On the weak monotonicity of Gini means and other mixture functions

Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.

Weak monotonicity of Lehmer and Gini means

We analyze directional monotonicity of several mixture functions in the direction (1,1...,1), called weak monotonicity. Our particular focus is on power weighting functions and the special cases of Lehmer and Gini means. We establish limits on the number of arguments of these means for which they are weakly monotone. These bounds significantly improve the earlier results and hence increase the range of applicability of Gini and Lehmer means. We also discuss the case of affine weighting functions and find the smallest constant which ensures weak monotonicity of such mixture functions.

Multi-agent based supply chain management with dynamic reconfiguration capability

Supply chain management (SCM) has received increased attention in a globally challenging environment as companies face the necessity to improve customer service and maximize profit. Therefore, dynamic reconfiguration capability is vital for supply chain management to respond to changing customer requirements and operating environments. On the other hand, for its flexible and autonomous characteristics, multi-agent systems are a viable technology for SCM, and have been widely applied in SCM. To this end, dynamic reconfiguration in agent-based SCM systems is proposed from autonomy oriented computing point of view. The performance of agent-based SCM with dynamic reconfiguration is evaluated under a modified TAC SCM scenario. With a dynamic reconfigurable SCM system, new products and processes can be introduced with considerably less expense and ramp-up time.

Income distribution in Australia 1986

This thesis focuses on the distribution of income across income units, as defined by the Australian Bureau of Statistics, in Australia in 1986. An examination of the conceptual issues involved in analysing income distribution is followed by a description of the various statistical and normative inequality measures that may be used to determine the level of inequality. Previous Australian studies is reported on before analysing the 1986 Income Distribution Survey. The analysis focuses on the summary statistical measures of the Gini coefficient the coefficient of variation and the percentile shares. In addition, the contribution of income of various population sub-groups to overall inequality is examined to provide insight into the sources of inequality. To this end, the Gini coefficient is decomposed using a method developed by Fodder (1991), whereby the population is divided into a number of subgroups based on one socio-demographic characteristic at a time. The exact effects of a percentage change in income for a particular sub-group to overall inequality, as well as the elasticity of the Gini coefficient with respect to a sub-group can be computed. The decomposition is undertaken using both the unadjusted and the equivalent gross weekly income. Policy considerations and conclusions regarding the level of inequality as existed in 1986 are suggested in the final chapter.

Global inequality in well-being dimensions

This paper contributes to the literature on global inequality in multidimensional well-being by examining inter-country disparities in the longevity, knowledge and standard of material living components of the well-known and widely-used Human Development Index for the years 1992-2004. It differs from previous studies by examining global inequality in each of the components of this index alongside that of the index as a whole, thus side-stepping ambiguities over weighting that are inherent to multidimensional well-being indices. The Gini coefficient, both population and non-population weighted, is used to measure the extent of inequality. Results indicate that the different components often provide very different information to the index as a whole, especially with respect to changes in global inequality over time. Most component variables show declines in global inequality, whereas the longevity component exhibits increased inequality since 1992.

Weakly monotone averaging functions

Averaging behaviour of aggregation functions depends on the fundamental property of monotonicity with respect to all arguments. Unfortunately this is a limiting property that ensures that many important averaging functions are excluded from the theoretical framework. We propose a definition for weakly monotone averaging functions to encompass the averaging aggregation functions in a framework with many commonly used non-monotonic means. Weakly monotonic averages are robust to outliers and noise, making them extremely important in practical applications. We show that several robust estimators of location are actually weakly monotone and we provide sufficient conditions for weak monotonicity of the Lehmer and Gini means and some mixture functions. In particular we show that mixture functions with Gaussian kernels, which arise frequently in image and signal processing applications, are actually weakly monotonic averages. Our concept of weak monotonicity provides a sound theoretical and practical basis for understanding both monotone and non-monotone averaging functions within the same framework. This allows us to effectively relate these previously disparate areas of research and gain a deeper understanding of averaging aggregation methods. © Springer International Publishing Switzerland 2014.

EEG data classification using wavelet features selected by Wilcoxon statistics

This paper introduces a method to classify EEG signals using features extracted by an integration of wavelet transform and the nonparametric Wilcoxon test. Orthogonal Haar wavelet coefficients are ranked based on the Wilcoxon test’s statistics. The most prominent discriminant wavelets are assembled to form a feature set that serves as inputs to the naïve Bayes classifier. Two benchmark datasets, named Ia and Ib, downloaded from the brain–computer interface (BCI) competition II are employed for the experiments. Classification performance is evaluated using accuracy, mutual information, Gini coefficient and F-measure. Widely used classifiers, including feedforward neural network, support vector machine, k-nearest neighbours, ensemble learning Adaboost and adaptive neuro-fuzzy inference system, are also implemented for comparisons. The proposed combination of Haar wavelet features and naïve Bayes classifier considerably dominates the competitive classification approaches and outperforms the best performance on the Ia and Ib datasets reported in the BCI competition II. Application of naïve Bayes also provides a low computational cost approach that promotes the implementation of a potential real-time BCI system.

Fuzzy system with tabu search learning for classification of motor imagery data

This paper introduces an approach to classify EEG signals using wavelet transform and a fuzzy standard additive model (FSAM) with tabu search learning mechanism. Wavelet coefficients are ranked based on statistics of the Wilcoxon test. The most informative coefficients are assembled to form a feature set that serves as inputs to the tabu-FSAM. Two benchmark datasets, named Ia and Ib, downloaded from the brain-computer interface (BCI) competition II are employed for the experiments. Classification performance is evaluated using accuracy, mutual information, Gini coefficient and F-measure. Widely-used classifiers, including feedforward neural network, support vector machine, k-nearest neighbours, ensemble learning Adaboost and adaptive neuro-fuzzy inference system, are also implemented for comparisons. The proposed tabu-FSAM method considerably dominates the competitive classifiers, and outperforms the best performance on the Ia and Ib datasets reported in the BCI competition II.