Linear discriminant analysis

About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.

Learning Regularized LDA by Clustering

Abstract: As a supervised dimensionality reduction technique, linear discriminant analysis has a serious overfitting problem when the number of training samples per class is small. The main reason is that the between- and within-class scatter matrices computed from the limited number of training samples deviate greatly from the underlying ones. To overcome the problem without increasing the number of training samples, we propose making use of the structure of the given training data to regularize the between- and within-class scatter matrices by between- and within-cluster scatter matrices, respectively, and simultaneously. The within- and between-cluster matrices are computed from unsupervised clustered data. The within-cluster scatter matrix contributes to encoding the possible variations in intraclasses and the between-cluster scatter matrix is useful for separating extra classes. The contributions are inversely proportional to the number of training samples per class. The advantages of the proposed method become more remarkable as the number of training samples per class decreases. Experimental results on the AR and Feret face databases demonstrate the effectiveness of the proposed method.

Hierarchical discriminant regression

Abstract: The main motivation of this paper is to propose a classification and regression method for challenging high-dimensional data. The proposed technique casts classification problems and regression problems into a unified regression problem. This unified view enables classification problems to use numeric information in the output space that is available for regression problems but are traditionally not readily available for classification problems. A doubly clustered subspace-based hierarchical discriminating regression (HDR) method is proposed. The major characteristics include: (1) Clustering is performed in both output space and input space at each internal node, termed "doubly clustered." Clustering in the output space provides virtual labels for computing clusters in the input space. (2) Discriminants in the input space are automatically derived from the clusters in the input space. (3) A hierarchical probability distribution model is applied to the resulting discriminating subspace at each internal node. This realizes a coarse-to-fine approximation of probability distribution of the input samples, in the hierarchical discriminating subspaces. (4) To relax the per class sample requirement of traditional discriminant analysis techniques, a sample-size dependent negative-log-likelihood (NLL) is introduced. This new technique is designed for automatically dealing with small-sample applications, large-sample applications, and unbalanced-sample applications. (5) The execution of the HDR method is fast, due to the empirical logarithmic time complexity of the HDR algorithm. Although the method is applicable to any data, we report the experimental results for three types of data: synthetic data for examining the near-optimal performance, large raw face-image databases, and traditional databases with manually selected features along with a comparison with some major existing methods.

Logistic Regression for Feature Selection and Soft Classification of Remote Sensing Data

Abstract: Feature selection is a key task in remote sensing data processing, particularly in case of classification from hyperspectral images. A logistic regression (LR) model may be used to predict the probabilities of the classes on the basis of the input features, after ranking them according to their relative importance. In this letter, the LR model is applied for both the feature selection and the classification of remotely sensed images, where more informative soft classifications are produced naturally. The results indicate that, with fewer restrictive assumptions, the LR model is able to reduce the features substantially without any significant decrease in the classification accuracy of both the soft and hard classifications