Over the last decade, supervised and unsupervised subspace learning methods, such as LDA and NPE, have been applied for face recognition. In real life applications, besides unlabeled image data, prior knowledge in the form of labeled data is also available, and can be incorporated in subspace learning algorithm resulting in improved performance. In this paper, we propose a subspace learning met...

We present a general framework of spectral methods for semi-supervised dimensionality reduction. Applying an approach called manifold regularization, our framework naturally generalizes existent supervised frameworks. Furthermore, by our two semi-supervised versions of the representer theorem, our framework can be kernelized as well. Using our framework, we give three examples of semi-supervise...

In this paper, we propose a new supervised feature extraction algorithm in synthetic aperture radar automatic target recognition (SAR ATR), called generalized neighbor discriminant embedding (GNDE). Based on manifold learning, GNDE integrates class and neighborhood information to enhance discriminative power of extracted feature. Besides, the kernelized counterpart of this algorithm is also pro...

Gene expression data collected from DNA microarray are characterized by a large amount of variables (genes), but with only a small amount of observations (experiments). In this paper, manifold learning method is proposed to map the gene expression data to a low dimensional space, and then explore the intrinsic structure of the features so as to classify the microarray data more accurately. The ...

Article history: Received 3 April 2011 Received in revised form 30 January 2012 Accepted 27 February 2012 Available online 4 March 2012

Recently, more and more approaches are emerging to solve the cross-view matching problem where reference samples and query samples are from different views. In this paper, inspired by Graph Embedding, we propose a unified framework for these cross-view methods called Cross-view Graph Embedding. The proposed framework can not only reformulate most traditional cross-view methods (e.g., CCA, PLS a...

In this paper, a manifold learning based method named local maximal margin discriminant embedding (LMMDE) is developed for feature extraction. The proposed algorithm LMMDE and other manifold learning based approaches have a point in common that the locality is preserved. Moreover, LMMDE takes consideration of intra-class compactness and inter-class separability of samples lying in each manifold...

Feature selection for face representation is one of the central issues for any face recognition system. Finding a lower dimensional feature space with enhanced discriminating power is one of the important tasks. The traditional subspace methods represent each face image as a point in the disciminant subspace that is shared by all faces of different subject (classes). Such type of representation...

We present a heuristic asymptotic formula as x → ∞ for the number of isogeny classes of pairing-friendly elliptic curves over prime fields with fixed embedding degree k ≥ 3, with fixed discriminant, with rho-value bounded by a fixed ρ0 such that 1 < ρ0 < 2, and with prime subgroup order at most x.