Null Linear Discriminant Analysis Research Articles

Application of Near-Infrared Spectroscopy and Fuzzy Improved Null Linear Discriminant Analysis for Rapid Discrimination of Milk Brands.

The quality of milk is tightly linked to its brand. A famous brand of milk always has good quality. Therefore, this study seeks to design a new fuzzy feature extraction method, called fuzzy improved null linear discriminant analysis (FiNLDA), to cluster the spectra of collected milk for identifying milk brands. To elevate the classification accuracy, FiNLDA was applied to process the near-infrared (NIR) spectra of milk acquired by the portable near-infrared spectrometer. The principal component analysis and Savitzky-Golay (SG) filtering algorithm were employed to lower dimensionality and eliminate noise in this system, respectively. Thereafter, improved null linear discriminant analysis (iNLDA) and FiNLDA were applied to attain the discriminant information of the NIR spectra. At last, the K-nearest neighbor classifier was utilized for assessing the performance of the identification system. The results indicated that the maximum classification accuracies of LDA, iNLDA and FiNLDA were 74.7%, 88% and 94.67%, respectively. Accordingly, the portable NIR spectrometer in combination with FiNLDA can classify milk brands correctly and effectively.

A theoretical contribution to the fast implementation of null linear discriminant analysis with random matrix multiplication

SummaryThe null linear discriminant analysis method is a competitive approach for dimensionality reduction. The implementation of this method, however, is computationally expensive. Recently, a fast implementation of null linear discriminant analysis method was proposed in the paper of Sharma et al. In this method, a random matrix multiplication with scatter matrix is used to produce the orientation matrix. In this paper, we consider whether the random matrix can be replaced by an arbitrary full rank matrix of appropriate size, and focus on the necessary and sufficient condition to guarantee full column rank of the orientation matrix. We investigate how to choose the matrix properly, such that the two criteria of the null linear discriminant analysis method are satisfied. Furthermore, we give a necessary and sufficient condition to guarantee full column rank of the orientation matrix, and describe the geometric characterization of this condition. Numerical experiments justify our theoretical analysis. Copyright © 2015 John Wiley & Sons, Ltd.

A new perspective to null linear discriminant analysis method and its fast implementation using random matrix multiplication with scatter matrices

Null linear discriminant analysis (LDA) method is a popular dimensionality reduction method for solving small sample size problem. The implementation of null LDA method is, however, computationally very expensive. In this paper, we theoretically derive the null LDA method from a different perspective and present a computationally efficient implementation of this method. Eigenvalue decomposition (EVD) of ST^+SB (where SB is the between-class scatter matrix and ST^+ is the pseudoinverse of the total scatter matrix ST) is shown here to be a sufficient condition for the null LDA method. As EVD of ST^+SBis computationally expensive, we show that the utilization of random matrix together with ST^+SB is also a sufficient condition for null LDA method. This condition is used here to derive a computationally fast implementation of the null LDA method. We show that the computational complexity of the proposed implementation is significantly lower than the other implementations of the null LDA method reported in the literature. This result is also confirmed by conducting classification experiments on several datasets.

Improved nearest centroid classifier with shrunken distance measure for null LDA method on cancer classification problem

Null linear discriminant analysis (LDA) is a well-known dimensionality reduction technique for the small sample size problem. When the null LDA technique projects the samples to a lower dimensional space, the covariance matrices of individual classes become zero, i.e. all the projected vectors of a given class merge into a single vector. In this case, only the nearest centroid classifier (NCC) can be applied for classification. To improve the classification performance of NCC in the reduced-dimensional space, a shrunken distance based NCC technique is proposed that uses class-conditional a priori probabilities for distance computation. Experiments on several DNA microarray gene expression datasets using the proposed technique show very encouraging results for cancer classification.