Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk

The purpose of this paper is to describe the R package {PTAk and how the spatio-temporal context can be taken into account in the analyses. Essentially PTAk() is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTAk-modes method proposes a way of generalizing SVD (singular value decomposition), as well as some other well known methods included in the R package, such as PARAFAC or CANDECOMP and the PCAn-modes or Tucker-n model. The example datasets cover different domains with various spatio-temporal characteristics and issues: (i)~medical imaging in neuropsychology with a functional MRI (magnetic resonance imaging) study, (ii)~pharmaceutical research with a pharmacodynamic study with EEG (electro-encephaloegraphic) data for a central nervous system (CNS) drug, and (iii)~geographical information system (GIS) with a climatic dataset that characterizes arid and semi-arid variations. All the methods implemented in the R package PTAk also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, PTAk constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints.

Quality of Life, Firm Productivity, and the Value of Amenities across Canadian Cities

This paper presents the first hedonic general-equilibrium estimates of quality-of-life and firm productivity differences across Canadian cities, using data on local wages and housing costs. These estimates account for the unobservability of land rents and geographic differences in federal and provincial tax burdens. Quality of life estimates are generally higher in Canada’s larger cities: Victoria, Vancouver are the nicest overall, particularly for Anglophones, while Montreal and Ottawa are the nicest for Francophones. These estimates are positively correlated with estimates in the popular literature and may be explained by differences in climate. Toronto is Canada’s most productive city; Vancouver, the overall most valued city.quality of life, firm productivity, cost-of-living, firm productivity, compensating wage differentials

Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk

The purpose of this paper is to describe the <b>R</b> package {<b>PTAk</b> and how the spatio-temporal context can be taken into account in the analyses. Essentially PTAk() is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTAk-modes method proposes a way of generalizing SVD (singular value decomposition), as well as some other well known methods included in the <b>R</b> package, such as PARAFAC or CANDECOMP and the PCAn-modes or Tucker-n model. The example datasets cover different domains with various spatio-temporal characteristics and issues: (i)~medical imaging in neuropsychology with a functional MRI (magnetic resonance imaging) study, (ii)~pharmaceutical research with a pharmacodynamic study with EEG (electro-encephaloegraphic) data for a central nervous system (CNS) drug, and (iii)~geographical information system (GIS) with a climatic dataset that characterizes arid and semi-arid variations. All the methods implemented in the <b>R</b> package <b>PTAk</b> also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, <b>PTAk</b> constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints

A singular value decomposition of a k-way array for a principal component analysis of multiway data, PTA-k

AbstractEmploying a tensorial approach to describe a k-way array, the singular value decomposition of this type of multiarray is established. The algorithm given to attain a singular value, based on a generalization of the transition formulae, has a Gauss-Seidel form. A recursive algorithm leads to the decomposition termed SVD-k. A generalization of the Eckart-Young theorem is introduced by consideration of new rank concepts: the orthogonal rank and the free orthogonal rank. The application of this generalization in data analysis is illustrated by a principal component analysis (PCA) over k modes, termed PTA-k, which conserves most of the properties of a PCA

Higher-order co-occurrences for exploratory point pattern analysis and decision tree clustering on spatial data

Analyzing geographical patterns by collocating events, objects or their attributes has a long history in surveillance and monitoring, and is particularly applied in environmental contexts, such as ecology or epidemiology. The identification of patterns or structures at some scales can be addressed using spatial statistics, particularly marked point processes methodologies. Classification and regression trees are also related to this goal of finding "patterns" by deducing the hierarchy of influence of variables on a dependent outcome. Such variable selection methods have been applied to spatial data, but, often without explicitly acknowledging the spatial dependence. Many methods routinely used in exploratory point pattern analysis are2nd-order statistics, used in a univariate context, though there is also a wide literature on modelling methods for multivariate point pattern processes. This paper proposes an exploratory approach for multivariate spatial data using higher-order statistics built from co-occurrences of events or marks given by the point processes. A spatial entropy measure, derived from these multinomial distributions of co-occurrences at a given order, constitutes the basis of the proposed exploratory methods. © 2010 Elsevier Ltd

Full Metadata Object profiling for flexible geoprocessing workflows

The design and running of complex geoprocessing workflows is an increasingly common geospatial modelling and analysis task. The Business Process Model and Notation (BPMN) standard, which provides a graphical representation of a workflow, allows stakeholders to discuss the scientific conceptual approach behind this modelling while also defining a machine-readable encoding in XML. Previous research has enabled the orchestration of Open Geospatial Consortium (OGC) Web Processing Services (WPS) with a BPMN workflow engine. However, the need for direct access to pre-defined data inputs and outputs results in a lack of flexibility during composition of the workflow and of efficiency during execution. This article develops metadata profiling approaches, described as two possible configurations, which enable workflow management at the meta-level through a coupling with a metadata catalogue. Specifically, a WPS profile and a BPMN profile are developed and tested using open-source components to achieve this coupling. A case study in the context of an event mapping task applied within a big data framework and based on analysis of the Global Database of Event Language and Tone (GDELT) database illustrates the two different architectures

A flexible framework for assessing the quality of crowdsourced data

Ponencias, comunicaciones y pósters presentados en el 17th AGILE Conference on Geographic Information Science "Connecting a Digital Europe through Location and Place", celebrado en la Universitat Jaume I del 3 al 6 de junio de 2014.Crowdsourcing as a means of data collection has produced previously unavailable data assets and enriched existing ones, but its quality can be highly variable. This presents several challenges to potential end users that are concerned with the validation and quality assurance of the data collected. Being able to quantify the uncertainty, define and measure the different quality elements associated with crowdsourced data, and introduce means for dynamically assessing and improving it is the focus of this paper. We argue that the required quality assurance and quality control is dependent on the studied domain, the style of crowdsourcing and the goals of the study. We describe a framework for qualifying geolocated data collected from non-authoritative sources that enables assessment for specific case studies by creating a workflow supported by an ontological description of a range of choices. The top levels of this ontology describe seven pillars of quality checks and assessments that present a range of techniques to qualify, improve or reject data. Our generic operational framework allows for extension of this ontology to specific applied domains. This will facilitate quality assurance in real-time or for post-processing to validate data and produce quality metadata. It enables a system that dynamically optimises the usability value of the data captured. A case study illustrates this framework