• The Journal of Korean Institute of Communications and Information Sciences
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• v.38C no.2
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• pp.208-212
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• 2013

Due to the singularity of the within-class scatter, linear discriminant analysis (LDA) becomes ill-posed for small sample size (SSS) problems. An extension of LDA, the null space-based LDA (NLDA) provides good discriminant performances for SSS problems. In this paper, by applying the Lagrange technique, the procedure of transforming the problem of finding the feature extractor of NLDA into a linear equation problem is derived.

• ETRI Journal
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• v.31 no.4
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• pp.438-447
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• 2009

In this paper, a novel image projection technique for face recognition application is proposed which is based on linear discriminant analysis (LDA) combined with the relevance-weighted (RW) method. The projection is performed through 2-directional and 2-dimensional LDA, or $(2D)^2$LDA, which simultaneously works in row and column directions to solve the small sample size problem. Moreover, a weighted discriminant hyperplane is used in the between-class scatter matrix, and an RW method is used in the within-class scatter matrix to weigh the information to resolve confusable data in these classes. This technique is called the relevance-weighted $(2D)^2$LDA, or RW$(2D)^2$LDA, which is used for a more accurate discriminant decision than that produced by the conventional LDA or 2DLDA. The proposed technique has been successfully tested on four face databases. Experimental results indicate that the proposed RW$(2D)^2$LDA algorithm is more computationally efficient than the conventional algorithms because it has fewer features and faster times. It can also improve performance and has a maximum recognition rate of over 97%.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4502-4518
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• 2015

Fisher linear discriminant analysis (LDA) is one of the most popular projection techniques for feature extraction and has been widely applied in face recognition. However, it cannot be used when encountering the single sample per person problem (SSPP) because the intra-class variations cannot be evaluated. In this paper, we propose a novel method called local similarity based linear discriminant analysis (LS_LDA) to solve this problem. Motivated by the "divide-conquer" strategy, we first divide the face into local blocks, and classify each local block, and then integrate all the classification results to make final decision. To make LDA feasible for SSPP problem, we further divide each block into overlapped patches and assume that these patches are from the same class. To improve the robustness of LS_LDA to outliers, we further propose local similarity based median discriminant analysis (LS_MDA), which uses class median vector to estimate the class population mean in LDA modeling. Experimental results on three popular databases show that our methods not only generalize well SSPP problem but also have strong robustness to expression, illumination, occlusion and time variation.

• Journal of the Korean Statistical Society
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• v.30 no.2
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• pp.193-217
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• 2001

Despite of the rich literature in discriminant analysis, this complicated subject remains much to be explored. In this article, we study the theoretical foundation that supports Fisher's linear discriminant analysis (LDA) by setting up the classification problem under the dimension reduction framework as in Li(1991) for introducing sliced inverse regression(SIR). Through the connection between SIR and LDA, our theory helps identify sources of strength and weakness in using CRIMCOORDS(Gnanadesikan 1977) as a graphical tool for displaying group separation patterns. This connection also leads to several ways of generalizing LDA for better exploration and exploitation of nonlinear data patterns.

• MALSORI
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• no.44
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• pp.105-113
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• 2002

In Korean, each digit is monosyllable and some pairs are known to have high confusability, causing performance degradation of connected digit recognition systems. To improve the performance, in this paper, we employ various discriminant analyses (DA) including Linear DA (LDA), Weighted Pairwise Scatter LDA WPS-LDA), Heteroscedastic Discriminant Analysis (HDA), and Maximum Likelihood Linear Transformation (MLLT). We also examine several combinations of various DA for additional performance improvement. Experimental results show that applying any DA mentioned above improves the string accuracy, but the amount of improvement of each DA method varies according to the model complexity or number of mixtures per state. Especially, more than 20% of string error reduction is achieved by applying MLLT after WPS-LDA, compared with the baseline system, when class level of DA is defined as a tied state and 1 mixture per state is used.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.22 no.1
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• pp.125-130
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• 2018

Linear discriminant analysis is a statistical analysis method that is generally used for dimensionality reduction of the feature vectors or for class classification. However, in the case of a data set that cannot be linearly separated, it is possible to make a linear separation by mapping a feature vector into a higher dimensional space using a nonlinear function. This method is called generalized discriminant analysis or kernel discriminant analysis. In this paper, we carried out target classification experiments with active sonar target signals available on the Internet using both liner discriminant and generalized discriminant analysis methods. Experimental results are analyzed and compared with discussions. For 104 test data, LDA method has shown correct recognition rate of 73.08%, however, GDA method achieved 95.19% that is also better than the conventional MLP or kernel-based SVM.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.21-37
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• 2021

There is a direct connection between linear discriminant analysis (LDA) and linear regression since the direction vector of the LDA can be obtained by the least square estimation. The connection motivates the penalized LDA when the model is high-dimensional where the number of predictive variables is larger than the sample size. In this paper, we study the penalized LDA for a class of penalties, called the moderately clipped LASSO (MCL), which interpolates between the least absolute shrinkage and selection operator (LASSO) and minimax concave penalty. We prove that the MCL penalized LDA correctly identifies the sparsity of the Bayes direction vector with probability tending to one, which is supported by better finite sample performance than LASSO based on concrete numerical studies.

• Journal of the Optical Society of Korea
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• v.12 no.2
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• pp.88-92
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• 2008

This paper discusses a photon-counting linear discriminant analysis (LDA) with computational integral imaging (II). The computational II method reconstructs three-dimensional (3D) objects on the reconstruction planes located at arbitrary depth-levels. A maximum likelihood estimation (MLE) can be used to estimate the Poisson parameters of photon counts in the reconstruction space. The photon-counting LDA combined with the computational II method is developed in order to classify partially occluded objects with photon-limited images. Unknown targets are classified with the estimated Poisson parameters while reconstructed irradiance images are trained. It is shown that a low number of photons are sufficient to classify occluded objects with the proposed method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.250-255
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• 2012

Face recognition has wide applications in security and surveillance systems as well as in robot vision and machine interfaces. Conventional challenges in face recognition include pose, illumination, and expression, and face recognition at a distance involves additional challenges because long-distance images are often degraded due to poor focusing and motion blurring. This study investigates the effectiveness of applying photon-counting linear discriminant analysis (Pc-LDA) to face recognition in harsh environments. A related technique, Fisher linear discriminant analysis, has been found to be optimal, but it often suffers from the singularity problem because the number of available training images is generally much smaller than the number of pixels. Pc-LDA, on the other hand, realizes the Fisher criterion in high-dimensional space without any dimensionality reduction. Therefore, it provides more invariant solutions to image recognition under distortion and degradation. Two decision rules are employed: one is based on Euclidean distance; the other, on normalized correlation. In the experiments, the asymptotic equivalence of the photon-counting method to the Fisher method is verified with simulated data. Degraded facial images are employed to demonstrate the robustness of the photon-counting classifier in harsh environments. Four types of blurring point spread functions are applied to the test images in order to simulate long-distance acquisition. The results are compared with those of conventional Eigen face and Fisher face methods. The results indicate that Pc-LDA is better than conventional facial recognition techniques.

• The Journal of the Korea Contents Association
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• v.5 no.6
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• pp.41-48
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• 2005

This paper presents a face recognition method based on the combination of well-known statistical representations of Principal Component Analysis(PCA), and Linear Discriminant Analysis(LDA) with Radial Basis Function Networks. The original face image is first processed by PCA to reduce the dimension, and thereby avoid the singularity of the within-class scatter matrix in LDA calculation. The result of PCA process is applied to LDA classifier. In the second approach, the LDA process Produce a discriminational features of the face image, which is taken as the input of the Radial Basis Function Network(RBFN). The proposed approaches has been tested on the ORL face database. The experimental results have been demonstrated, and the recognition rate of more than 93.5% has been achieved.