Bart Kuijpers

A model for enriching trajectories with semantic geographical information

The collection of moving object data is becoming more and more common, and therefore there is an increasing need for the efficient analysis and knowledge extraction of these data in different application domains. Trajectory data are normally available as sample points, and do not carry semantic information, which is of fundamental importance for the comprehension of these data. Therefore, the analysis of trajectory data becomes expensive from a computational point of view and complex from a users perspective. Enriching trajectories with semantic geographical information may simplify queries, analysis, and mining of moving object data. In this paper we propose a data preprocessing model to add semantic information to trajectories in order to facilitate trajectory data analysis in different application domains. The model is generic enough to represent the important parts of trajectories that are relevant to the application, not being restricted to one specific application. We present an algorithm to compute the important parts and show that the query complexity for the semantic analysis of trajectories will be significantly reduced with the proposed model.

A clustering-based approach for discovering interesting places in trajectories

Because of the large amount of trajectory data produced by mobile devices, there is an increasing need for mechanisms to extract knowledge from this data. Most existing works have focused on the geometric properties of trajectories, but recently emerged the concept of semantic trajectories, in which the background geographic information is integrated to trajectory sample points. In this new concept, trajectories are observed as a set of stops and moves, where stops are the most important parts of the trajectory. Stops and moves have been computed by testing the intersections of trajectories with a set of geographic objects given by the user. In this paper we present an alternative solution with the capability of finding interesting places that are not expected by the user. The proposed solution is a spatio-temporal clustering method, based on speed, to work with single trajectories. We compare the two different approaches with experiments on real data and show that the computation of stops using the concept of speed can be interesting for several applications.

ST‐DMQL: A Semantic Trajectory Data Mining Query Language

Mobile devices are becoming very popular in recent years, and large amounts of trajectory data are generated by these devices. Trajectories left behind cars, humans, birds or other objects are a new kind of data which can be very useful in the decision making process in several application domains. These data, however, are normally available as sample points, and therefore have very little or no semantics. The analysis and knowledge extraction from trajectory sample points is very difficult from the users point of view, and there is an emerging need for new data models, manipulation techniques, and tools to extract meaningful patterns from these data. In this paper we propose a new methodology for knowledge discovery from trajectories. We propose through a semantic trajectory data mining query language several functionalities to select, preprocess, and transform trajectory sample points into semantic trajectories at higher abstraction levels, in order to allow the user to extract meaningful, understandable, and useful patterns from trajectories. We claim that meaningful patterns can only be extracted from trajectories if the background geographical information is considered. Therefore we build the proposed methodology considering both moving object data and geographic information. The proposed language has been implemented in a toolkit in order to provide a first software prototype for trajectory knowledge discovery.

A qualitative trajectory calculus and the composition of its relations

Continuously moving objects are prevalent in many domains. Although there have been attempts to combine both spatial and temporal relationships from a reasoning, a database, as well as from a logical perspective, the question remains how to describe motion adequately within a qualitative calculus. In this paper, a Qualitative Trajectory Calculus (QTC) for representing and reasoning about moving objects in two dimensions is presented. Specific attention is given to a central concept in qualitative reasoning, namely the composition of relations. The so-called composition-rule table is presented, which is a neat way of representing a composition table. The usefulness of QTC and the composition-rule table is illustrated by an example.

Modeling uncertainty of moving objects on road networks via space–time prisms

Moving objects produce trajectories, which are typically observed in a finite sample of time‐stamped locations. Between sample points, we are uncertain about the moving objectss location. When we assume extra information about an object, for instance, a (possibly location‐dependent) speed limit, we can use space–time prisms to model the uncertainty of an objects location. Until now, space–time prisms have been studied for unconstrained movement in the 2D plane. In this paper, we study space–time prisms for objects that are constrained to travel on a road network. Movement on a road network can be viewed as essentially one‐dimensional. We describe the geometry of a space–time prism on a road network and give an algorithm to compute and visualize space–time prisms. For experiments and illustration, we have implemented this algorithm in MATHEMATICA. Furthermore, we study the alibi query, which asks whether two moving objects could have possibly met or not. This comes down to deciding if the chains of space–time prisms produced by these moving objects intersect. We give an efficient algorithm to answer the alibi query for moving objects on a road network. This algorithm also determines where and when two moving objects may have met.

Anchor uncertainty and space-time prisms on road networks

Space-time prisms capture all possible locations of a moving person or object between two known locations and times given the maximum travel velocities in the environment. These known locations or ‘anchor points’ can represent observed locations or mandatory locations because of scheduling constraints. The classic space-time prism as well as more recent analytical and computational versions in planar space and networks assume that these anchor points are perfectly known or fixed. In reality, observations of anchor points can have error, or the scheduling constraints may have some degree of pliability. This article generalizes the concept of anchor points to anchor regions: these are bounded, possibly disconnected, subsets of space-time containing all possible locations for the anchor points, with each location labelled with an anchor probability. We develop two algorithms for calculating network-based space-time prisms based on these probabilistic anchor regions. The first algorithm calculates the envelope of all space-time prisms having an anchor point within a particular anchor region. The second algorithm calculates, for any space-time point, the probability that a space-time prism with given anchor regions contains that particular point. Both algorithms are implemented in Mathematica to visualize travel possibilities in case the anchor points of a space-time prism are uncertain. We also discuss the complexity of the procedures, their use in analysing uncertainty or flexibility in network-based prisms and future research directions.

Lossless Representation of Topological Spatial Data

We present a data structure used to represent planar spatial databases in the topological data model. Conceptually, such databases consist of points, lines between these points, and areas formed by these lines. The data structure has the distinctive feature that it is geared toward supporting queries involving topological properties of the database only: two databases that are topologically equivalent have the same representation. Moreover, no information is lost in this way: two databases that are not topologically equivalent never have the same representation.

Trajectory databases: Data models, uncertainty and complete query languages

Moving objects produce trajectories. We describe a data model for trajectories and trajectory samples and an efficient way of modeling uncertainty via beads for trajectory samples. We study transformations for which important physical properties of trajectories, such as speed, are invariant. We also determine which transformations preserve beads. We give conceptually easy first-order complete query languages and computationally complete query languages for trajectory databases, which allow to talk directly about speed and beads. The queries expressible in these languages are invariant under speed- and bead-preserving transformations.

Spatiotemporal Data Mining

After the introduction and development of the relational database model between 1970 and the 1980s, this model proved to be insufficiently expressive for specific applications dealing with, for instance, temporal data, spatial data and multi-media data. From the mid-1980s, this has led to the development of domain-specific database systems, the first being temporal databases, later followed by spatial database systems. In the area of data mining, we have seen a similar development. Many data mining techniques – such as frequent set and association rule mining, classification, prediction and clustering – were first developed for typical alpha-numerical business data. From the second half of the 1990s, these techniques were studied for temporal and spatial data and sometimes specific, previously well studied, techniques such as time-series analysis were introduced in the data mining field. For an overview of mining techniques in spatial and geographic data, we refer to Chap. 9. For spatiotemporal data, this development has only just started. This field is no longer in an embryonic state; now, in 2007, we can say that with the organization of a few workshops, this field has just been born. In this chapter, we give an overview of what has been done in spatiotemporal data mining, with a focus on mining trajectories of moving objects, and we mainly emphasize the challenges that this field faces. This chapter is organized as follows. In Sect. 10.2, we outline, by means of examples, challenging tasks for spatiotemporal mining. In Sects. 10.3 and 10.4, we discuss, respectively, spatiotemporal clustering and patterns. Spatiotemporal prediction and classification, including time series, are discussed in Sect. 10.5. In Sect. 10.6, the role played by uncertainty in spatiotemporal data mining is briefly described. Finally, in Sect. 10.7, we summarize the main problems and issues

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.