independently of subsequent feature selection. As a result the performance of feature selection is largely determined by the effectiveness of graph construction. In this paper, on the other hand, we attempt to learn a graph strucure closely linked with the feature selection process. The idea is to unify graph construction and data transformation, resulting in a new framework which results in an optimal graph rather than a predefined one. Moreover, the 2,1-norm is imposed on the transformation matrix to achieve row sparsity when selecting relevant features. We derive an efficient algorithm to optimize the proposed unified problem. Extensive experimental results on real-world benchmark data sets show that our method consistently outperforms the alternative feature selection methods.

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