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.

Identification of species of the Euterpe genus by rare earth elements using inductively coupled plasma mass spectrometry and linear discriminant analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

Approccio network-based alla discriminant analysis mediante HPC per la ricerca di signature ottimali in dati ad alta dimensionalità

Il presente lavoro di tesi si inserisce nell’ambito della classificazione di dati ad alta dimensionalità, sviluppando un algoritmo basato sul metodo della Discriminant Analysis. Esso classifica i campioni attraverso le variabili prese a coppie formando un network a partire da quelle che hanno una performance sufficientemente elevata. Successivamente, l’algoritmo si avvale di proprietà topologiche dei network (in particolare la ricerca di subnetwork e misure di centralità di singoli nodi) per ottenere varie signature (sottoinsiemi delle variabili iniziali) con performance ottimali di classificazione e caratterizzate da una bassa dimensionalità (dell’ordine di 101, inferiore di almeno un fattore 103 rispetto alle variabili di partenza nei problemi trattati). Per fare ciò, l’algoritmo comprende una parte di definizione del network e un’altra di selezione e riduzione della signature, calcolando ad ogni passaggio la nuova capacità di classificazione operando test di cross-validazione (k-fold o leave- one-out). Considerato l’alto numero di variabili coinvolte nei problemi trattati – dell’ordine di 104 – l’algoritmo è stato necessariamente implementato su High-Performance Computer, con lo sviluppo in parallelo delle parti più onerose del codice C++, nella fattispecie il calcolo vero e proprio del di- scriminante e il sorting finale dei risultati. L’applicazione qui studiata è a dati high-throughput in ambito genetico, riguardanti l’espressione genica a livello cellulare, settore in cui i database frequentemente sono costituiti da un numero elevato di variabili (104 −105) a fronte di un basso numero di campioni (101 −102). In campo medico-clinico, la determinazione di signature a bassa dimensionalità per la discriminazione e classificazione di campioni (e.g. sano/malato, responder/not-responder, ecc.) è un problema di fondamentale importanza, ad esempio per la messa a punto di strategie terapeutiche personalizzate per specifici sottogruppi di pazienti attraverso la realizzazione di kit diagnostici per l’analisi di profili di espressione applicabili su larga scala. L’analisi effettuata in questa tesi su vari tipi di dati reali mostra che il metodo proposto, anche in confronto ad altri metodi esistenti basati o me- no sull’approccio a network, fornisce performance ottime, tenendo conto del fatto che il metodo produce signature con elevate performance di classifica- zione e contemporaneamente mantenendo molto ridotto il numero di variabili utilizzate per questo scopo.

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.