A relational algebra approach to ETL modeling

The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and Porto

A spatial multicriteria model for urban accessibility mapping

Accessibility is nowadays an important issue for the development of cities. It is seen as a priority in order toguarantee equal access to fundamental rights, to improve the quality of life of citizens and to ensure that everyone, regardless of age, mobility or ability, have equal access to all the resources and benefits cities have to offer. Consequently, factors closely related to the accessibility have gained a higher relevance for identifying and assessing the location of urban facilities. The main goal of the paper is to present an accessibility evaluation model applied in Santarém, in Brazil, a city located midway between the larger cities of Belem and Manaus. The research instruments, sampling method and data analysis proposed for mapping urban accessibility are described. Daily activities were used to identify and group key destinations. The model was implemented within a geographic information system and integrates the individualâ s perspective through the definition of each key destination weight, reflecting their significance for daily activities in the urban area. Accessibility to key destinations was mapped over 24 districts of the city of Santarém. The results of this model application can support city administration decision-making for new investments in order to improve urban quality of life.

Using relational algebra on the specification of real world ETL processes

Modeling Extract-Transform-Load (ETL) processes of a Data Warehousing System has always been a challenge. The heterogeneity of the sources, the quality of the data obtained and the conciliation process are some of the issues that must be addressed in the design phase of this critical component. Commercial ETL tools often provide proprietary diagrammatic components and modeling languages that are not standard, thus not providing the ideal separation between a modeling platform and an execution platform. This separation in conjunction with the use of standard notations and languages is critical in a system that tends to evolve through time and which cannot be undermined by a normally expensive tool that becomes an unsatisfactory component. In this paper we demonstrate the application of Relational Algebra as a modeling language of an ETL system as an effort to standardize operations and provide a basis for uncommon ETL execution platforms.

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.