Two-Group Classification when Both Groups are Mixtures of Normals

In this paper we consider a two-group discriminant analysis problem where each group is a mixture of two subgroups. Based upon data from a clinical study of alcohol involvement and diseases, simulation experiments were performed for three different configurations of means and covariance matrices. Expected actual non-error rates are estimated for the linear, quadratic, and kernel discriminant functions for sample sizes 30, 50, 75, 100, 150 and 200. A conclusion of the article is that the kernel discriminant function performs as well as or better than quadratic discriminant function. However, the linear discriminant function was clearly inferior to either the quadratic or kernel discriminant functions.     

Conditional Quadratic Discrimination in the Identification of Biological Markers for Disease Screening

Conditional multivariate normal density functions are used to construct conditional quadratic discriminant functions that adjust for covariate differences between disease groups. An expected actual error rate for the conditional discriminant function is defined. The purpose of this paper is to use the conditional quadratic discriminant function and its misolassification error rate in order to help determine if a set of discriminators is a good biological marker for disease screening. The conditional quadratic discriminant analysis is illustrated using data from two alcoholism classification problems. It is shown how the discriminant functions can identify a set of variables that can be used as biological markers.     

Generalized Walker-Duncan Procedure for Obtaining Maximum Likelihood Estimates of Parameters of Logistic Discriminant Function

A recursive method of obtaining the maximum likelihood estimates of the parameters of the quadratic logistic discriminant function is presented. This method is an extension of the Walker and Duncan procedure (1967) proposed for the linear logistic discriminant function in a dichotomous case. A generalization of the method to the problem of discrimination between several populations is also given in the paper. It works for both linear and quadratic logistic discriminant function. After an estimation of the parameters of the logistic function a classification can be performed. An example of application of the method to automatic diagnosis of some respiratory diseases is presented. Comparison with the standard procedures used for the estimation is done by a short simulation study.     

Identifying infertile homozygous Inverdale (FecXI) ewe lambs on the basis of genotype differences in reproductive hormone concentrations

Introduction of the Inverdale prolificacy gene (FecX^I) could markedly improve reproductive efficiency in commercial flocks, but as homozygous carrier Inverdale ewes are infertile, it is imperative that these animals are identified at an early age and excluded from breeding stock. As the ovaries of homozygous carrier ewes are nonfunctional, there are wide differences in reproductive hormone levels between these and other Inverdale genotypes. This study assesses the accuracy of using hormone concentrations alone, to identify infertile homozygous ewe lambs. Ewe lambs were blood sampled at 2, 5 and/or 8 months of age, and plasma analyzed for follicle-stimulating hormone (FSH), luteinizing hormone (LH) and inhibin content. These animals were either the offspring of both known carrier rams and known carrier ewes, and therefore would be either homozygous (II) or heterozygous (I +) for the Inverdale gene (group 1, N = 122), or had one parent that was a carrier and therefore would be either heterozygous or noncarriers (+ +) of the gene (group 2, N = 32). Animals were designated as either II or I + / + + on the basis of their plasma hormone concentrations. Inverdale genotype was also assigned from laparoscopic observation of the ovaries at each of these occasions. Definitive assignment of genotype was made at laparoscopy as adults during the breeding season. On the basis of laparoscopy as adults, 62 (51%) lambs in group 1 were identified as homozygous and 60 (49%) as heterozygous. At all three ages, both mean FSH and mean LH concentrations were significantly higher in II than in I + lambs. Mean inhibin concentrations were significantly lower in II lambs at 8 months, but did not differ significantly between genotypes at 2 or 5 months of age. The use of discriminant analysis techniques to segregate individual animals in group 1 on the basis of their plasma FSH and LH concentrations, correctly identified Inverdale genotype in 50/52 (96%) lambs at 2 months, 75/79 (95%) at 5 months and 118/122 (97%) at 8 months of age. Discriminant analysis was equally effective for segregating II ewe lambs (group 1) from fertile ewe lambs of I + and + + genotype (group 2, 97% correct at 5 months and 98% at 8 months). At no stage did inclusion of inhibin concentrations into the discriminant function alter the number of homozygous ewes misclassified. This demonstrates that infertile homozygous ewe lambs can accurately be distinguished from their fertile flockmates by using plasma concentrations of gonadotrophins alone, and that this can be achieved from as early as 2 months of age.     

Contribution of physical fitness component to health status in middle-aged and elderly females

This study determined the physical fitness component that contributes to improving and maintaining health status for each age group as well as quantifying the degree of the relationship between health status and physical fitness in middle-aged and elderly females. The participants were 2,371 females aged 30 to 69 years. Ten physical fitness tests and medical checkups were performed. The participants were divided into a healthy group and an unhealthy group according to health status. Multiple discriminant analysis was applied to the multivariate data. Correct discriminant probabilities of the multiple discriminant function to discriminate the healthy and unhealthy groups for females ranged from 63.0% to 77.5%. These results suggest that there is a relatively high relationship between health status and physical fitness level for middle-aged and elderly females. With each individual's discriminant score calculated by the obtained multiple discriminant function as the index of the degree of health, the Pearson's correlation coefficient of the discriminant score and the performance in each physical fitness test were calculated. The aging change from 30 to 69 years old was classified into four patterns according to the contribution. The result of this study is considered to be useful as objective data to prepare an exercise program considering the contribution of the physical fitness component of health status.     

Bias‐Corrected Diagonal Discriminant Rules for High‐Dimensional Classification

Summary Diagonal discriminant rules have been successfully used for high‐dimensional classification problems, but suffer from the serious drawback of biased discriminant scores. In this article, we propose improved diagonal discriminant rules with bias‐corrected discriminant scores for high‐dimensional classification. We show that the proposed discriminant scores dominate the standard ones under the quadratic loss function. Analytical results on why the bias‐corrected rules can potentially improve the predication accuracy are also provided. Finally, we demonstrate the improvement of the proposed rules over the original ones through extensive simulation studies and real case studies.     

Contribution of physical fitness component to health status in middle-aged and elderly males

This study determined the physical fitness component that contributes to improving and maintaining health status for each age group as well as quantifying the degree of the relationship between health status and physical fitness in middle-aged and elderly males. The participants were 995 males aged 30 to 69 years. Ten physical fitness tests and medical checkups were performed. The participants were divided into a healthy group and an unhealthy group according to health status. Multiple discriminant analysis was applied to the multivariate data. Correct discriminant probabilities of the multiple discriminant function to discriminate the healthy and unhealthy groups for males ranged from 67.0% to 75.1%. These findings suggest that there is a relatively high relationship between the health status and physical fitness level for middle-aged and elderly males. With each individual's discriminant score calculated using the multiple discriminant function as the index of the degree of health, the Pearson's correlation coefficient of the discriminant score and the performance in each physical fitness test were calculated. The age change between 30 and 69 years old was classified into five patterns according to the contribution. The result of this study is considered to be useful as objective data to prepare an exercise program considering the contribution of the physical fitness component of health status.     

Intensity and the ratios of compounds in the scent of snapdragon flowers affect scent discrimination by honeybees (<Emphasis Type="Italic">Apis mellifera</Emphasis>)

Floral scent is used by pollinators during foraging to identify and discriminate among flowers. The ability to discriminate among scents may depend on both scent intensity and the ratios of the concentrations of the volatile compounds of a complex mixture rather than on the presence of a few compounds. We used four scent-emitting cultivars of snapdragon (Antirrhinum majus) to test this hypothesis by examining the ability of honeybees to differentiate among their scents. Each cultivar produced three monoterpenes (myrcene, E--ocimene, and linalool) and five phenylpropanoids (methylbenzoate, acetophenone, dimethoxytoluene, cis-methylcinnamate, and trans-methylcinnamate). Cultivars were reliably classified by their scents in a canonical discriminant analysis. Honeybees were unable to discriminate among the scents of flowers of the same cultivar in our assay. The ability of honeybees to discriminate among the scents of different cultivars was a function of the intensity of the floral scent. Discrimination was also correlated to the distance among the scents described by the discriminant analysis; the cultivars that had the greatest differences observed in the discriminant analysis were the easiest to discriminate. Our results show that honeybees are capable of using all of the floral volatiles to discriminate subtle differences in scent.     

On the Performance of Some Classification Rules for Qualitative Data for Simulated Underlying Distributions

Two linear functions for discriminating with qualitative variables (Fisher's linear discriminant function and the independence rule) are compared with the general multinomial procedure, a rule based on Lancaster's definition of higher order interactions and the quadratic discriminant function. The evaluation of these functions is carried out within Monte Carlo experiments. Various types of underlying distributions generated by a special algorithm are used.     

Identification of protein-coding regions in Arabidopsis thaliana genome based on quadratic discriminant analysis

A new method (MZEF) for predicting internal coding exons in genomic DNA sequences has been developed. This method is based on a prediction algorithm that uses the quadratic discriminant function for multivariate statistical pattern recognition. With improved feature measures, an Arabidopsis thaliana-specific implementation of MZEF is completed and made available to the plant genome community.     

Assessing data quality of peptide mass spectra obtained by quadrupole ion trap mass spectrometry

An algorithm is introduced to assess spectral quality for peptide CID spectra acquired by a quadrupole ion trap mass spectrometer. The method employs a quadratic discriminant function calibrated with manually classified 'bad' and 'good' quality spectra, producing a single 'spectral quality' score. Many spectra examined that do not have significant matches are assessed to have good spectral quality, indicating that advances in search methods may yield substantial improvements in results.     

A new discriminant NMF algorithm and its application to the extraction of subtle emotional differences in speech

In this study we propose a new feature extraction algorithm, dNMF (discriminant non-negative matrix factorization), to learn subtle class-related differences while maintaining an accurate generative capability. In addition to the minimum representation error for the standard NMF (non-negative matrix factorization) algorithm, the dNMF algorithm also results in higher between-class variance for discriminant power. The multiplicative NMF learning algorithm has been modified to cope with this additional constraint. The cost function was carefully designed so that the extraction of feature coefficients from a single testing pattern with pre-trained feature vectors resulted in a quadratic convex optimization problem in non-negative space for uniqueness. It also resolves issues related to the previous discriminant NMF algorithms. The developed dNMF algorithm has been applied to the emotion recognition task for speech, where it needs to emphasize the emotional differences while de-emphasizing the dominant phonetic components. The dNMF algorithm successfully extracted subtle emotional differences, demonstrated much better recognition performance and showed a smaller representation error from an emotional speech database.     

Robust discriminant analysis and its application to identify protein coding regions of rice genes

Identification of protein coding regions is fundamentally a statistical pattern recognition problem. Discriminant analysis is a statistical technique for classifying a set of observations into predefined classes and it is useful to solve such problems. It is well known that outliers are present in virtually every data set in any application domain, and classical discriminant analysis methods (including linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA)) do not work well if the data set has outliers. In order to overcome the difficulty, the robust statistical method is used in this paper. We choose four different coding characters as discriminant variables and an approving result is presented by the method of robust discriminant analysis.     

A weight array method for splicing signal analysis

A new method of sequence analysis, using a weight array method(WAM), which generalizes the traditional Staden weight matrixmethod (WMM), is proposed. With the help of a statistical mechanicalmodel, the discriminant function is ident with the energy functiondescribing macromolecular interactions. The method is appliedto the study of 5'-splice signals in Schizosaccharomyces pombepre-mRNA sequences. The results show that there may exist weakpairwise correlations within the signals and that our methodcan help to better discriminate these signals. Experiments areproposed to test the predictions of the theory.     

Carrier detection of Duchenne dystrophy by frequency analysis of the electromyogram

A new method for Duchenne muscular dystrophy (DMD) carrier detection based on frequency analysis of electromyograms (EMG) taken from relative force contractions shows great promise in classifying possible carriers. Nine carriers were examined and compared to nineteen normals in an attempt to define a discriminant function that would be effective in classification of possible carriers of the gene responsible for DMD. EMG data were taken at 20%, 40%, and 60% of maximum effort from the biceps brachii using a specially designed dynamometer apparatus. The apparatus was able to isolate the biceps muscle group and allowed for adjustment to accommodate different body sizes. Three signal processing methods were used to find variables in the frequency domain that would provide the best discriminant function based on the jackknife classification method. Of these methods, the most promising appears to be the high-to-low ratio method at 20% maximum contraction. When combining the high and low values found with this test in conjunction with the peak cepstrum values also found at 20% maximum contraction, discrimination was found to be 83.8% accurate. Because this classification is not based solely on definite carriers, and appears to be independent of serum creatine phosphokinase (CPK) values, it would seem that classification based on a definite carrier population could be performed with greater accuracy, especially with the addition of CPK values.     

Heterozygous carriage of a dysfunctional Toll-like receptor 9 allele affects CpG oligonucleotide responses in B cells

Toll-like receptors (TLR) are employed by the innate immune system to detect microbial pathogens based on conserved microbial pathogen molecules. For example, TLR9 is a receptor for CpG-containing microbial DNA, and its activation results in the production of cytokines and type I interferons from human B cells and plasmacytoid dendritic cells, respectively. Both are required for mounting an efficient antibacterial or antiviral immune response. These effects are mimicked by synthetic CpG oligodeoxynucleotides (ODN). Although several hyporesponsive TLR9 variants have been reported, their functional relevance in human primary cells has not been addressed. Here we report a novel TLR9 allele, R892W, which is hyporesponsive to CpG ODN and acts as a dominant-negative in a cellular model system. The R892W variant is characterized by increased MyD88 binding and defective co-localization with CpG ODN. Whereas primary plasmacytoid dendritic cells isolated from a heterozygous R892W carrier responded normally to CpG by interferon-α production, carrier B cells showed impaired IL-6 and IL-10 production. This suggests that heterozygous carriage of a hyporesponsive TLR9 allele is not associated with complete loss of TLR9 function but that TLR9 signals elicited in different cell types are regulated differently in human primary cells.     

Chemometric discrimination of unfractionated plant extracts analyzed by electrospray mass spectrometry

Metabolic fingerprints were obtained from unfractionated Pharbitis nil leaf sap samples by direct infusion into an electrospray ionization mass spectrometer. Analyses took less than 30 s per sample and yielded complex mass spectra. Various chemometric methods, including discriminant function analysis and the machine-learning methods of artificial neural networks and genetic programming, could discriminate the metabolic fingerprints of plants subjected to different photoperiod treatments. This rapid automated analytical procedure could find use in a variety of phytochemical applications requiring high sample throughput.     

Associations between Allozyme Genotypes and Quantitative Traits in Douglas-Fir [PSEUDOTSUGA MENZIESII (Mirb.) Franco

Effects of maternal genotypes for eight enzyme loci on seven quantitative traits in 41 half-sib families were determined. Heritability estimates for the quantitative traits were highly significant and ranged from 0.57 to 0.86. Only six of 112 comparisons (56 comparisons for each of the genotypes and 56 for homozygous versus heterozygous contrasts) were statistically significant (P < 0.05). None of these significant comparisons could be associated with either a particular allele or a particular genotype. No heterotic effects were observed when the homozygous genotypes were compared with the heterozygous ones. Because the quantitative traits are highly correlated, a discriminant function analysis was performed to obtain the two most important canonical variates that accounted for 75% of the variance in the quantitative traits. There were no significant associations among enzyme loci and the two canonical variates. I conclude that, in this study, enzyme genotypic differences do not influence the quantitative traits to a major extent.     

雌雄蚕蛹近红外反射光谱的差异及其模式识别

采用6250型近红外光谱分析仪,从波长6印到1 235nm分别对日系蚕蛹217颗、中系蚕蛹174颗、杂交种蚕蛹330颗做了扫描测试,结果表明：雌雄蚕蛹的近红外光谱有极显著的差异。从日系217颗蚕蛹中随机选取雌雄各50颗作为学习样本,采用逐步判别方法从其二阶导数光谱中抽取5个特征波长作为观测向量,利用二次型判别函数对其余621颗蚕蛹的性别进行识别,其准确率达98.7%。该方法明显优于以蚕蛹重量或大小识别蚕蛹雌雄的方法。     

一种基于BIOLOG代谢指纹分析的油气微生物勘探新方法

【目的】建立基于土壤微生物群落生理功能代谢的油气微生物勘探新方法。【方法】采集新疆玛北油气藏区浅层地表土壤样品45份,非油气藏区样品25份,利用BIOLOG微平板,测定微生物群落代谢活性,采用判别分析模型判断油气藏区微生物异常。【结果】从95种碳源中,筛选到10种能够体现油气藏区与非油气藏区土壤微生物群落结构差异的典型碳源,利用判别函数对试验及对照区进行回判,油气藏区判别正确率为97.8%,非油藏区判别正确率为100%,总判别正确率为98.6%。【结论】BIOLOG技术能高效准确的用于油气藏初步勘测。