Influence analysis on discriminant coordinates

Discriminant analysis (DA), particularly Discriminant Coordinates (DC), is broadly applied in the scientific literature and included in many statistical software packages. DC is used to analyze biomedical data, especially for differential diagnosis on the basis of laboratory profiles. Papers handling influence analysis in DA can be found in the literature; however this topic has been scarcely touched upon in DC. In this paper the case-deletion approach is followed to introduce a perturbation in the data and influence measures are proposed to assess the effect on three statistics of interest: the transformation matrix, canonical directions and configuration of the sample centroids.Ministerio de Ciencia y Tecnologí

The use of otolith morphology to indicate the stock structure of common coral trout (Plectropomus leopardus) on the Great Barrier Reef, Australia

We investigated the use of otolith morphology to indicate the stock structure of an exploited serranid coral reef fish, Plectropomus leopardus, on the Great Barrier Reef (GBR), Australia. Otoliths were measured by traditional one-and two-dimensional measures (otolith length, width, area, perimeter, circularity, and rectangularity), as well as by Fourier analysis to capture the finer details of otolith shape. Variables were compared among four regions of the GBR separated by hundreds of kilometers, as well as among three reefs within each region, hundreds of meters to tens of kilometers apart. The temporal stability in otolith structure was examined by comparing two cohorts of fully recruited four-year-old P. leopardus collected two years before and two years after a signif icant disturbance in the southern parts of the GBR caused by a large tropical cyclone in March 1997. Results indicated the presence of at least two stocks of P. leopardus, although the structure of each stock varied depending on the cohort considered. The results highlight the importance of incorporating data from several years in studies using otolith morphology to discriminate temporary and possibly misleading signals from those that indicate persistent spatial structure in stocks. We conclude that otolith morphology can be used as an initial step to direct further research on groups of P. leopardus that have lived at least a part of their life in different environments

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning

Influence of observations on the misclassification probability in quadratic discriminant analysis.

In this paper it is analyzed how observations in the training sample affect the misclassification probability of a quadratic discriminant rule. An approach based on partial influence functions is followed. It allows to quantify the effect of observations in the training sample on the quality of the associated classification rule. Focus is more on the effect on the future misclassification rate, than on the influence on the parameters of the quadratic discriminant rule. The expression for the influence function is then used to construct a diagnostic tool for detecting influential observations. Applications on real data sets are provided.Applications; Classification; Data; Diagnostics; Discriminant analysis; Functions; Influence function; Misclassification probability; Outliers; Partial influence functions; Probability; Quadratic discriminant analysis; Quality; Robust covariance estimation; Robust regression; Training;

IVUS-based histology of atherosclerotic plaques: improving longitudinal resolution

Although Virtual Histology (VH) is the in-vivo gold standard for atherosclerosis plaque characterization in IVUS images, it suffers from a poor longitudinal resolution due to ECG-gating. In this paper, we propose an image- based approach to overcome this limitation. Since each tissue have different echogenic characteristics, they show in IVUS images different local frequency components. By using Redundant Wavelet Packet Transform (RWPT), IVUS images are decomposed in multiple sub-band images. To encode the textural statistics of each resulting image, run-length features are extracted from the neighborhood centered on each pixel. To provide the best discrimination power according to these features, relevant sub-bands are selected by using Local Discriminant Bases (LDB) algorithm in combination with Fisher’s criterion. A structure of weighted multi-class SVM permits the classification of the extracted feature vectors into three tissue classes, namely fibro-fatty, necrotic core and dense calcified tissues. Results shows the superiority of our approach with an overall accuracy of 72% in comparison to methods based on Local Binary Pattern and Co-occurrence, which respectively give accuracy rates of 70% and 71%