Leticia I. Gómez

A generic data model and query language for spatiotemporal OLAP cube analysis

Nowadays, organizations need to use OLAP (On Line Analytical Processing) tools together with geographical information. To support this, the notion of SOLAP (Spatial OLAP) arouse, aimed at exploring spatial data in the same way as OLAP operates over tables. SOLAP however, only accounts for discrete spatial data. More sophisticated GIS-based decision support systems are increasingly being needed, to handle more complex types of data, like continuous fields. Fields describe physical phenomena that change continuously in time and/or space (e.g., temperature). Although many models have been proposed for adding spatial information to OLAP tools, no one allows the user to perceive data as a cube, and analyze any type of spatial data, continuous or discrete, together with typical alphanumerical discrete OLAP data, using only the classic OLAP operators (e.g., Roll-up, Drill-down). In this paper we propose an algebra that operates over data cubes, independently of the underlying data types and physical data representation. That means, in our approach, the final user only sees the typical OLAP operators at the query level. At lower abstraction levels we provide discrete and continuous spatial data support as well as different ways of partitioning the space. We also describe a proof-of-concept implementation to illustrate the ideas presented in the paper. As far as we are aware of, this is the first proposal that allows analyzing discrete and continuous spatiotemporal data and OLAP cubes together, using just the traditional OLAP operations, thus providing a very general framework for spatiotemporal data analysis.

Piet: a GIS-OLAP implementation

Data aggregation in Geographic Information Systems (GIS) is a desirable feature, although only marginally present in commercial systems, which also fail to provide integration between GIS and OLAP (On Line Analytical Processing). With this in mind, we have developed Piet, a system that makes use of a novel query processing technique: first, a process called sub-polygonization decomposes each thematic layer in a GIS, into open convex polygons; then, another process computes and stores in a database the overlay of those layers for later use by a query processor. We describe the implementation of Piet, and provide experimental evidence that overlay precomputation can outperform GIS systems that employ indexing schemes based on R-trees.

Cube Algebra: A Generic User-Centric Model and Query Language for OLAP Cubes

The lack of an appropriate conceptual model for data warehouses and OLAP systems has led to the tendency to deploy logical models for example, star, snowflake, and constellation schemas for them as conceptual models. ER model extensions, UML extensions, special graphical user interfaces, and dashboards have been proposed as conceptual approaches. However, they introduce their own problems, are somehow complex and difficult to understand, and are not always user-friendly. They also require a high learning curve, and most of them address only structural design, not considering associated operations. Therefore, they are not really an improvement and, in the end, only represent a reflection of the logical model. The essential drawback of offering this system-centric view as a user concept is that knowledge workers are confronted with the full and overwhelming complexity of these systems as well as complicated and user-unfriendly query languages such as SQL OLAP and MDX. In this article, the authors propose a user-centric conceptual model for data warehouses and OLAP systems, called the Cube Algebra. It takes the cube metaphor literally and provides the knowledge worker with high-level cube objects and related concepts. A novel query language leverages well known high-level operations such as roll-up, drill-down, slice, and drill-across. As a result, the logical and physical levels are hidden from the unskilled end user.

A Survey of Spatio-Temporal Data Warehousing

Geographic Information Systems (GIS) have been extensively used in various application domains, ranging from economical, ecological and demographic analysis, to city and route planning. Nowadays, organizations need sophisticated GIS-based Decision Support System (DSS) to analyze their data with respect to geographic information, represented not only as attribute data, but also in maps. Thus, vendors are increasingly integrating their products, leading to the concept of SOLAP (Spatial OLAP). Also, in the last years, and motivated by the explosive growth in the use of PDA devices, the field of moving object data has been receiving attention from the GIS community. However, not much has been done in providing moving object databases with OLAP functionality. In the first part of this article we survey the SOLAP literature. We then move to Spatio-Temporal OLAP, in particular addressing the problem of trajectory analysis. We finally provide an in-depth comparative analysis between two proposals introduced in the context of the GeoPKDD EU project: the Hermes-MDC system, and Piet, a proposal for SOLAP and moving objects, developed at the University of Buenos Aires, Argentina.

Aggregation languages for moving object and places of interest

We address aggregate queries over GIS data and moving object data, where non-spatial information is stored in a data warehouse. We propose a formal data model and query language to express complex aggregate queries. Next, we study the compression of trajectory data, produced by moving objects, using the notions of stops and moves. We show that stops and moves are expressible in our query language and we consider a fragment of this language, consisting of regular expressions to talk about temporally ordered sequences of stops and moves. This fragment can be used not only for querying, but also for expressing data mining and pattern matching tasks over trajectory data.

Physical design and implementation of spatial data warehouses supporting continuous fields

Although many proposals exist for extending Geographic Information Systems (GIS) with OLAP and data warehousing capabilities (a topic denoted SOLAP), only recently the importance of supporting continuous fields (i.e., phenomena that are perceived as having a value at each point in space and/or time) has been acknowledged. Examples of such phenomena include temperature, altitude, or land use. In this paper we discuss physical design issues arising when a spatial data warehouse includes a combination of spatial and non-spatial dimensions and measures, and spatio-temporal dimensions representing continuous fields. We give the syntax and semantics of the data types (and their operators) needed to support fields in SOLAP environments, and present an implementation of these types, on top of spatial-SQL. We also show how queries using the spatio-temporal operators for fields are written, parsed, and executed.

A data model and query language for spatio-temporal decision support

In recent years, applications aimed at exploring and analyzing spatial data have emerged, powered by the increasing need of software that integrates Geographic Information Systems (GIS) and On-Line Analytical Processing (OLAP). These applications have been called SOLAP (Spatial OLAP). In previous work, the authors have introduced Piet, a system based on a formal data model that integrates in a single framework GIS, OLAP (On-Line Analytical Processing), and Moving Object data. Real-world problems are inherently spatio-temporal. Thus, in this paper we present a data model that extends Piet, allowing tracking the history of spatial data in the GIS layers. We present a formal study of the two typical ways of introducing time into Piet: timestamping the thematic layers in the GIS, and timestamping the spatial objects in each layer. We denote these strategies snapshot-based and timestamp-based representations, respectively, following well-known terminology borrowed from temporal databases. We present and discuss the formal model for both alternatives. Based on the timestamp-based representation, we introduce a formal First-Order spatio-temporal query language, which we denote

Efficient constraint evaluation in categorical sequential pattern mining for trajectory databases

\mathcal{L}_t,

Querying and Mining Trajectory Databases Using Places of Interest

able to express spatio-temporal queries over GIS, OLAP, and trajectory data. Finally, we discuss implementation issues, the update operators that must be supported by the model, and sketch a temporal extension to Piet-QL, the SQL-like query language that supports Piet.

Piet-QL: a query language for GIS-OLAP integration

The classic Generalized Sequential Patterns (GSP) algorithm returns all frequent sequences present in a database. However, usually a few ones are interesting from a users point of view. Thus, post-processing tasks are required in order to discard uninteresting sequences. To avoid this drawback, languages based on regular expressions (RE) were proposed to restrict frequent sequences to the ones that satisfy user-specified constraints. In all of these languages, REs are applied over items, which limits their applicability in complex real-world situations. We propose a much powerful language, based on regular expressions, denoted RE-SPaM, where the basic elements are constraints defined over the (temporal and non-temporal) attributes of the items to be mined. Expressions in this language may include attributes, functions over attributes, and variables. We specify the syntax and semantics of RE-SPaM, and present a comprehensive set of examples to illustrate its expressive power. We study in detail how the expressions can be used to prune the resulting sequences in the mining process. In addition, we introduce techniques that allow pruning sequences in the early stages of the process, reducing the need to access the database, making use of the categorization of the attributes that compose the items, and of the automaton that accepts the language generated by the RE. Finally, we present experimental results. Although in this paper we focus on trajectory databases, our approach is general enough for being applied to other settings.