Learning image manifold via local tensor subspace alignment

In this paper, we propose an Local Tensor Subspace Alignment algorithm (LTESA) for capturing the underlying geometric structure of images distributed on a manifold embedded in high-dimensional ambient space. The basic idea is to represent images as tensor objects and obtain locally linear structures by local rank one tensor projection (ROTP), then align the local structures to get global parameterizations of the image manifold. In multilinear subspace learning of image manifold, ROTP based methods achieve a compact representation in vector form for image tensors, but they only recover the Euclidean structure. Conventional manifold learning methods based on vectorization of image such as Isomap and LLE have been developed to discover the nonlinear structure of images, but they have the drawback of notable computational time and memory requirements of training and the loss of structure information among pixels. Our method can be viewed as a nonlinear extension of ROTP based multilinear subspace learning, achieving the compactness and nonlinearity of manifold parameterizations simultaneously. Besides, we propose a novel approach to select appropriate landmark points. Thus, LTESA could analyze large scale image data more efficiently and solve the ''out-of-sample'' problem naturally with the chosen landmark points. The performances of LTESA are evaluated by comparison with representative manifold learning methods and multilinear subspace learning methods on face and digit image databases. The experimental results demonstrate the effectiveness of our method in unsupervised learning for image manifold.