Orthogonal Tensor Neighborhood Preserving Embedding (OTNPE) is an efficient dimensionality reduction algorithm for two-dimensional images. However, insufficiencies of the robustness performance and deficiencies of supervised discriminant information are remained. Motivated by the sparse learning, an algorithm called Orthogonal Tensor Sparse Neighborhood Embedding (OTSNPE) for two-dimensional im...

In this paper, we propose a novel method for image feature extraction, namely the twodimensional local graph embedding, which is based on maximum margin criterion and thus not necessary to convert the image matrix into high-dimensional image vector and directly avoid computing the inverse matrix in the discriminant criterion. This method directly learns the optimal projective vectors from 2D im...

In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field Fp and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.

In this paper, we describe our model designed for automatic prediction of media interestingness. Specifically, a two-stage learning framework is proposed. In the first stage, supervised dimensionality reduction is employed to discover the key discriminant information embedded in the original feature space. We present a new algorithm dubbed biased discriminant embedding (BDE) to extract discrimi...

This paper addresses the problem of how to learn an appropriate representation from video to benefit video-based face recognition. We pose it as learning spatio-temporal embedding (STE) from raw video. STE of a video sequence is defined as its condensed version capturing the essence of space-time characteristics of the video. Relying on co-occurrence statistics of training videos, Bayesian keyf...

Subspace learning techniques have been extensively used for dimensionality reduction (DR) in many pattern classification problem domains. Recently, methods like Subclass Discriminant Analysis (SDA) and Clusteringbased Discriminant Analysis (CDA), which use subclass information for the discrimination between the data classes, have attracted much attention. In parallel, important work has been ac...

In this paper, we present the algorithm designed for mining emotional features of movies. The algorithm dubbed Arousal-Valence Discriminant Preserving Embedding (AVDPE) is proposed to extract the intrinsic features embedded in movies that are essentially differentiating in both arousal and valence directions. After dimensionality reduction, we use the neural network and support vector regressor...

We present a new method for analyzing classifiers by visualization, which we call visual nonlinear discriminant analysis. Classifiers that output posterior probabilities are visualized by embedding samples and classes so as to approximate posterior probabilities using parametric embedding. The visualization provides a better intuitive understanding of such classifier characteristics as separabi...

Neighborhood Preserving Embedding (NPE) is a subspace learning algorithm. Since NPE is a linear approximation to Locally Linear Embedding (LLE) algorithm, it has good neighborhood-preserving properties. Although NPE has been applied in many fields, it has limitations to solve recognition task. In this paper, a novel subspace method, named Kernel Fisher Neighborhood Preserving Embedding (KFNPE),...