Constrained Linear Discriminant Analysis Research Articles

Online discriminative component analysis feature extraction from stream data with domain knowledge

In this paper, we introduce an incremental version of recently proposed constrained Linear Discriminant Analysis (LDA). In addition of application in constrained LDA problems, our algorithm which we call Online Discriminative Component Analysis (ODCA) is usable in standard incremental LDA problems. ODCA incrementally computes the solution of LDA with the time complexity lower than most incremental algorithm for LDA while keeps the accuracy of final result as close as possible to offline version. This is done using a special formulation for the scatter matrix updating along with Eigen-space calculation. By exploiting such formulation, the proposed algorithm made capable of updating the solution where a data point added or removed from the problem. It is also usable in problems where its data points have concept drift property. To show efficiency of proposed algorithm, its speed is compared to other existing incremental algorithms as order of complexity. In addition, the classification accuracy of our approach is experimentally compared to other algorithms.

Feature selection based on linear discriminant analysis

The paper proposed a new approach of feature selection based on Constrained Linear Discriminant Analysis(CLDA),which modeled feature selection as a search problem in subspace and made optimal solution subject to some restrictions.Furthermore,CLDA optimization problem was transformed into a process of scoring and sorting features.Experiments on UCI machine learning repository and Reuters-21578 dataset show that the proposed approach can consistently obtain better results with fewer features than that with all features.

Unsupervised real-time constrained linear discriminant analysis to hyperspectral image classification

We have proposed a constrained linear discriminant analysis (CLDA) approach for classifying the remotely sensed hyperspectral images. Its basic idea is to design an optimal linear transformation operator which can maximize the ratio of inter-class to intra-class distance while satisfying the constraint that the different class centers after transformation are aligned along different directions. Its major advantage over the traditional Fisher's linear discriminant analysis is that the classification can be achieved simultaneously with the transformation. The CLDA is a supervised approach, i.e., the class spectral signatures need to be known a priori. But, in practice, these informations may be difficult or even impossible to obtain. So in this paper we will extend the CLDA algorithm into an unsupervised version, where the class spectral signatures are to be directly generated from an unknown image scene. Computer simulation is used to evaluate how well the algorithm performs in terms of finding the pure signatures. We will also discuss how to implement the unsupervised CLDA algorithm in real-time for resolving the critical situations when the immediate data analysis results are required.

Implementation of real-time constrained linear discriminant analysis to remote sensing image classification

In this paper, we investigate the practical implementation issues of the real-time constrained linear discriminant analysis (CLDA) approach for remotely sensed image classification. Specifically, two issues are to be resolved: (1) what is the best implementation scheme that yields lowest chip design complexity with comparable classification performance, and (2) how to extend CLDA algorithm for multispectral image classification. Two limitations about data dimensionality have to be relaxed. One is in real-time hyperspectral image classification, where the number of linearly independent pixels received for classification must be larger than the data dimensionality (i.e., the number of spectral bands) in order to generate a non-singular sample correlation matrix R for the classifier, and relaxing this limitation can help to resolve the aforementioned first issue. The other is in multispectral image classification, where the number of classes to be classified cannot be greater than the data dimensionality, and relaxing this limitation can help to resolve the aforementioned second issue. The former can be solved by introducing a pseudo inverse initiate of sample correlation matrix for R - 1 adaptation, and the latter is taken care of by expanding the data dimensionality via the operation of band multiplication. Experiments on classification performance using these modifications are conducted to demonstrate their feasibility. All these investigations lead to a detailed ASIC chip design scheme for the real-time CLDA algorithm suitable to both hyperspectral and multispectral images. The proposed techniques to resolving these two dimensionality limitations are instructive to the real-time implementation of several popular detection and classification approaches in remote sensing image exploitation.

Real-time constrained linear discriminant analysis to target detection and classification in hyperspectral imagery

In this paper, we present a constrained linear discriminant analysis (CLDA) approach to hyperspectral image detection and classification as well as its real-time implementation. The basic idea of CLDA is to design an optimal transformation matrix which can maximize the ratio of inter-class distance to intra-class distance while imposing the constraint that different class centers after transformation are along different directions such that different classes can be better separated. The solution turns out to be a constrained version of orthogonal subspace projection (OSP) implemented with a data whitening process. The CLDA approach can be applied to solve both detection and classification problems. In particular, by introducing color for display the classification is achieved with a single classified image where a pre-assigned color is used to display a specified class. The real-time implementation is also developed to meet the requirement of on-line image analysis when the immediate data assessment is critical. The experiments using HYDICE data demonstrate the strength of CLDA approach in discriminating the targets with subtle spectral difference.