We introduce a probabilistic model that generalizes classical linear discriminant analysis and gives an interpretation for the components as informative or relevant components of data. The components maximize the predictability of class distribution which is asymptotically equivalent to (i) maximizing mutual information with the classes, and (ii) finding principal components in the so-called le...

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, the method of kernel Fisher discriminant (KFD) is analyzed and its nature is revealed, i.e., KFD is equivalent to kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). Based on this result, a more transparent KFD algorithm is proposed. That is, KPCA is ;rst performed and then LDA is used for a second feature extraction in the KPCA-transformed ...

In this paper, a new statistical projection method called Bilinear Discriminant Analysis (BDA) is presented. The proposed method efficiently combines two complementary versions of Two-Dimensional-Oriented Linear Discriminant Analysis (2DoLDA), namely Column-Oriented Linear Discriminant Analysis (CoLDA) and Row-Oriented Linear Discriminant Analysis (RoLDA), through an iterative algorithm using a...

Distance metric learning is widely used in many visual computing methods, especially image classification. Among various metric learning approaches, Fisher Discriminant Analysis (FDA) is a classical metric learning approach utilizing the pair-wise semantic similarity and dissimilarity in image classification. Moreover, Local Fisher Discriminant Analysis (LFDA) takes advantage of local data stru...