Theories And Algorithms Of Manifold Learning And Applications In Biometric Authentication

As one of the hottest topics in machine learning in the recent years, manifold learn-ing mainly aims at discovering the underlying low dimensional manifold embedded in high dimensional data space. This paper addresses some problems encountered in manifold learning domain including 1) how to develop a robust metric between man-ifolds; 2) how to efficiently discover and unfold the non-linear manifold structures in data, and at the same time use them for discriminant analysis; 3) how to discover and restore the intrinsic dimensions of the embedded manifolds, whose corresponding sub-space can reflect the true structure of the manifolds; 4) how to generalize the traditional semi-supervised manifold learning using kernel methods. Specifically, we propose the following theories and algorithms as:●We proposed a tangent distance based algorithm Tangent Distance Inva-riance Fused with LDA (TDIFL) with strong discriminant ability to mea-sure distance between manifolds. TDIFL approximates the true manifolds by their corresponding tangent space, which can be used to approximate the dis-tance between manifolds. At the same time, we proposed a theoretically con-ditional converged prototype learning algorithm to learning one prototype for each manifold.●We proposed a geodesic length preserving algorithm Tensor based RIeman-nian Manifold distance Approximating Projection (TRIMAP) to preserve distance between points on a Remannian Manifold when projected to a sub-space. TRIMAP is solved by optimizing a convex upper bound of the ob-jective function, making the points on a non-linear manifold easy to be mapped onto a flat subspace. We generalized TRIMAP using multi-linear tensor analysis to make it suitable for arbitrary order tensor data, the convergence of the pro-posed algorithm is guaranteed.●We proposed an automatically optimal subspace selection algorithm Multi-1-inear Tensor-based learning without tuning Parameters (MTP) for manifold learning based on graph embedding framework, and theoretically analyze the relationship between graph Laplacian and automatic sub-space de- termination.●We proposed a semi-supervised kernel learning algorithm Efficient Non-PA-rametric Kernel Learning (ENPAKL) based on manifold assumption, w-hich uses the objective function of graph embedding to generalize semi-supervised manifold learning to kernel learning by adding some prior knowledge in semi-supervised learning and some regularizer reflecting the smoothness of manifolds to the objective function. We also proposed a fast and theoretically correct algo-rithm to approximate the true solution.Except for theoretical analysis, we also conducted large number of experiments in-cluding face and gait recognition, semi-supervised clustering and etc., to justify the ef-fectiveness of our proposed algorithms.