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Linear discriminant analysis (LDA) has been proven to be effective in dimensionality reduction. However, the performance of LDA depends on the consistency assumption of the global structure and the local structure. Some work extended LDA along this line of research and proposed local formulations of LDA. Unfortunately, the learning scheme of these algorithms is suboptimal in that the intrinsic relationship between data points is pre-learned in the original space, which is usually affected by the noise and redundant features. Besides, the time cost is relatively high. To alleviate these drawbacks, we propose a Fast Locality Discriminant Analysis framework (FLDA), which has three advantages: (1) It can divide a non-Gaussian distribution class into many sub-blocks that obey Gaussian distributions by using the anchor-based strategy. (2) It captures the manifold structure of data by learning the fuzzy membership relationship between data points and the corresponding anchor points, which can reduce computation time. (3) The weights between data points and anchor points are adaptively updated in the subspace where the irrelevant information and the noise in high-dimensional space have been effectively suppressed. Extensive experiments on toy data sets, UCI benchmark data sets and imbalanced data sets demonstrate the efficiency and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The purpose of this study was to implement principal component analysis (PCA) on videocapsule endoscopy (VE) images to develop a new computerized tool for celiac disease recognition. Three PCA algorithms were implemented for feature extraction and sparse representation. A novel strip PCA (SPCA) with nongreedy L1-norm maximization is proposed for VE image analysis. The extracted principal components were interpreted by a non-parametric k-nearest neighbor (k-NN) method for automated celiac disease classification. A benchmark dataset of 460 images (240 from celiac disease patients with small intestinal villous atrophy versus 220 control patients lacking villous atrophy) was constructed from the clinical VE series. It was found that the newly developed SPCA with nongreedy L1-norm maximization was most efficient for computerized celiac disease recognition, having a robust performance with an average recognition accuracy of 93.9 percent. Furthermore, SPCA also has a reduced computation time as compared with other methods. Therefore, it is likely that SPCA will be a helpful adjunct for the diagnosis of celiac disease. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) is one of commonly used supervised subspace learning methods. However, LDA will be powerless faced with the no-label situation. In this paper, the unsupervised LDA (Un-LDA) is proposed and first formulated as a seamlessly unified objective optimization which guarantees convergence during the iteratively alternative solving process. The objective optimization is in both the ratio trace and the trace ratio forms, forming a complete framework of a new approach to jointly clustering and unsupervised subspace learning. The extension of LDA into Un-LDA enables to not only complete unsupervised subspace learning via the explicitly presented subspace projection matrix but also simultaneously finish clustering and even clustering out-of-sample data via the explicitly presented transformation matrix. To overcome the difficulty in solving the non-convex objective optimization, we mathematically prove that the Un-LDA optimization in both forms can be transformed into the simple K-means clustering optimization when the subspace is determined. The Un-LDA optimization is eventually completed by alternatively optimizing the clusters using K-means and the subspace using the supervised LDA methods and iterating this whole process until convergence or stopping criterion. The experiments demonstrate that our proposed Un-LDA algorithms are comparable or even much superior to the counterparts. [ABSTRACT FROM AUTHOR]