L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction.

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.

Structure–activity relationship study of oxindole-based inhibitors of cyclin-dependent kinases based on least-squares support vector machines

Tensor Rank One Discriminant Analysis—A convergent method for discriminative multilinear subspace selection

This paper aims to understand how the discriminative information of neuronal population activity evolves and accumulates over time. We present two classes of approaches namely the probability-based and response-based approaches to predict the perceptual reports of a trained macaque monkey on a single-trial basis by integrating neural signals from multiple electrodes across time. We extend the probability-based integration originally using only the quadratic discriminant analysis (QDA) by considering also the linear discriminant analysis (LDA) and logistic regression methods. Furthermore, we introduce the response-based integration for the QDA, LDA and logistic regression methods. Experimental examples demonstrate the effectiveness of these approaches for determining the perceptual state of a brain under study by integrating its localized spatiotemporal neuronal activity.

Accuracy of discriminant analysis methods to classify activities of subjects with Parkinson's Disease using wearable sensors

Linear discriminant classification tree: A user-driven multicriteria classification method

The probability of occurrence of natural resources, such as petroleum deposits, can be assessed by a combination of multivariate statistical and geostatistical techniques. The area of study is partitioned into regions that are as homogeneous as possible internally while simultaneously as distinct as possible. Fisher's discriminant criterion is used to select geological variables that best distinguish productive from nonproductive localities, based on a sample of previously drilled exploratory wells. On the basis of these geological variables, each wildcat well is assigned to the production class (dry or producer in the two-class case) for which the Mahalanobis' distance from the observation to the class centroid is a minimum. Universal kriging is used to interpolate values of the Mahalanobis' distances to all locations not yet drilled. The probability that an undrilled locality belongs to the productive class can be found, using the kriging estimation variances to assess the probability of misclassification. Finally, Bayes' relationship can be used to determine the probability that an undrilled location will be a discovery, regardless of the production class in which it is placed. The method is illustrated with a study of oil prospects in the Lansing/Kansas City interval of western Kansas, using geological variables derived from well logs.

This paper introduces a novel variant of video summarization, namely building a summary that depends on the particular aspect of a video the viewer focuses on. We refer to this as viewpoint. To infer what the desired viewpoint may be, we assume that several other videos are available, especially groups of videos, e.g., as folders on a person's phone or laptop. The semantic similarity between videos in a group vs. the dissimilarity between groups is used to produce viewpoint-specific summaries. For considering similarity as well as avoiding redundancy, output summary should be (A) diverse, (B) representative of videos in the same group, and (C) discriminative against videos in the different groups. To satisfy these requirements (A)-(C) simultaneously, we proposed a novel video summarization method from multiple groups of videos. Inspired by Fisher's discriminant criteria, it selects summary by optimizing the combination of three terms (a) inner-summary, (b) inner-group, and (c) between-group variances defined on the feature representation of summary, which can simply represent (A)-(C). Moreover, we developed a novel dataset to investigate how well the generated summary reflects the underlying viewpoint. Quantitative and qualitative experiments conducted on the dataset demonstrate the effectiveness of proposed method.

Defect recognition plays an important part in the health monitoring of in-service equipment. Surface defects and sub-surface defects of key components have different effects on the safety of the equipment. Sub-surface defects are difficult to be identified, and it is more likely to cause unpredictable damage than surface defects. However, the existing characteristic cannot accurately identify the defect type. Therefore, it is critical to find features that are useful for defect classification. The fusion of multiple feature values facilitates defect classification. For obtaining multi-feature fusion eigenvalues, this article introduces a fusion matrix based on Fisher's discriminant criterion and correlation analysis, which realizes the fusion of two dimensions of the whole and the local and different aspects. The BP neural network classifier is then used to discriminate and classify surface defects and sub-surface defects. The recognition accuracy of surface defects and sub-surface defects can reach 98.1%. The classification accuracy of this approach is significantly improved compared with the method based on a single feature value and other state-of-the-art methods. The approach can also be used to identify defects with different cross-sectional shapes, indicating that this approach is suited for nature defects.

We propose a novel set of features extracted using Hybrid Discriminant Analysis (HDA) for use in a facial expression recognition task. HDA is formulated by combining the optimization problems which are solved in Linear Discriminant Analysis (LDA) and Principal Component Analysis (PCA) methods. By tuning weighting parameters, new sets of discriminant directions are obtained. Using these directions for feature extraction, we show that we can obtain excellent recognition rates of 95.9% on a database of 6 expressions plus neutral which is much better than that obtained using PCA or LDA. The performance of HDA is comparable to that of Gabor wavelet based methods. However, the computation time required to form a HDA feature vector is significantly lower than the time required to form a Gabor feature vector making this method very attractive for real-time applications.

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.

A novel Bayesian logistic discriminant model: An application to face recognition

BackgroundAlthough a majority of studies in cancer biomarker discovery claim to use proportional hazards regression (PHREG) to the study the ability of a biomarker to predict survival, few studies use the predicted probabilities obtained from the model to test the quality of the model. In this paper, we compared the quality of predictions by a PHREG model to that of a linear discriminant analysis (LDA) in both training and test set settings.MethodsThe PHREG and LDA models were built on a 491 colorectal cancer (CRC) patient dataset comprised of demographic and clinicopathologic variables, and phenotypic expression of p53 and Bcl-2. Two variable selection methods, stepwise discriminant analysis and the backward selection, were used to identify the final models. The endpoint of prediction in these models was five-year post-surgery survival. We also used linear regression model to examine the effect of bin size in the training set on the accuracy of prediction in the test set.ResultsThe two variable selection techniques resulted in different models when stage was included in the list of variables available for selection. However, the proportion of survivors and non-survivors correctly identified was identical in both of these models. When stage was excluded from the variable list, the error rate for the LDA model was 42% as compared to an error rate of 34% for the PHREG model.ConclusionsThis study suggests that a PHREG model can perform as well or better than a traditional classifier such as LDA to classify patients into prognostic classes. Also, this study suggests that in the absence of the tumor stage as a variable, Bcl-2 expression is a strong prognostic molecular marker of CRC.

Kernel quadratic discriminant analysis for small sample size problem

Local Discriminant Embedding (LDE) was recently proposed to overcome some limitations of the global Linear Discriminant Analysis (LDA) method. In the case of a small training data set, however, LDE cannot directly be applied to high-dimensional data. This case is the so-called small-sample-size (SSS) problem. In this paper, we introduce an Exponential Local Discriminant Embedding (ELDE) technique to overcome the SSS problem. The advantages of ELDE are that, compared with Principal Component Analysis (PCA) + LDE, the ELDE method can extract the most discriminant information that was contained in the null space of the locality preserving between-class and within-class scatter matrices. In addition, the proposed ELDE is equivalent to transforming original data into a new space by distance diffusion mapping, and then, LDE is applied in such a new space. As a result of diffusion mapping, the margin between samples belonging to different classes is enlarged, which is helpful in improving classification accuracy. The experiments are conducted on four public face databases, YALE, PIE, Extended Yale and PF01. Experiments conducted on real data show that the performance of ELDE is better than that of LDE and many state-of-the-art discriminant analysis techniques.