Geometric Distribution Weight Information Modeled Using Radial Basis Function with Fractional Order for Linear Discriminant Analysis Method

A new face recognition method via semi-discrete decomposition for one sample problem

In this paper, we investigate the application of Fisher’s linear discriminant analysis (FLDA) to hyperspectral remote sensing image classification. The basic idea of FLDA is to design an optimal transform so that the classes can be well separated in the low-dimensional space. The practical difficulty of applying FLDA to hyperspectral images includes the unavailability of enough training samples and unknown information for all the classes present. So the original FLDA is modified to avoid the requirements of complete class knowledge, such as the number of actual classes present. We also investigate the performance of the class of principal component analysis (PCA) techniques prior to FLDA and find that the interference and noise adjusted PCA (INAPCA) can provide the improvement in the final classification.KeywordsFisher’s Linear Discriminant AnalysisDimensionality ReductionClassificationHyperspectral Imagery

Fisher's Linear Discriminant Analysis (LDA) is a traditional dimensionality reduction method that has been proven to be successful for decades. To enhance the LDA's power for high-dimensional pattern classification, such as face recognition, numerous LDA-extension approaches have been proposed in the literature. This paper proposes a new method that improves the performance of LDA-based classification by simply increasing the number of (sub)-classes through clustering a few of classes of the training set prior to the execution of LDA. This is based on the fact that the eigen space of the training set consists of the range space and the null space, and that the dimensionality of the range space increases as the number of classes increases. Therefore, when constructing the transformation matrix, through minimizing the null space, the loss of discriminative information resulted from this space can be minimized. To select the classes to be clustered, in the present paper, the intraset distance is employed as a criterion and the k-means clustering is performed to divide them. Our experimental results for an artificial data set of XOR-type samples and a well-known benchmark face database of Yale demonstrate that the classification efficiency of the proposed method could be improved.

In this paper, an adaptive approximation image reconstruction method based on orthogonal triangular with column pivoting (QRCP) decomposition algorithm is proposed for single sample problem in face recognition. By using QRCP the single sample and its transpose are decomposed to two sets of basis images. Then an adaptive approximation image reconstruction method is proposed to reconstruct two approximation images from the two basis image sets respectively. The single training sample and its two approximation images of each object form a new training set, which can make the fisher linear discriminant analysis (FLDA) be applied to single sample problem in face recognition. The performance of the proposed method is verified on Yale, FERET, and ORL face databases. The experimental results indicate that the proposed method is efficient and outperforms some existing methods which are proposed to overcome the single sample problem.

A computer vision system for automatic recognition and classification of five varieties of plant leaves under controlled laboratory imaging conditions, comprising: 1–Cydonia oblonga (quince), 2–Eucalyptus camaldulensis dehn (river red gum), 3–Malus pumila (apple), 4–Pistacia atlantica (mt. Atlas mastic tree) and 5–Prunus armeniaca (apricot), is proposed. 516 tree leaves images were taken and 285 features computed from each object including shape features, color features, texture features based on the gray level co-occurrence matrix, texture descriptors based on histogram and moment invariants. Seven discriminant features were selected and input for classification purposes using three classifiers: hybrid artificial neural network–ant bee colony (ANN–ABC), hybrid artificial neural network–biogeography based optimization (ANN–BBO) and Fisher linear discriminant analysis (LDA). Mean correct classification rates (CCR), resulted in 94.04%, 89.23%, and 93.99%, for hybrid ANN–ABC; hybrid ANN–BBO; and LDA classifiers, respectively. Best classifier mean area under curve (AUC), mean sensitivity, and mean specificity, were computed for the five tree varieties under study, resulting in: 1–Cydonia oblonga (quince) 0.991 (ANN–ABC), 95.89% (ANN–ABC), 95.91% (ANN–ABC); 2–Eucalyptus camaldulensis dehn (river red gum) 1.00 (LDA), 100% (LDA), 100% (LDA); 3–Malus pumila (apple) 0.996 (LDA), 96.63% (LDA), 94.99% (LDA); 4–Pistacia atlantica (mt. Atlas mastic tree) 0.979 (LDA), 91.71% (LDA), 82.57% (LDA); and 5–Prunus armeniaca (apricot) 0.994 (LDA), 88.67% (LDA), 94.65% (LDA), respectively.

In this paper a novel non-linear subspace method for face verification is proposed. The problem of face verification is considered as a two-class problem (genuine versus impostor class). The typical Fisher's linear discriminant analysis (FLDA) gives only one or two projections in a two-class problem. This is a very strict limitation to the search of discriminant dimensions. As for the FLDA for N class problems (N is greater than two) the transformation is not person specific. In order to remedy these limitations of FLDA, exploit the individuality of human faces and take into consideration the fact that the distribution of facial images, under different viewpoints, illumination variations and facial expression is highly complex and non-linear, novel kernel discriminant algorithms are proposed. The new methods are tested in the face verification problem using the XM2VTS database where it is verified that they outperform other commonly used kernel approaches.

The Fisher's linear discriminant analysis (FLDA) is a successful linear feature extraction method which aims to maximize the between-class separability and to minimize the within-class variability. In order to accomplish its goal, FLDA maximizes the Fisher's linear discriminant analysis criterion given in the paper. In this paper we first address the limitations of the classical FLDA criterion and then discuss new criterion functions which were introduced to overcome those limitations. Finally, we demonstrate the capability of the new criteria both theoretically and empirically.

Linear Discriminant Analysis (LDA) is a popular statistical method for both feature extraction and dimensionality reduction in face recognition. The major drawback of LDA is the so-called small sample size (3S) problem. This problem always occurs when the total number of training samples is smaller than the dimension of feature space. Under this situation, the within-class scatter matrix Sw becomes singular and LDA approach cannot be implemented directly. To overcome the 3S problem, this paper proposes a novel wavelet-face based subspace LDA algorithm. Wavelet-face feature extraction and dimensionality reduction are based on two-level D4-filter wavelet transform and discarding the null space of total class scatter matrix St. It is shown that our obtained projection matrix satisfies the uncorrelated constraint conditions. Hence in the sense of statistical uncorrelation, this projection matrix is optimal. The proposed method for face recognition has been evaluated with two public available databases, namely ORL and FERET databases. Comparing with existing LDA-based methods to solve the 3S problem, our method gives the best performance.

Subspace analysis is an effective technique for dimensionality reduction, which aims at finding a low-dimensional space of high-dimensional data. Fisher linear discriminant analysis (FLD) and Neural Networks are commonly used techniques of image processing and recognition. In this paper, a new scheme of image feature extraction namely, the FLD and Generalized Regression Neural Networks (GRNN) approach for image recognition is presented. Linear discriminant analysis is usually performed to investigate differences among multivariate classes, to determine which attributes discriminate between the classes, and to determine the most parsimonious way to distinguish among classes. Two-dimensional linear discriminative features and GRNN are used to perform the classification. Experiments on the image database (Face, Object and Character) demonstrate the effectiveness and feasibility of the proposed method.

An algorithm for gamma-ray identification applications has been developed and evaluated. The algorithm is based on a Fisher Linear Discriminant Analysis (FLDA) technique that generates loading coefficients that maximize the separation of a particular radionuclide from all the other radionuclides in a training library. Separate experimental data sets were obtained for the algorithms training data and for the performance evaluation. The algorithm was evaluated against a range of radionuclides and acquisitions times. An inverse square root relationship between the cluster standard deviation and its gross mean counts enabled the production of an adaptable threshold. The inverse square relationship between the Mahalanobis distance metric and the 137Cs standoff distance demonstrated a means to quantify the measured number of counts. The FLDA identification performance, for a number of threat radionuclides (including special nuclear materials), exceeded that of a commercially available peak search algorithm. The high sensitivity and specificity, of the FLDA algorithm, was maintained in low count situations. The poor performance for some radionuclides was attributed to the measured number of counts being below the minimal detectable limit. The FLDA algorithm has the potential to be used in gamma-ray identification applications and, in particular, count starved situations.

Land degradation (LD) is the decline in a land's functional capacity and productive potential, which includes various anthropogenic and natural drivers. This study focuses on three primary manifestations of LD including soil erosion, landslides, and rockfalls, which are the most prevalent in the Shaqlawa district. A set of 22 LD conditioning factors, encompassing curvature, lithology, aspect, river density, soil type, lineament density, river distance, elevation, road distance, length slope (LS), land use land cover (LULC), stream power index (SPI), valley depth, profile curvature, slope, solar radiation, road density, lineament distance, rainfall, topographic wetness index (TWI), plan curvature, and normalized difference vegetation index (NDVI), were integrated into the analysis. Variance inflation factors (VIF) and tolerance (TOL) values from linear regression indicate that most LD factors have acceptable levels of multicollinearity. The Information Gain Ratio (IGR) identified key variables TWI, NDVI, and lithology-as pivotal factors for predicting LD. Additionally, the study evaluated degradation factors using various machine learning (ML) algorithms, including random forest (RF), Naive Bayes, logistic regression, rotation forest, forest penalized attributes (FPA), and Fisher's Linear discriminant analysis (FLDA). This facilitated categorizing the study area into five susceptibility categories. The FLDA model categorized the highest area under very high degradation risk at 26.72%, emphasizing the varied insights each algorithm brought to characterizing the degradation risk. Additionally, the receiver operating characteristic curves (ROC) were employed for model validation, identifying RF as the most successful model in the training dataset with an area under the curve (AUC) of 0.882, while FLDA outperformed in the testing dataset with an AUC of 0.883. The identified LD-prone areas will help land-use planners and emergency management officials apply effective mitigation strategies for similar terrains.

A derivative of Fisher's Linear Discriminant Analysis (FLDA), named Fisherapples for the recognition of apple lesions which is not sensitive to large variations in illumination is proposed in this paper. We make use of the linear projection that is orthogonal to the within-class scatter of the apple images from a high-dimensional image space to a considerably low-dimensional image space. It separates the data-cases well, projecting away variations in lighting. Our approach maximizes the ratio of between-class scatter to that of within-class scatter of apple lesions, i.e., we can get maximal between-class distances and minimal within-class distances after projection. This implies that the gap between the classes becomes bigger and ensures optimal separability in the new space. Besides, we take advantage of Principal Component Analysis (PCA) to project the set of apple images to a lower dimensional space in order to overcome the complication of the singular within-class scatter matrix. After that, the resulting within-class scatter becomes nonsingular and subsequently we can use standard FLDA to reduce the dimension further. Consequently, it is effortless for the computer to calculate the result. Experimental results demonstrate that Fisherapples performs better in apple lesion recognition than PCA.

Driver’s condition plays a critical role in driving safety. The fact that about 20 percent of automobile accidents occurred due to driver fatigue leads to a demand for developing a method to monitor driver’s status. In this study, we acquired brain signals such as oxy- and deoxyhemoglobin and neuronal electrical activity by a hybrid fNIRS/EEG system. Experiments were conducted with 11 subjects under two conditions: Normal condition, when subjects had enough sleep, and sleep deprivation condition, when subject did not sleep previous night. During experiment, subject performed a driving task with a car simulation system for 30 minutes. After experiment, oxy-hemoglobin and deoxy-hemoglobin changes were derived from fNIRS data, while beta and alpha band relative power were calculated from EEG data. Decrement of oxy-hemoglobin, beta band power, and increment of alpha band power were found in sleep deprivation condition compare to normal condition. These features were then applied to classify two conditions by Fisher’s linear discriminant analysis (FLDA). The ratio of alpha-beta relative power showed classification accuracy with a range between 62% and 99% depending on a subject. However, utilization of both EEG and fNIRS features increased accuracy in the range between 68% and 100%. The highest increase of accuracy is from 63% using EEG to 99% using both EEG and fNIRS features. In conclusion, the enhancement of classification accuracy is shown by adding a feature from fNIRS to the feature from EEG using FLDA which provides the need of developing a hybrid fNIRS/EEG system.

Fisher linear discriminant analysis (LDA) is widely used to solve classification problems. The classical LDA is developed based on the L2-norm, which is very sensitive to outliers. In this paper, we propose a new LDA with generalized correntropic loss function (GCLF), termed as LDA-GCLF, to improve the robustness of LDA. LDA-GCLF is realized by the alternating direction method of multipliers (ADMM) and the gradient descent method. Experiments results on synthetic and real-world datasets demonstrate the effectiveness of LDA-GCLF.

Fisher linear discriminant analysis (LDA) involves within-class and between-class covariance matrices. For 2-D data such as images, regularized LDA (RLDA) can improve LDA due to the regularized eigenvalues of the estimated within-class matrix. However, it fails to consider the eigenvectors and the estimated between-class matrix. To improve these two matrices simultaneously, we propose in this paper a new two-stage method for 2-D data, namely a bidirectional LDA (BLDA) in the first stage and the RLDA in the second stage, where both BLDA and RLDA are based on the Fisher criterion that tackles correlation. BLDA performs the LDA under special separable covariance constraints that incorporate the row and column correlations inherent in 2-D data. The main novelty is that we propose a simple but effective statistical test to determine the subspace dimensionality in the first stage. As a result, the first stage reduces the dimensionality substantially while keeping the significant discriminant information in the data. This enables the second stage to perform RLDA in a much lower dimensional subspace, and thus improves the two estimated matrices simultaneously. Experiments on a number of 2-D synthetic and real-world data sets show that BLDA+RLDA outperforms several closely related competitors.