Fisher Linear Discriminant Analysis and Connectionist Model for Efficient Image Recognition

In this study, the relationship between weathering and glass type, decoration and colour was first analysed using Goodman and Kruskal's tau-y coefficients, and a chi-squared test was performed, which showed that weathering was most influenced by glass type, and was influenced by glass decoration but very little by glass colour. A Fisher linear discriminant analysis model was then established, and the eight chemical components with the greatest correlation to artefact type were calculated using SPSS software under the conditions of the two glass types respectively, and optimised using a grey correlation algorithm with specified thresholds for screening components, resulting in four final elements affecting high potassium glass as potassium oxide, magnesium oxide, iron oxide and copper oxide, and affecting lead and barium types as calcium oxide, aluminium oxide, lead oxide and barium oxide, aluminium oxide, lead oxide, barium oxide and strontium oxide.

Near infrared reflectance spectroscopy was used to discriminate different species of freshwater fish samples. Samples from seven freshwater fish species of the family Cyprinidae (black carp ( Mylopharyngodon piceus), grass carp ( Ctenopharyngodon idellus), silver carp ( Hypophthalmichthys molitrix), bighead carp ( Aristichthys nobilis), common carp ( Cyprinus carpio), crucian ( Carassius auratus), and bream ( Parabramis pekinensis)) were scanned by near infrared reflectance spectroscopy from 1000 nm to 1799 nm. Linear discriminant analysis models were built for the classification of species. We inspected the effect of partial least square, principal component analysis, competitive adaptive reweighted sampling, and fast Fourier transform on linear discriminant analysis. The results showed that the dimension reduction methods worked very well for this example. Linear discriminant analysis models which were combined with principal component analysis and fast Fourier transform could classify accurately all the samples under multiplicative scatter correction pre-processing. According to the loadings in principal component analysis, spectra wavelengths 1000, 1001, 1154, 1208, 1284, 1288, 1497, 1665, and 1770 nm were selected as effective wavelengths in linear discriminant analysis. The discriminant analysis was simplified by using effective wavelengths as independent variables in a linear discriminant analysis model. This study indicated that linear discriminant analysis combined with near infrared reflectance spectroscopy could be an effective strategy for the classification of freshwater fish species.

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

In order to increase the accuracy and performance of classification models, the quality of data must be guaranteed. There are various factors that affect the quality of these data, such as measurement accuracy, missing value, and sampling biases. This study focuses on the robustness of the classification model for mislabeled data. The reason we are interested in mislabeled data is that it significantly degrades the performance of the model more than other common measurement errors. In this study, the efficiency of various classification methods for data with mislabels is reviewed. Fisher's linear discriminant analysis model (LDA), quadratic discriminant analysis model (QDA), and logistic regression model were considered in the statistical model-based method, and SVM (support vector machine) and boosting are compared in the algorithm-based method. As a result of simulation study, it is found that the statistical model based approaches show better results in terms of robustness in the data assuming various situations of mislabels.

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.

Fisher linear discriminant analysis (FLDA) is a classic linear feature extraction and dimensionality reduction approach for face recognition. It is known that geometric distribution weight information of image data plays an important role in machine learning approaches. However, FLDA does not employ the geometric distribution weight information of facial images in the training stage. Hence, its recognition accuracy will be affected. In order to enhance the classification power of FLDA method, this paper utilizes radial basis function (RBF) with fractional order to model the geometric distribution weight information of the training samples and proposes a novel geometric distribution weight information based Fisher discriminant criterion. Subsequently, a geometric distribution weight information based LDA (GLDA) algorithm is developed and successfully applied to face recognition. Two publicly available face databases, namely, ORL and FERET databases, are selected for evaluation. Compared with some LDA-based algorithms, experimental results exhibit that our GLDA approach gives superior performance.

Common vector approach and its combination with GMM for text-independent speaker recognition

In this paper, a new Face image classification or Recognition method based on Two Dimensional Discrete Cosine Transform (2D - DCT) with Linear Discriminant Analysis (LDA) and Probabilistic Neural Network (PNN) is proposed. This method consists of three steps, i) Transformation of images from special to frequency domain using Two dimensional discrete cosine transform ii) Feature extraction using Linear Discriminant Analysis and iii) classification using Probabilistic Neural Network. Linear Discriminant Analysis searches the directions for maximum discrimination of classes in addition to dimensionality reduction. Combination of Two Dimensional Discrete Cosine transform and Linear Discriminant Analysis is used for improving the capability of Linear Discriminant Analysis when few samples of images are available. Probabilistic Neural network (PNN) is a promising tool and gives fast and accurate classification of face images. Evaluation was performed on two face data bases. First database of 400 face images from AT&T (ORL) face database, and the second database of thirteen students are taken. The proposed method gives fast and better recognition rate when compared to other classifiers. The main advantage of this method is its high speed processing capability and low computational requirements in terms of both speed and memory utilizations.

Small sample image recognition using improved Convolutional Neural Network

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.

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.