Multi Dimensional Analysis

This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.

Multi-Dimensional Analysis: Research Methods and Current Issues provides a comprehensive guide both to the statistical methods in Multi-Dimensional Analysis (MDA) and its key elements, such as corpus building, tagging, and tools. The major goal is to explain the steps involved in the method so that readers may better understand this complex research framework and conduct MD research on their own. Multi-Dimensional Analysis is a method that allows the researcher to describe different registers (textual varieties defined by their social use) such as academic settings, regional discourse, social media, movies, and pop songs. Through multivariate statistical techniques, MDA identifies complementary correlation groupings of dozens of variables, including variables which belong both to the grammatical and semantic domains. Such groupings are then associated with situational variables of texts like information density, orality, and narrativity to determine linguistic constructs known as dimensions of variation, which provide a scale for the comparison of a large number of texts and registers. This book is a comprehensive research guide to MDA.

Poverty is a paradoxical state. Recognizable in the eld for any sensitive observer who travels in remote rural areas and urban slums and meets marginalized people in a given society, poverty still remains a challenge to conceptual formalization and to measurement that is consistent with such formalization. The analysis of poverty is multidisciplinary. It goes from ethics to economics, from political science to human biology, and any type of measurement rests on mathematics. Moreover, poverty is multifaceted according to the types of deprivation, and it is also gender and age speci c. A vector of variables is required, which raises a substantial problem for individual and group comparisons necessary to equity analysis. Multidimension- ity also complicates the aggregation necessary to perform the ef ciency analysis of policies. In the case of income poverty, these two problems, equity and ef ciency, have bene ted from very signi cant progress in the eld of economics. Similar achievements are still to come in the area of multidimensional poverty. Within this general background, this book has a very modest and narrow-scoped objective. It proposes an operational methodology for measuring multidimensional poverty, independent from the conceptual origin, the size and the qualitative as well as the quantitative nature of the primary indicators used to describe the poverty of an individual, a household or a sociodemographic entity.

Approximately a quarter of a century ago, the Multi-Dimensional (MD) approach—one of the most powerful (and controversial) methods in Corpus Linguistics—saw its first book-length treatment. In its eleven chapters, this volume presents all new contributions covering a wide range of written and spoken registers, such as movies, music, magazine texts, student writing, social media, letters to the editor, and reports, in different languages (English, Spanish, Portuguese) and contexts (engineering, journalism, the classroom, the entertainment industry, the Internet, etc.). The book also includes a personal account of the development of the method by its creator, Doug Biber, an introduction to MD statistics, as well as an application of MD analysis to corpus design. The book should be essential reading to anyone with an interest in how texts, genres, and registers are used in society, what their lexis and grammar look like, and how they are interrelated.

Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sam

This book highlights recent developments in multidimensional data visualization, presenting both new methods and modifications on classic techniques. Throughout the book, various applications of multidimensional data visualization are presented including its uses in social sciences (economy, education, politics, psychology), environmetrics, and medicine (ophthalmology, sport medicine, pharmacology, sleep medicine). The book provides recent research results in optimization-based visualization. Evolutionary algorithms and a two-level optimization method, based on combinatorial optimization and quadratic programming, are analyzed in detail. The performance of these algorithms and the development of parallel versions are discussed. The utilization of new visualization techniques to improve the capabilies of artificial neural networks (self-organizing maps, feed-forward networks) is also discussed. The book includes over 100 detailed images presenting examples of the many different visualization techniques that the book presents. This book is intended for scientists and researchers in any field of study where complex and multidimensional data must be represented visually.

The concept of a big data warehouse appeared in order to store moving data objects and temporal data information. Moving objects are geometries that change their position and shape continuously over time. In order to support spatio-temporal data, a data model and associated query language is needed for supporting moving objects. Emerging Perspectives in Big Data Warehousing is an essential research publication that explores current innovative activities focusing on the integration between data warehousing and data mining with an emphasis on the applicability to real-world problems. Featuring a wide range of topics such as index structures, ontology, and user behavior, this book is ideally designed for IT consultants, researchers, professionals, computer scientists, academicians, and managers.

Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.