Quadratic Distance Measure Research Articles

Validity and reliability of the volleyball serve accuracy-test

This study aimed to examine the content, face, and sensitive validity, and test-retest reliability of a volleyball overhand serve accuracy-test. Four experts – university professors evaluated the content validity; 50 volleyball coaches, teachers, and athletes were enrolled in the face validity. Thirty-three undergraduate students (18 experienced and 15 novices) participated in the study to assess the test capability to detect different performance levels. The sensitive validity was examined by comparing differences in the serving accuracy among experience levels using the t-test for independent samples. A cluster analysis (hierarchical cluster) was conducted using the between-groups linkage method and the Euclidean quadratic distance measure. The test-retest reliability was analysed using intraclass correlation coefficients and the standard error. Satisfactory results were found for experts’ agreement regarding the test’s accuracy and content validity. Face validity was adequate regarding clarity, pertinence, and applicability (78% to 86% of agreement). A high degree of test-retest reliability was observed for both novices (ICC = 0.81) and experienced (ICC = 0.84) participants; experienced group (p = .001) had higher means. The volleyball serve accuracy-test is a viable alternative to assess beginners’ performance in a teaching-learning context.

A hybrid CBIR system using novel local tetra angle patterns and color moment features

The exponential growth of communal media platforms including Facebook and Twitter, and the accessibility of low-cost digital capturing devices have generated an enormous number of multimedia content including images. Effective handling of such massive image collection has boosted the development of content-based image retrieval (CBIR) approaches. Researchers have suggested both machine learning and non-learning-based techniques for CBIR. However, machine learning-based methods outperform the non-learning-based methods in the CBIR domain. The CBIR demands the development of reliable descriptors to attain the most appropriate images from the depository and better address the semantic gap problem. To counter these problems, we suggest a novel second-order Local Tetra Angle Patterns (LTAP) to better capture the texture features from the image. LTAPs are computed from adjacent pixels of 0°, 45°, 90°, and 135° using the second-order directional derivatives. Further, we propose a hybrid feature vector by concatenating LTAPs and RGB color features and using the genetic algorithm (GA) to select the finest appropriate features that enhance the image retrieval performance of our system. We employed our hybrid descriptor with the GA to optimize the support vector machine (SVM) for the image classification task and used the Chi-square quadratic distance measure to determine the resemblance between the query image and the images in the repository. Experimental results on three standard datasets including the Corel 1 k, Oxford flower, and CIFAR-10 indicate the effectiveness of the presented system over the contemporary CBIR methods.

Statistical framework for evaluation of climate model simulations by use of climate proxy data from the last millennium – Part 1: Theory

Abstract. A statistical framework for comparing the output of ensemble simulations from global climate models with networks of climate proxy and instrumental records has been developed, focusing on near-surface temperatures for the last millennium. This framework includes the formulation of a joint statistical model for proxy data, instrumental data and simulation data, which is used to optimize a quadratic distance measure for ranking climate model simulations. An essential underlying assumption is that the simulations and the proxy/instrumental series have a shared component of variability that is due to temporal changes in external forcing, such as volcanic aerosol load, solar irradiance or greenhouse gas concentrations. Two statistical tests have been formulated. Firstly, a preliminary test establishes whether a significant temporal correlation exists between instrumental/proxy and simulation data. Secondly, the distance measure is expressed in the form of a test statistic of whether a forced simulation is closer to the instrumental/proxy series than unforced simulations. The proposed framework allows any number of proxy locations to be used jointly, with different seasons, record lengths and statistical precision. The goal is to objectively rank several competing climate model simulations (e.g. with alternative model parameterizations or alternative forcing histories) by means of their goodness of fit to the unobservable true past climate variations, as estimated from noisy proxy data and instrumental observations.

Identification of Terrain Cover Using the Optimum Polarimetric Classifier

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow-covered fields is developed using the optimum polarimetric classifier. The covariance matrices for various terrain cover are computed from theoretical models of random medium by evaluating the scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Analytical and Monte Carlo simulated classification errors using the fully polarimetric feature vector are compared with classification based on single features which include the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements.

Homogeneity tests among groups for microsatellite data

We propose a homogeneity test among groups on a quadratic distance measure. The underlying mutation process in the microsatellite loci is studied using the stepwise mutation model. Asymptotic normality of the test statistic is proved under very mild regularity conditions. Resampling methods, such as jackknife, are used in the application to build confidence intervals for the difference in allelic variation between and within groups. The method is applied in a real data to test whether there are differences in the distribution of the repeated sequence among groups defined by ethnicity and alcoholism index (ALDX1).

Fast indexing method for image retrieval using k nearest neighbors searches by principal axis analysis

This paper presents a fast indexing scheme for content-based image retrieval based on the principal axis analysis. Image databases often represent the image objects as high-dimensional feature vectors and access them via the feature vectors and similarity measure. A similarity measure similar to the quadratic histogram distance measure is defined for this indexing method. The computational complexity of similarity measure in high-dimensional image database is very huge and hence the applications of image retrieval are restricted to certain areas. In this work, feature vectors in a given image are ordered by the principal axis analysis to speed up the similarity search in a high-dimensional image database using k nearest neighbor searches. To demonstrate the effectiveness of the proposed algorithm, we conducted extensive experiments and compared the performance with the IBM’s query by image content (QBIC) method, Jain and Vailay’s method, and the LPC-file method. The experimental results demonstrate that the proposed method outperforms the compared methods in retrieval accuracy and execution speed. The execution speed of the proposed method is much faster than that of QBIC method and it can achieve good results in terms of retrieval accuracy compared with Jain’s method and QBIC method.

Maximum within-cluster association

This paper addresses a new method and aspect of information-theoretic clustering where we exploit the minimum entropy principle and the quadratic distance measure between probability densities. We present a new minimum entropy objective function which leads to the maximization of within-cluster association. A simple implementation using the gradient ascent method is given. In addition, we show that the minimum entropy principle leads to the objective function of the k-means clustering, and the maximum within-cluster association is closed related to the spectral clustering which is an eigen-decomposition-based method. This information-theoretic view of spectral clustering leads us to use the kernel density estimation method in constructing an affinity matrix.

Colour and texture segmentation using wavelet frame analysis, deterministic relaxation, and fast marching algorithms

Luminance, colour, and/or texture features may be used, either alone or in combination, for segmentation. In this paper luminance and colour classes are described using the corresponding empirical probability distributions. For texture analysis and characterisation a multichannel scale/orientation decomposition is performed using wavelet frame analysis. Knowing only the number of the different classes of the image, regions of homogeneous patterns are identified. On these regions the features characterising and describing the different classes are estimated. Two labelling algorithms are proposed. The first, a deterministic relaxation algorithm using a quadratic distance measure, yields the labelling of pixels to the different colour–texture classes. The second is a new Multi-label Fast Marching algorithm utilising a level set boundary determination.

Asymptotic Properties of a Family of Minimum Quantile Distance Estimators

Abstract A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M approaches infinity. The asymptotic relative efficiency is computed for various sets of quantiles and various parameter values of the three-parameter lognormal distribution. The small-sample properties and robustness of the optimal M-quantile estimator for the three-parameter lognormal distribution are investigated in Monte Carlo studies.

Asymptotic Properties of a Family of Minimum Quantile Distance Estimators

Abstract A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M approaches infinity. The asymptotic relative efficiency is computed for various sets of quantiles and various parameter values of the three-parameter lognormal distribution. The small-sample properties and robustness of the optimal M-quantile estimator for the three-parameter lognormal distribution are investigated in Monte Carlo studies.