Two-Stage Regularized Linear Discriminant Analysis for 2-D Data.

Boosting is a general method for improving the accuracy of any given learning algorithm. In this paper, we have proposed the boosting method for face recognition (FR) that improves the linear discriminant analysis (LDA)-based technique. The improvement is achieved by incorporating the regularized LDA (R-LDA) technique into the boosting framework. R-LDA is based on a new regularized Fisher’s discriminant criterion, which is particularly robust against the small sample size problem compared to the traditional one used in LDA. The AdaBoost technique is utilized within this framework to generalize a set of simple FR subproblems and their corresponding LDA solutions and combines the results from the multiple, relatively weak, LDA solutions to form a strong solution. The comparative experimental result on FERET database demonstrates that the proposed boosting method achieves more accurate results over the individual algorithms.

Although mostly used for pattern classification, linear discriminant analysis (LDA) may also be used for feature selection. When employed to select genes for microarray data, which has high dimensionality and small sample size, LDA encounters three problems, including singularity of scatter matrix, overfitting and prohibitive computational complexity. In this study, we propose a new regularization technique to address the singularity and overfitting problem. In addition, we develop a recursive implementation for LDA to reduce computational overhead. Experimental studies on 5 gene microarray problems show that the regularized linear discriminant analysis (RLDA) and its recursive implementation produce gene subsets with excellent classification performance.

A new face recognition method is proposed in this paper. The proposed method is based on fuzzy regularized linear discriminant analysis (FR-LDA) and combines the regularized linear discriminant analysis (R-LDA) and the fuzzy set theory. R-LDA is based on a new regularized Fisher's discriminant criterion, which is particularly robust against the small sample size problem compared to the traditional one used in LDA. In the proposed method, we calculate the membership degree matrix by Fuzzy K-nearest neighbor (FKNN) and then incorporate the membership degree into the definition of the between-class and within-class scatter matrices and get the fuzzy between-class and within-class scatter matrices. Experimental results obtained on the FERET database demonstrate that the proposed method improves the classification rate performance.

A fundamental question in neuroscience is how sensory signals are decoded from noisy cortical activity. We address this question in the olfactory system, decoding the route by which odorants arrive into the nasal cavity: through the nostrils (orthonasal), or through the back of the throat (retronasal). We recently showed with modeling and novel experiments on anesthetized rats that orthonasal versus retronasal modality information is encoded in the olfactory bulb (OB, a pre-cortical region). However, key questions remain: is modality information transmitted from OB to anterior piriform cortex (aPC)? How can this information be extracted from a much noisier cortical population with overall less firing? With simultaneous spike recordings of populations of neurons in OB and aPC, we show that an unsupervised and biologically plausible algorithm, Shared Covariance Decoding (SCD), can indeed linearly encode modality in low dimensional subspaces. Specifically, SCD improves encoding of ortho/retro in aPC compared to Fisher's linear discriminant analysis (LDA). Consistent with our theoretical analysis, when noise correlations between OB and aPC are low and OB well-encodes modality, modality in aPC tends to be encoded optimally with SCD. We observe that with several algorithms (LDA, SCD, optimal) the decoding accuracy distributions are invariant when GABA[Formula: see text] (ant-)agonists (bicuculline and muscimol) are applied to OB, which is consistent with invariance in population firing in aPC. Overall, we show modality information can be encoded efficiently in piriform cortex.

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.

Background The diagnosis of chronic rhinosinusitis (CRS) is a complicated procedure. An electronic nose (eNose) is a novel method that detects disease from gas-phase mixtures, such as human breath. Aims/Objectives To determine whether an eNose based on differential mobility spectrometry (DMS) can detect chronic rhinosinusitis without nasal polyps (CRSsNP) by analyzing aspirated nasal air. Materials and methods Adult patients with CRSsNP were examined. The control group consisted of patients with septal deviation. Nasal air was aspirated into a collection bag and analyzed with DMS. The DMS data were classified using regularized linear discriminant analysis (LDA) models with 10-fold cross-validation. Results The accuracy of the DMS to distinguish CRSsNP from patients with septal deviation was 69%. Sensitivity and specificity were 67 and 70%, respectively. Bonferroni-corrected statistical differences were clearly noted. When a subgroup with more severe inflammatory disease was compared to controls, the classification accuracy increased to 82%. Conclusions The results of this feasibility study demonstrate that CRSsNP can potentially be differentiated distinguished from patients with similar nasal symptoms by analyzing the aspirated nasal air using DMS. Further research is warranted to evaluate the ability of this novel method in the differential diagnostics of CRS.

Hyperspectral image based automatic target recognition (ATR) systems often project the high dimensional hyperspectral reflectance signatures onto a lower dimensional subspace using techniques such as principal components analysis (PCA), Fisher's linear discriminant analysis (LDA) and stepwise LDA. In a general classification framework, these projections are sub-optimal, and in the absence of sufficient training data, are likely to be ill conditioned. In recent work, the authors proposed a divide and conquer approach that partitions the hyperspectral space into contiguous subspaces followed by multi-classifiers and decision fusion. Although this technique alleviated the small sample size problem and provided a good recognition performance in light and moderate pixel mixing, the performance significantly decreased under severe mixing conditions, as does with conventional ATR techniques. In this work, the authors propose a kernel discriminant analysis based projection in each subspace of the partition, followed by the multi-classifier, decision fusion framework to ensure robust recognition even in severe pixel mixing conditions. The performance of the proposed system (as measured by overall target recognition accuracies) is greatly superior to conventional dimensionality reduction techniques, as well as the more recently proposed divide-and-conquer technique.

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.

Face recognition using direct, weighted linear discriminant analysis and modular subspaces

Hyperspectral-based automatic target recognition (ATR) and classification systems often project the high-dimensional hyperspectral reflectance signatures onto a lower dimensional subspace using techniques such as principal component analysis, Fisher's linear discriminant analysis (LDA), and stepwise LDA. In a general classification framework, these projections are suboptimal and, in the absence of sufficient training data, are likely to be ill conditioned. In recent work, the authors proposed a divide-and-conquer approach that partitions the hyperspectral space into contiguous subspaces followed by a multiclassifier and decision-fusion (MCDF) framework. Although this technique alleviated the small-sample-size problem and provided a good recognition performance in light and moderate pixel mixing, the performance significantly decreased under severe mixing conditions, as it does with conventional ATR techniques. In this letter, the authors propose a kernel discriminant analysis-based projection in each subspace of the partition, followed by the MCDF framework to ensure robust recognition even in severe pixel-mixing conditions. The performance of the proposed system (as measured by overall recognition accuracies) is greatly superior to conventional dimensionality-reduction techniques as well as the more recently proposed LDA-based MCDF technique.

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

Face recognition using direct, weighted linear discriminant analysis and modular subspaces

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.