Communications inspired linear discriminant analysis

We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label. By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods, and comparisons are also made with a method in which Rényi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets. Copyright 2012 by the author(s)/owner(s).

Geostatistical Fisher discriminant analysis

A geostatistical version of the classical Fisher rule (linear discriminant analysis) is presented.This method is applicable when a large dataset of multivariate observations is available within a domain split in several known subdomains, and it assumes that the variograms (or covariance functions) are comparable between subdomains, which only differ in the mean values of the available variables. The method consists on finding the eigen-decomposition of the matrix W-1B, where W is the matrix of sills of all direct- and cross-variograms, and B is the covariance matrix of the vectors of weighted means within each subdomain, obtained by generalized least squares. The method is used to map peat blanket occurrence in Northern Ireland, with data from the Tellus
survey, which requires a minimal change to the general recipe: to use compositionally-compliant variogram tools and models, and work with log-ratio transformed data.

Brief report : The defense mechanisms of homophobic adolescent males : a descriptive discriminant analysis

The study examined the role of defense mechanisms in homophobic attitudes of older male adolescents aged 17e18 years. A cross-sectional survey collected data from final year high school students (N ¼ 86) attending an all male school in a regional centre in Victoria, Australia. The school was identified by teachers as having a problematic culture of homophobic intolerance. Participants were divided into homophobic and non-homophobic groups based on their scores on the Homophobia Scale Questionnaire. Discriminant analysis was conducted to identify the predictors that would best categorise students into those two groups on the basis of defense styles derived from the Defense Style Questionnaire-40 (DSQ-40). The strongest predictors of homophobia amongst defense styles were idealisation, denial, somatisation and devaluation accounting for 18.31%, 17.64%, 13.10% and 11.35% of the variance, respectively. Results generally supported the larger contribution of more immature defenses to higher levels of homophobia.

Boosting performance for 2D linear discriminant analysis via regression

Two Dimensional Linear Discriminant Analysis (2DLDA) has received much interest in recent years. However, 2DLDA could make pairwise distances between any two classes become significantly unbalanced, which may affect its performance. Moreover 2DLDA could also suffer from the small sample size problem. Based on these observations, we propose two novel algorithms called Regularized 2DLDA and Ridge Regression for 2DLDA (RR-2DLDA). Regularized 2DLDA is an extension of 2DLDA with the introduction of a regularization parameter to deal with the small sample size problem. RR-2DLDA integrates ridge regression into Regularized 2DLDA to balance the distances among different classes after the transformation. These proposed algorithms overcome the limitations of 2DLDA and boost recognition accuracy. The experimental results on the Yale, PIE and FERET databases showed that RR-2DLDA is superior not only to 2DLDA but also other state-of-the-art algorithms.

DDoS discrimination by linear discriminant analysis (LDA)

In this paper, we propose an effective approach with a supervised learning system based on Linear Discriminant Analysis (LDA) to discriminate legitimate traffic from DDoS attack traffic. Currently there is a wide outbreak of DDoS attacks that remain risky for the entire Internet. Different attack methods and strategies are trying to challenge defence systems. Among the behaviours of attack sources, repeatable and predictable features differ from source of legitimate traffic. In addition, the DDoS defence systems lack the learning ability to fine-tune their accuracy. This paper analyses real trace traffic from publicly available datasets. Pearson's correlation coefficient and Shannon's entropy are deployed for extracting dependency and predictability of traffic data respectively. Then, LDA is used to train and classify legitimate and attack traffic flows. From the results of our experiment, we can confirm that the proposed discrimination system can differentiate DDoS attacks from legitimate traffic with a high rate of accuracy.

Discriminant analysis of neuromuscular variables in chronic low back pain

Background: Investigation and discrimination of neuromuscular variables related to the complex aetiology of low back pain could contribute to clarifying the factors associated with symptoms. Objective: Analysing the discriminative power of neuromuscular variables in low back pain. Methods: This study compared muscle endurance, proprioception and isometric trunk assessments between women with low back pain (LBP, n=14) and a control group (CG, n=14). Multivariate analysis of variance and discriminant analysis of the data were performed. Results: The muscle endurance time (s) was shorter in the LBP group than in the CG (p=0.004) with values of 85.81 (37.79) and 134.25 (43.88), respectively. The peak torque (Nm/kg) for trunk extension was 2.48 (0.69) in the LBP group and 3.56 (0.88) in the GG (p=0.001); for trunk flexion, the mean torque was 1.49 (0.40) in the LBP group and 1.85 (0.39) in the CG (p=0.023). The repositioning error (degrees) before the endurance test was 2.66 (1.36) in the LBP group and 2.41 (1.46) in the CG (p=0.664), and after the endurance test, it was 2.95 (1.94) in the LBP group and 2.00 (1.16) in the CG (p=0.06). Furthermore, the variables showed discrimination between the groups (p=0.007), with 78.6% of the individuals with low back pain correctly classified in the LBP group. In turn, variables related to muscle activation showed no difference in discrimination between the groups (p=0.369). Conclusion: Based on these findings, the clinical management of low back pain should consist of both resistance and strength training, particularly in the extensor muscles.

Application of discriminant analysis-based model for prediction of risk of low back disorders due to workplace design in industrial jobs

The occupational exposure limits of different risk factors for development of low back disorders (LBDs) have not yet been established. One of the main problems in setting such guidelines is the limited understanding of how different risk factors for LBDs interact in causing injury, since the nature and mechanism of these disorders are relatively unknown phenomena. Industrial ergonomists' role becomes further complicated because the potential risk factors that may contribute towards the onset of LBDs interact in a complex manner, which makes it difficult to discriminate in detail among the jobs that place workers at high or low risk of LBDs. The purpose of this paper was to develop a comparative study between predictions based on the neural network-based model proposed by Zurada, Karwowski & Marras (1997) and a linear discriminant analysis model, for making predictions about industrial jobs according to their potential risk of low back disorders due to workplace design. The results obtained through applying the discriminant analysis-based model proved that it is as effective as the neural network-based model. Moreover, the discriminant analysis-based model proved to be more advantageous regarding cost and time savings for future data gathering.

Discriminant analysis of the specialty of elite cyclist

The different demands of competition coupled with the morphological and physiological characteristics of cyclists have led to the appearance of cycling specialities. The aims of this study were to determine the differences in the anthropometric and physiological features in road cyclists with different specialities, and to develop a multivariate model to classify these specialities and predict which speciality may be appropriate to a given cyclist. Twenty male, elite amateur cyclists were classified by their trainers as either flat terrain riders, hill climbers, or all-terrain riders. Anthropometric and cardiorespiratory studies were then undertaken. The results were analysed by MANOVA and two discriminant tests. Most differences between the speciality groups were of an anthropometric nature. The only cardiorespiratory variable that differed significantly (p < 0.05) was maximum oxygen consumption with respect to body weight (VO2max/kg). The first discriminant test classified 100% of the cyclists within their true speciality; the second, which took into account only anthropometric variables, correctly classified 75%. The first discriminant model allows the likely speciality of still non-elite cyclists to be predicted from a small number of variables, and may therefore help in their specific training.

A robustness verification system for mobile phone authentication based on gestures using Linear Discriminant Analysis

This article evaluates an authentication technique for mobiles based on gestures. Users create a remindful identifying gesture to be considered as their in-air signature. This work analyzes a database of 120 gestures of different vulnerability, obtaining an Equal Error Rate (EER) of 9.19% when robustness of gestures is not verified. Most of the errors in this EER come from very simple and easily forgeable gestures that should be discarded at enrollment phase. Therefore, an in-air signature robustness verification system using Linear Discriminant Analysis is proposed to infer automatically whether the gesture is secure or not. Different configurations have been tested obtaining a lowest EER of 4.01% when 45.02% of gestures were discarded, and an optimal compromise of EER of 4.82% when 19.19% of gestures were automatically rejected.

Statnote 29:discriminant analysis

Discriminant analysis (also known as discriminant function analysis or multiple discriminant analysis) is a multivariate statistical method of testing the degree to which two or more populations may overlap with each other. It was devised independently by several statisticians including Fisher, Mahalanobis, and Hotelling ). The technique has several possible applications in Microbiology. First, in a clinical microbiological setting, if two different infectious diseases were defined by a number of clinical and pathological variables, it may be useful to decide which measurements were the most effective at distinguishing between the two diseases. Second, in an environmental microbiological setting, the technique could be used to study the relationships between different populations, e.g., to what extent do the properties of soils in which the bacterium Azotobacter is found differ from those in which it is absent? Third, the method can be used as a multivariate ‘t’ test , i.e., given a number of related measurements on two groups, the analysis can provide a single test of the hypothesis that the two populations have the same means for all the variables studied. This statnote describes one of the most popular applications of discriminant analysis in identifying the descriptive variables that can distinguish between two populations.

Incremental tensor biased discriminant analysis:a new color-based visual tracking method

Most existing color-based tracking algorithms utilize the statistical color information of the object as the tracking clues, without maintaining the spatial structure within a single chromatic image. Recently, the researches on the multilinear algebra provide the possibility to hold the spatial structural relationship in a representation of the image ensembles. In this paper, a third-order color tensor is constructed to represent the object to be tracked. Considering the influence of the environment changing on the tracking, the biased discriminant analysis (BDA) is extended to the tensor biased discriminant analysis (TBDA) for distinguishing the object from the background. At the same time, an incremental scheme for the TBDA is developed for the tensor biased discriminant subspace online learning, which can be used to adapt to the appearance variant of both the object and background. The experimental results show that the proposed method can track objects precisely undergoing large pose, scale and lighting changes, as well as partial occlusion. © 2009 Elsevier B.V.

Application of Regularized Discriminant Analysis

2000 Mathematics Subject Classification: 62H30, 62P99