Karol R. Opara

Efficient Calculation of Kendall’s τ for Interval Data

Calculation of the strength of dependence in the case of interval data is computation-wise a very demanding task. We consider the case of Kendall’s τ statistic, and calculate approximations of its minimal and maximal values using very easy to compute heuristic approximations. Using Monte Carlo simulations and more accurate calculations based on an evolutionary algorithm we have evaluated the effectiveness of proposed heuristics.

Grammatical rhymes in Polish poetry: A quantitative analysis

Analysis and interpretation of poetry is based on qualitative features of its text such as its semantics or means of expression as well as on general knowledge about the author and artistic period. Recent advances in automatic text processing allow for performing quantitative analysis of large sets of poetry. Their results may facilitate assessment of linguistic capabilities of its author or, in other words, his poetic mastery. This contribution presents a method of calculating the share of grammatical rhymes in Polish poetry. It is used to create a ranking of both historic and contemporary Polish poets. Comparative study and statistical analysis is developed using Pan Tadeusz by Adam Mickiewicz as a reference poem for Polish poetry. Assessment of technical mastery is one step towards the introduction of objective measures of poetic quality.

Control Charts Designed Using Model Averaging Approach for Phase Change Detection in Bipolar Disorder

Bipolar disorder is a mental illness affecting over 1% of the world’s population. In the course of disease there are episodic fluctuations between different mood phases, ranging from depression to manic episodes and mixed states. Early detection and treatment of prodromal symptoms of affective episode recurrence is crucial since it reduces the conversion rates to full-blown illness and decreases the symptoms severity. This can be achieved by monitoring the mood stability with the use of data collected from patients’ smartphones. We provide an illustrative example of the application of control charts to early and reliably generate notifications about the change of the bipolarity phase. Our charts are designed with the weighted model averaging approaches WAM* and WAMs for the detection of disturbances in the stability of the monitored processes. The models are selected in a novel way using the autocorrelation functions. The proposed approach delivers results that have clear, psychiatric interpretation. Control charts based on weighted model averaging are a promising tool for monitoring patients suffering from bipolar disorder, especially in case of limited amount of diagnostic data.

Differential Evolution: A survey of theoretical analyses

Abstract Differential Evolution (DE) is a state-of-the art global optimization technique. Considerable research effort has been made to improve this algorithm and apply it to a variety of practical problems. Nevertheless, analytical studies concerning DE are rather rare. This paper surveys the theoretical results obtained so far for DE. A discussion of genetic operators characteristic of DE is coupled with an overview of the population diversity and dynamics models. A comprehensive view on the current-day understanding of the underlying mechanisms of DE is complemented by a list of promising research directions.

Reverse clustering: an outline for a concept and its use

ABSTRACT In this study, a new perspective on the application of the clustering approach is proposed. The perspective aims to identify the values of the parameters of clustering, including the choice of the algorithm itself, which lead to a possibly faithful rendering of a partition of data, which is known a priori. Motivation and possible interpretations are discussed which can be associated with such a reverse identification process. The essential motivation is associated, but not limited, to the primary objective of cluster analysis, i.e. gaining insight into the structure of the given data-set or family of data-sets. We propose to use evolutionary strategies for reverse analysis to be carried out in view of the characteristics of the problem considered. The concept and the feasibility of the proposed computational approach are illustrated by the analysis of an exemplary data-set. The preliminary results obtained are promising in both technical and cognitive terms.

Using a Reverse Engineering Type Paradigm in Clustering. An Evolutionary Programming Based Approach

The aim of this work is to propose a novel view on the well-known clustering approach that is here dealt with from a different perspective. We consider a kind of a reverse engineering related approach, which basically consists in discovering the broadly meant values of the parameters of the clustering algorithm, including the choice of the algorithm itself, or even – more generally – its class, and some other parameters, that have possibly led to a given partition of data, known a priori. We discuss the motivation and possible interpretations related to such a novel reversed process. In fact the main motivation is gaining insight into the structure of the given data set or even a family of data sets. The use of the evolutionary strategies is proposed to computationally implement such a reverse analysis. The idea and feasibility of the proposed computational approach is illustrated on two benchmark type data sets. The preliminary results obtained are promising in terms of a balance between analytic and computational effectiveness and efficiency, quality of results obtained and their comprehensiveness and intuitive appeal, a high application potential, as well as possibilities for further extensions.

Computation of general correlation coefficients for interval data

This paper provides a comprehensive analysis of computational problems concerning calculation of general correlation coefficients for interval data. Exact algorithms solving this task have unacceptable computational complexity for larger samples, therefore we concentrate on computational problems arising in approximate algorithms. General correlation coefficients for interval data are also given by intervals. We derive bounds on their lower and upper endpoints. Moreover, we propose a set of heuristic solutions and optimization methods for approximate computation. Extensive simulation experiments show that the heuristics yield very good solutions for strong dependencies. In other cases, global optimization using evolutionary algorithm performs best. A real data example of autocorrelation of cloud cover data confirms the applicability of the approach. Crisp and interval generalized correlation coefficients are discussed.Outer bounds for Spearmans rho and Kendalls tau are derived.Comparison of algorithms computing correlation coefficients for interval data.Simple heuristic solutions prove effective for strong dependencies.Simulation study and a real data example show applicability of the approach.