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.

Methodological shifts in ratio-based modelling of corporate collapse

The year 1968 saw a major shift from univariate to multivariate methodological approaches to ratio-based modelling of corporate collapse. This was facilitated by the introduction of a new statistical tool called Multiple Discriminant Analysis (MDA). However, it did not take long before other statistical tools were developed. The primary objective for developing these tools was to enable deriving models that would at least do as good a job asMDA, but rely on fewer assumptions. With the introduction of new statistical tools, researchers became pre-occupied with testing them in signalling collapse. lLTUong the ratio-based approaches were Logit analysis, Neural Network analysis, Probit analysis, ID3, Recursive Partitioning Algorithm, Rough Sets analysis, Decomposition analysis, Going Concern Advisor, Koundinya and Purl judgmental approach, Tabu Search and Mixed Logit analysis. Regardless of which methodological approach was chosen, most were compared to MDA. This paper reviews these various approaches. Emphasis is placed on how they fared against MDA in signalling corporate collapse.

Benchmarking new statistical techniques in ration-based modelling of corporate collapse

Up until 1979, Multiple Discriminant Analysis (MDA) was the primary multivariate methodological approaches to ratio-based modelling of corporate collapse. However, as new statistical tools became available, researchers started testing them with the primary objective of deriving models that would at least do as good a job as MDA, but that rely on fewer assumptions. Regardless of which methodological approach was chosen, most were compared to MDA. This paper analyses 84 studies on ratio based modelling of corporate collapse over the period 1968 to 2004. The results indicate that when MDA was not the primary methodology it was the benchmark of choice for comparison; thereby, demonstrating its importance as a foundation multivariate methodological approach in signalling corporate collapse.

Optimising errors in signaling corporate collapse using MCCCRA

Purpose – The purpose of this paper is to put forward an innovative approach for reducing the variation between Type I and Type II errors in the context of ratio-based modeling of corporate collapse, without compromising the accuracy of the predictive model. Its contribution to the literature lies in resolving the problematic trade-off between predictive accuracy and variations between the two types of errors.

Design/methodology/approach – The methodological approach in this paper – called MCCCRA – utilizes a novel multi-classification matrix based on a combination of correlation and regression analysis, with the former being subject to optimisation criteria. In order to ascertain its accuracy in signaling collapse, MCCCRA is empirically tested against multiple discriminant analysis (MDA).

Findings – Based on a data sample of 899 US publicly listed companies, the empirical results indicate that in addition to a high level of accuracy in signaling collapse, MCCCRA generates lower variability between Type I and Type II errors when compared to MDA.

Originality/value – Although correlation and regression analysis are long-standing statistical tools, the optimisation constraints that are applied to the correlations are unique. Moreover, the multi-classification matrix is a first in signaling collapse. By providing economic insight into more stable financial modeling, these innovations make an original contribution to the literature.

Predicting biological parameters of estuarine benthic communities using models based on environmental data

Este trabalho objetivou predizer parâmetros da estrutura de associações macrobentônicas (composição específica, abundância, riqueza, diversidade e equitatividade) em estuários do Sul do Brasil, utilizando modelos baseados em dados ambientais (características dos sedimentos, salinidade, temperaturas do ar e da água, e profundidade). As amostragens foram realizadas sazonalmente em cinco estuários entre o inverno de 1996 e o verão de 1998. Em cada estuário as amostras foram coletadas em áreas não poluídas, com características semelhantes quanto a presença ou ausência de vegetação, profundidade e distância da desenbocadura. Para a obtenção dos modelos de predição, foram utilizados dois métodos: o primeiro baseado em Análise Discriminante Múltipla (ADM) e o segundo em Regressão Linear Múltipla (RLM). Os modelos baseados em ADM apresentaram resultados melhores do que os baseados em regressão linear. Os melhores resultados usando RLM foram obtidos para diversidade e riqueza. É possível então, concluir que modelos como aqui derivados podem representar ferramentas muito úteis em estudos de monitoramento ambiental em estuários.

Predicting class I major histocompatibility complex (MHC) binders using multivariate statistics:comparison of discriminant analysis and multiple linear regression

The accurate in silico identification of T-cell epitopes is a critical step in the development of peptide-based vaccines, reagents, and diagnostics. It has a direct impact on the success of subsequent experimental work. Epitopes arise as a consequence of complex proteolytic processing within the cell. Prior to being recognized by T cells, an epitope is presented on the cell surface as a complex with a major histocompatibility complex (MHC) protein. A prerequisite therefore for T-cell recognition is that an epitope is also a good MHC binder. Thus, T-cell epitope prediction overlaps strongly with the prediction of MHC binding. In the present study, we compare discriminant analysis and multiple linear regression as algorithmic engines for the definition of quantitative matrices for binding affinity prediction. We apply these methods to peptides which bind the well-studied human MHC allele HLA-A*0201. A matrix which results from combining results of the two methods proved powerfully predictive under cross-validation. The new matrix was also tested on an external set of 160 binders to HLA-A*0201; it was able to recognize 135 (84%) of them.

On the application of the probabilistic linear discriminant analysis to face recognition across expression

Facial expression is one of the main issues of face recognition in uncontrolled environments. In this paper, we apply the probabilistic linear discriminant analysis (PLDA) method to recognize faces across expressions. Several PLDA approaches are tested and cross-evaluated on the Cohn-Kanade and JAFFE databases. With less samples per gallery subject, high recognition rates comparable to previous works have been achieved indicating the robustness of the approaches. Among the approaches, the mixture of PLDAs has demonstrated better performances. The experimental results also indicate that facial regions around the cheeks, eyes, and eyebrows are more discriminative than regions around the mouth, jaw, chin, and nose.

Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

Predicting survival of western rock lobsters Panulirus cygnus using discriminant analysis of hemolymph parameters taken immediately following simulated handling treatments

Instances of morbidity amongst rock lobsters (Panulirus cygnus) arriving at factories in Western Australia (WA) have been attributed to stress during post-harvest handling. This study used discriminant analysis to determine whether physiological correlates of stress following a period of simulated post-harvest handling had any validity as predictors of future rejection or morbidity of western rock lobsters. Groups of 230 western rock lobsters were stored for 6 h in five environments (submerged/flowing sea water, submerged/re-circulating sea water, humid air, flowing sea water spray, and re-circulated sea water spray). The experiment was conducted in late spring (ambient sea water 22°C), and repeated again in early autumn (ambient sea water 26°C). After 6 h treatment, each lobster was graded for acceptability for live export, numbered, and its hemolymph was sampled. The samples were analysed for a number of physiological and health status parameters. The lobsters were then stored for a week in tanks in the live lobster factory to record mortality. The mortality of lobsters in the factory was associated with earlier deviations in hemolymph parameters as they emerged from the storage treatments. Discriminant analysis (DA) of the hemolymph assays enabled the fate of 80-90% of the lobsters to be correctly categorised within each experiment. However, functions derived from one experiment were less accurate at predicting mortality when applied to the other experiments. One of the reasons for this was the higher mortality and the more severe patho-physiological changes observed in lobsters stored in humid air or sprays at the higher temperature. The analysis identified lactate accumulation during emersion and associated physiological and hemocyte-related effects as a major correlate of mortality. Reducing these deviations, for example by submerged transport, is expected to ensure high levels of survival. None of the indicators tested predicted mortality with total accuracy. The simplest and most accurate means of comparing emersed treatments was to count the mortality afterwards.

Incremental Linear Discriminant Analysis Using Sufficient Spanning Sets and Its Applications

This paper presents an incremental learning solution for Linear Discriminant Analysis (LDA) and its applications to object recognition problems. We apply the sufficient spanning set approximation in three steps i.e. update for the total scatter matrix, between-class scatter matrix and the projected data matrix, which leads an online solution which closely agrees with the batch solution in accuracy while significantly reducing the computational complexity. The algorithm yields an efficient solution to incremental LDA even when the number of classes as well as the set size is large. The incremental LDA method has been also shown useful for semi-supervised online learning. Label propagation is done by integrating the incremental LDA into an EM framework. The method has been demonstrated in the task of merging large datasets which were collected during MPEG standardization for face image retrieval, face authentication using the BANCA dataset, and object categorisation using the Caltech101 dataset. © 2010 Springer Science+Business Media, LLC.