Abstract not found

Trace ratio is a natural criterion in discriminant analysis as it directly connects to the Euclidean distances between training data points. This criterion is re-analyzed in this paper and a fast algorithm is developed to find the global optimum for the orthogonal constrained trace ratio problem. Based on this problem, we propose a novel semi-supervised orthogonal discriminant analysis via label propagation. Differing from the existing semi-supervised dimensionality reduction algorithms, our algorithm propagates the label information from the labeled data to the unlabeled data through a specially designed label propagation, and thus the distribution of the unlabeled data can be explored more effectively to learn a better subspace. Extensive experiments on toy examples and real world applications verify the effectiveness of our algorithm, and demonstrate much improvement over the state-of-the-art algorithms. Key words: Subspace learning; discriminant Analysis; dimensionality Reduction; trace ratio; semi-supervised learning 1

Discriminant feature extraction plays a central role in pattern recognition and classification. Linear Discriminant Analysis (LDA) is a traditional algorithm for supervised feature extraction. Recently, unlabeled data have been utilized to improve LDA. However, the intrinsic problems of LDA still exist and only the similarity among the unlabeled data is utilized. In this paper, we propose a novel algorithm, called Semisupervised Semi-Riemannian Metric Map (S³RMM), following the geometric framework of semi-Riemannian manifolds. S³RMM maximizes the discrepancy of the separability and similarity measures of scatters formulated by using semi-Riemannian metric tensors. The metric tensor of each sample is learned via semisupervised regression. Our method can also be a general framework for proposing new semisupervised algorithms, utilizing the existing discrepancy-criterion-based algorithms. The experiments demonstrated on faces and handwritten digits show that S 3 RMM is promising for semisupervised feature extraction.

Abstract. Semi-supervised learning effectively integrates labeled and unlabeled samples for classification, and most of the methods are founded on the pair-wise similarities between the samples. In this paper, we propose methods to construct similarities from the probabilistic viewpoint, whilst the similarities have so far been formulated in a heuristic manner such as by k-NN. We first propose the kernel-based formulation of transition probabilities via considering kernel least squares in the probabilistic framework. The similarities are consequently derived from the kernel-based transition probabilities which are efficiently computed, and the similarities are inherently sparse without applying k-NN. In the case of multiple types of kernel functions, the multiple transition probabilities are also obtained correspondingly. From the probabilistic viewpoint, they can be integrated with prior probabilities, i.e., linear weights, and we propose a computationally efficient method to optimize the weights in a discriminative manner, as in multiple kernel learning. The novel similarity is thereby constructed by the composite transition probability and it benefits the semi-supervised learning methods as well. In the various experiments on semi-supervised learning problems, the proposed methods demonstrate favorable performances, compared to the other methods, in terms of classification performances and computation time. 1