Parametric Discriminant Analysis Research Articles

Using multivariate methods to infer knowledge from genomic data

Since the introduction of genome sequencing techniques several methods for genomic data preprocessing and analysis have been published and applied to answer different biological questions. Rarely, multivariate methods have been used to extract knowledge about protein roles. Two of the most informative types of data are gene expression data (microarrays) and phylogenetic profiles indicating presence of genes in other organisms and therefore providing information about their co-evolution. Here we show that these two types of data, analyzed by means of principal component analysis and non parametric discriminant analysis, provide useful information about protein function and their participation in virulence processes.

An approach for the two-group discriminant analysis: An application of DEA

This paper proposes a novel procedure based on a benchmarking model of data envelopment analysis (DEA) to solve the two-group classification problem. The idea was inspired by the fact that benchmarks dominate their own production possibility set (PPS). If observations belong to the same group, they should be in the same PPS and dominated by the same benchmarks. Therefore, the benchmarks of two groups were identified to construct a pair of nonlinear discriminant frontiers without pre-specifying the classification function form as in other parametric discriminant analysis (DA) approaches. Since the discriminant frontiers are established by the boundary of two groups, the proposed procedure differs from some existing discriminant approaches that establish the discriminant function by minimizing the total deviation of all observations from their group mean. Two applications are illustrated to support the validation of the proposed procedure even though the data sets may have outliers or an unequal number of observations.

Nonparametric weighted feature extraction for classification

In this paper, a new nonparametric feature extraction method is proposed for high-dimensional multiclass pattern recognition problems. It is based on a nonparametric extension of scatter matrices. There are at least two advantages to using the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired and to reduce the effect of the singularity problem. This is in contrast to parametric discriminant analysis, which usually only can extract L-1 (number of classes minus one) features. In a real situation, this may not be enough. Second, the nonparametric nature of scatter matrices reduces the effects of outliers and works well even for nonnormal datasets. The new method provides greater weight to samples near the expected decision boundary. This tends to provide for increased classification accuracy.

Segmentation of magnetic resonance brain images through discriminant analysis

Segmentation (tissue classification) of medical images obtained from a magnetic resonance (MR) system is a primary step in most applications of medical image post-processing. This paper describes nonparametric discriminant analysis methods to segment multispectral MR images of the brain. Starting from routinely available spin-lattice relaxation time, spin–spin relaxation time, and proton density weighted images ( T 1w, T 2w, P Dw), the proposed family of statistical methods is based on: (i) a transform of the images into components that are statistically independent from each other; (ii) a nonparametric estimate of probability density functions of each tissue starting from a training set; (iii) a classic Bayes 0–1 classification rule. Experiments based on a computer built brain phantom ( brainweb) and on eight real patient data sets are shown. A comparison with parametric discriminant analysis is also reported. The capability of nonparametric discriminant analysis in improving brain tissue classification of parametric methods is demonstrated. Finally, an assessment of the role of multispectrality in classifying brain tissues is discussed.

Mineral Favorability Mapping: A Comparison of Artificial Neural Networks, Logistic Regression, and Discriminant Analysis

A Probabilistic Neural Network (PNN) was trained to classify mineralized and nonmineralized cells using eight geological, geochemical, and geophysical variables. When applied to a second (validation) set of well-explored cells that had been excluded from the training set, the trained PNN generalized well, giving true positive percentages of 86.7 and 93.8 for the mineralized and nonmineralized cells, respectively. All artifical neural networks and statistical models were analyzed and compared by the percentages of mineralized cells and barren cells that would be retained and rejected correctly respectively, for specified cutoff probabilities for mineralization. For example, a cutoff probability for mineralization of 0.5 applied to the PNN probabilities would have retained correctly 87.66% of the mineralized cells and correctly rejected 93.25% of the barren cells of the validation set. Nonparametric discriminant analysis, based upon the Epanechnikov Kernel performed better than logistic regression or parametric discriminant analysis. Moreover, it generalized well to the validation set of well-explored cells, particularly to those cells that were mineralized. However, PNN performed better overall than nonparametric discriminant analysis in that it achieved higher percentages of correct retention and correct rejection of mineralized and barren cells, respectively. Although the generalized regression neural network (GRNN) is not designed for a binary—presence or absence of mineralization— dependent variable, it also performed well in mapping favorability by an index valued on the interval [0, 1]. However, PNN outperformed GRNN in correctly retaining mineralized cells and rejecting barren cells of the validation set.

Numerical avalanche prediction: Kootenay Pass, British Columbia, Canada

AbstractA numerical avalanche-prediction scheme was developed for highway applications at Kootenay Pass, British Columbia. The model features parametric discriminant analysis using Bayesian statistics to predict avalanche occurrences. Cluster techniques are then employed in discriminant space to analyze avalanche occurrences by the method of nearest neighbours. Extensive numerical testing of the model using an historical data base indicates that prediction accuracy may be 70% or better for both avalanche and non-avalanche time intervals.

Numerical avalanche prediction: Kootenay Pass, British Columbia, Canada

AbstractA numerical avalanche-prediction scheme was developed for highway applications at Kootenay Pass, British Columbia. The model features parametric discriminant analysis using Bayesian statistics to predict avalanche occurrences. Cluster techniques are then employed in discriminant space to analyze avalanche occurrences by the method of nearest neighbours. Extensive numerical testing of the model using an historical data base indicates that prediction accuracy may be 70% or better for both avalanche and non-avalanche time intervals.

Automatic classification of chromosomes as part of a routine system for clinical analysis.

A procedure for automatic classification of G-banded human chromosomes has been implemented on a semiautomated system for routine clinical analysis. Chromosomes represented by their density profiles are described by so-called weighted density distributions (WDDs) by application of a number of weighting functions and classified by a parametric discriminant analysis. During 16 mo of routine use of the system, 2,794 metaphases (127,925 chromosomes) from amniotic fluid have been karyotyped by the system with an error rate of 8-9%. This corresponds to 4-5 errors per metaphase. These errors can immediately be corrected by the operator on a displayed karyogram with a light pen.

Some fundamentals and procedures of parametric, distribution-free and discrete discriminant analysis

The concepts of local, global and hybrid classification rules, which allow a syste¬matic description of the most important parametric and nonparametric classification rules and of their interconnexions and properties, .are presented. Some new procedures are devel¬oped. These procedures include the maximum likelihood ratio rule, empirical globally optimal linear rules, hybrid rules, some of them also for discrete cases

Nonparametric Discriminant Analysis

A nonparametric method of discriminant analysis is proposed. It is based on nonparametric extensions of commonly used scatter matrices. Two advantages result from the use of the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired. This is in contrast to parametric discriminant analysis, which for an L class problem typically can determine at most L 1 features. Second, the nonparametric nature of the scatter matrices allows the procedure to work well even for non-Gaussian data sets. Using the same basic framework, a procedure is proposed to test the structural similarity of two distributions. The procedure works in high-dimensional space. It specifies a linear decomposition of the original data space in which a relative indication of dissimilarity along each new basis vector is provided. The nonparametric scatter matrices are also used to derive a clustering procedure, which is recognized as a k-nearest neighbor version of the nonparametric valley seeking algorithm. The form which results provides a unified view of the parametric nearest mean reclassification algorithm and the nonparametric valley seeking algorithm.

The effect of the law of small numbers on the perceived clinical value of NMR measurements on biopsy specimens. Parametric discriminant analysis of proton [formula omitted] and [formula omitted] measurements in vitro

The effect of the law of small numbers on the perceived clinical value of NMR measurements on biopsy specimens. Parametric discriminant analysis of proton [formula omitted] and [formula omitted] measurements in vitro