The aim of this work is to develop a method for the simultaneous analysis of multiple groups and their members based on hierarchical tensor manifold modeling. The method is particularly designed to analyze multiple teams, such as sports teams and business teams. The proposed method represents members' data using a nonlinear manifold for each team, and then these manifolds are further modeled using another nonlinear manifold in the model space. For this purpose, the method estimates the role of each member in the team, and discovers correspondences between members that play similar roles in different teams. The proposed method was applied to basketball league data, and it demonstrated the ability of knowledge discovery from players' statistics. We also demonstrated that the method could be used as a general tool for multi-level multi-group analysis by applying it to marketing data.

In this paper, we propose N-Dimensional (ND) Tensor Supervised Neighborhood Embedding (ND TSNE) for discriminant feature representation, which is used for view-based object recognition. ND TSNE uses a general Nth order tensor discriminant and neighborhood-embedding analysis approach for object representation. The benefits of ND TSNE include: (1) a natural way of representing data without losing structure information, i.e., the information about the relative positions of pixels or regions; (2) a reduction in the small sample size problem, which occurs in conventional supervised learning because the number of training samples is much less than the dimensionality of the feature space; (3) preserving a neighborhood structure in tensor feature space for object recognition and a good convergence property in training procedure. With Tensor-subspace features, the random forests is used as a multi-way classifier for object recognition, which is much easier for training and testing compared with multi-way SVM. We demonstrate the performance advantages of our proposed approach over existing techniques using experiments on the COIL-100 and the ETH-80 datasets.

Surface integrity of 3D medical data is crucial for surgery simulation or virtual diagnoses. However, undesirable holes often exist due to external damage on bodies or accessibility limitation on scanners. To bridge the gap, hole-filling for medical imaging is a popular research topic in recent years [1]-[3]. Considering that a medical image, e.g. CT or MRI, has the natural form of a tensor, we recognize the problem of medical hole-filling as the extension of Principal Component Pursuit (PCP) problem from matrix case to tensor case. Since the new problem in the tensor case is much more difficult than the matrix case, an efficient algorithm for the extension is presented by relaxation technique. The most significant feature of our algorithm is that unlike traditional methods which follow a strictly local approach, our method fixes the hole by the global structure in the specific medical data. Another important difference from the previous algorithm [4] is that our algorithm is able to automatically separate the completed data from the hole in an implicit manner. Our experiments demonstrate that the proposed method can lead to satisfactory results.

Subspace learning based face recognition methods have attracted considerable interest in recent years, including Principal Component Analysis (PCA), Independent Component Analysis (ICA), Linear Discriminant Analysis (LDA), and some extensions for 2D analysis. However, a disadvantage of all these approaches is that they perform subspace analysis directly on the reshaped vector or matrix of pixel-level intensity, which is usually unstable under illumination or pose variance. In this paper, we propose to represent a face image as a local descriptor tensor, which is a combination of the descriptor of local regions (K*K-pixel patch) in the image, and is more efficient than the popular Bag-Of-Feature (BOF) model for local descriptor combination. Furthermore, we propose to use a multilinear subspace learning algorithm (Supervised Neighborhood Embedding-SNE) for discriminant feature extraction from the local descriptor tensor of face images, which can preserve local sample structure in feature space. We validate our proposed algorithm on Benchmark database Yale and PIE, and experimental results show recognition rate with our method can be greatly improved compared conventional subspace analysis methods especially for small training sample number.