Complete Linear Discriminant Analysis Research Articles

Geographical origin discrimination of black beans using near-infrared (NIR) spectroscopy combined with fuzzy regularized complete linear discriminant analysis (FRCLDA)

Black beans from different geographical origins exhibit variations in terms of their nutritional and economic values. Therefore, ensuring traceability of the geographical origin of black beans is essential for both consumers and the product processing industries. The study designed a comprehensive black bean origin identification model using near-infrared (NIR) spectroscopy combined with discriminant analysis algorithms. To enhance the performance of the model, this study incorporated fuzzy logic into regularized complete linear discriminant analysis (RCLDA) and proposed the fuzzy regularized complete linear discriminant analysis (FRCLDA). This innovative approach aims to extract additional information from overlapping NIR spectra of black beans. NIR spectra of black beans from five locations were collected employing a portable near-infrared spectrometer. In the preprocessing stage, the Savitzky–Golay (SG) and mean centering (MC) were applied to process the raw spectra. Subsequently, complete linear discriminant analysis (CLDA), RCLDA, and FRCLDA were utilized to extract the information from the processed data. Finally, k-nearest neighbor (KNN), support vector machines (SVM), and extreme learning machine (ELM) were employed to classify the black bean samples based on the extracted features. The results indicated that KNN achieved the best classification performance. The FRCLDA-KNN model achieved the exceptional performance with a classification accuracy of 99.23% on the test set. Therefore, the system demonstrates satisfactory accuracy and performance in accurately identifying black beans from different geographical origins.

Regularized complete linear discriminant analysis

Linear discriminant analysis (LDA) searches for a linear transformation that maximizes class separability in a reduced dimensional space. Because LDA requires the within-class scatter matrix to be non-singular, it cannot be directly applied to small sample size (SSS) problems in which the number of available training samples is smaller than the dimensionality of the sample space. To solve SSS problems, this paper develops a system of regularized complete linear discriminant analysis (RCLDA). In RCLDA, two regularized criteria are used to derive discriminant vectors that include “regular” and “irregular” discriminant vectors in the range space and null space, respectively, of the within-class scatter matrix. Extensive experiments on the SSS problem of image recognition are performed to evaluate the proposed algorithm in terms of classification accuracy, and the experimental results demonstrate its effectiveness.

Complexity-reduced implementations of complete and null-space-based linear discriminant analysis

Dimensionality reduction has become an important data preprocessing step in a lot of applications. Linear discriminant analysis (LDA) is one of the most well-known dimensionality reduction methods. However, the classical LDA cannot be used directly in the small sample size (SSS) problem where the within-class scatter matrix is singular. In the past, many generalized LDA methods has been reported to address the SSS problem. Among these methods, complete linear discriminant analysis (CLDA) and null-space-based LDA (NLDA) provide good performances. The existing implementations of CLDA are computationally expensive. In this paper, we propose a new and fast implementation of CLDA. Our proposed implementation of CLDA, which is the most efficient one, is equivalent to the existing implementations of CLDA in theory. Since CLDA is an extension of null-space-based LDA (NLDA), our implementation of CLDA also provides a fast implementation of NLDA. Experiments on some real-world data sets demonstrate the effectiveness of our proposed new CLDA and NLDA algorithms.

Incremental learning of complete linear discriminant analysis for face recognition

The complete linear discriminant analysis (CLDA) algorithm has been successfully employed for face recognition. The CLDA method can make full use of the discriminant information of the training samples. However, CLDA suffers from the scalability problem. In this paper, we propose an incremental CLDA (ICLDA) to overcome this limitation. We first propose a new implementation of CLDA in which two steps of QR decomposition, rather than singular value decomposition (SVD), are used to get the orthonormal bases of the range and null spaces of the within-class scatter matrix. Then, by using efficient QR-updating technique, we propose the ICLDA method which can accurately incrementally update the discriminant vectors of CLDA instead of recomputing the CLDA again. Experiments on PIE and FERET face databases show the efficiency of our proposed CLDA algorithms over the original implementation of CLDA.

Incremental complete LDA for face recognition

The complete linear discriminant analysis (CLDA) algorithm has been proven to be an effective tool for face recognition. The CLDA method can make full use of the discriminant information of the training samples. However, the original implementation of CLDA may not suitable for incremental learning problem. In this paper, we first propose a new implementation of CLDA, which is theoretically equivalent to the original implementation of CLDA but is more efficient than the original one. Then, based on our proposed novel implementation of CLDA, we propose the incremental CLDA method which can accurately update the discriminant vectors of CLDA when new samples are inserted into the training set. Experiments on ORL, AR and PIE face databases show the efficiency of our proposed CLDA algorithms over the original implementation of CLDA.

FUSING GLOBAL AND LOCAL COMPLETE LINEAR DISCRIMINANT FEATURES BY FUZZY INTEGRAL FOR FACE RECOGNITION

Face recognition becomes very difficult in a complex environment, and the combination of multiple classifiers is a good solution to this problem. A novel face recognition algorithm GLCFDA-FI is proposed in this paper, which fuses the complementary information extracted by complete linear discriminant analysis from the global and local features of a face to improve the performance. The Choquet fuzzy integral is used as the fusing tool due to its suitable properties for information aggregation. Experiments are carried out on the CAS-PEAL-R1 database, the Harvard database and the FERET database to demonstrate the effectiveness of the proposed method. Results also indicate that the proposed method GLCFDA-FI outperforms five other commonly used algorithms — namely, Fisherfaces, null space-based linear discriminant analysis (NLDA), cascaded-LDA, kernel-Fisher discriminant analysis (KFDA), and null-space based KFDA (NKFDA).

A Multiple Maximum Scatter Difference Discriminant Criterion for Facial Feature Extraction

Maximum scatter difference (MSD) discriminant criterion was a recently presented binary discriminant criterion for pattern classification that utilizes the generalized scatter difference rather than the generalized Rayleigh quotient as a class separability measure, thereby avoiding the singularity problem when addressing small-sample-size problems. MSD classifiers based on this criterion have been quite effective on face-recognition tasks, but as they are binary classifiers, they are not as efficient on large-scale classification tasks. To address the problem, this paper generalizes the classification-oriented binary criterion to its multiple counterpart--multiple MSD (MMSD) discriminant criterion for facial feature extraction. The MMSD feature-extraction method, which is based on this novel discriminant criterion, is a new subspace-based feature-extraction method. Unlike most other subspace-based feature-extraction methods, the MMSD computes its discriminant vectors from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix. The MMSD is theoretically elegant and easy to calculate. Extensive experimental studies conducted on the benchmark database, FERET, show that the MMSD out-performs state-of-the-art facial feature-extraction methods such as null space method, direct linear discriminant analysis (LDA), eigenface, Fisherface, and complete LDA.