Synthetic Generation of Cellular Network Positioning Data

Transcription

1 Synthetic Generation of Cellular Network Positioning Data F. Giannotti, A.Mazzoni, KDDlab ISTI - CNR, Pisa {giannotti,mazzoni}@isti.cnr.it S. Puntoni KDDlab ISTI - CNR, Pisa puntoni@isti.cnr.it C. Renso KDDlab ISTI - CNR, Pisa c.renso@isti.cnr.it ABSTRACT The flow of data coming from wireless telecommunication devices enables a novel classes of applications of high societal and economic impact. However, to make this flow of data useful, techniques for the discovery of consumable and concise knowledge out of these raw data have to be developed. Within the long term goal of devising knowledge discovery and analysis methods for trajectories of moving objects, this paper focuses on providing a system to build benchmark datasets for cellular devices positioning data, that typically will not be easily publicly available for scientific research. We called this system CENTRE (CEllular Network Trajectories Reconstruction Environment), and it aims at randomly generating movement data of users through cellular network by simulating semantic-based movement behaviours from a setting of user parameters. CENTRE allows to combine user preferences which may influence the random distributions, domain semantics such as those depending on the cartography and by interesting geo-referenced objects or spatial constraints. The system is composed by three components, namely the Synthetic Trajectories Generation, able to generate possible objects behaviour on a specific space, the Logs generation, which is designed to take into account the various network technological requirements and the Approximated Trajectories Reconstruction which performs the reconstruction taking into account the approximation of the data. Categories and Subject Descriptors H.2.8 [Database Management]: Database Applications Spatial databases and GIS; H.2.8 [Database Management]: Database Applications Data mining General Terms Algorithms Keywords Spatio-temporal Data Generators, Trajectories, Data Mining, Mobile Devices Positioning Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. GIS 05, November 4, 2005, Bremen, Germany. Copyright 2005 ACM /05/ $ INTRODUCTION A flood of data pertinent to moving objects is available today, and will be more in the near future, particularly due to the automated collection of telecom data from mobile phones and other location-aware devices. Such wealth of data, referenced both in space and time, may enable novel classes of applications of high societal and economic impact, provided that the discovery of consumable and concise knowledge out of these raw data is made possible. We aim at devising knowledge discovery and analysis methods for trajectories of moving objects. The fundamental hypothesis is that it is possible, in principle, to aid citizens in their mobile activities by analysing the traces of their past activities by means of data mining techniques. For instance, behavioural patterns derived from mobile trajectories may allow inducing traffic flow information, capable to help people travel efficiently, to help public administrations in traffic-related decision making for sustainable mobility and security management, as well as to help mobile operators in optimising bandwidth and power allocation on the network. Indeed mobile device location data are critical for the owner telecom company, mainly due to privacy concerns, but also due to technical reasons, making difficult for the analysts to access tracking data. However, it is clear that such valuable data, so rich of personal sensitive information will not be easily publicly available for scientific research. Having benchmark data sets which allow to compare and validate analysis algorithms will be a hard task when synthetic data generators are not provided. The long term research goal is to define a knowledge discovery support environment for automatic extraction of patterns and models from movement data. This paper concentrates on the crucial bootstrap action of automatic generation of movement data, in particular related to the generation of movement data of mobile telephones. Our objective is to provide a system, called CENTRE (CEllular Network Trajectories Reconstruction Environment), able to randomly generate movement data by simulating different movement behaviours specified by some user preferences, defining user defined topologies and cellular network requirements. Moreover, such data are referenced on a geographic scenario which provides further constraints and background knowledge. Problem statement: the problem is to produce a data set of Logs representing temporal and spatial locations of a mobile telephone as detected by a cellular network. This Location Information represents movements of persons owning a mobile phone, which sometime are speaking, sometimes are idle, simultaneously they are moving in a variety of ways: by car, by foot, inside a building, outside etc. These Logs are generated by a network of antennas whose position and power may vary according to the characteristics of the territory, for instance urban versus country side.

2 Since we are interested in generating Logs with realistic semantics, we have divided the problem in two steps: the first one generates synthetic trajectories of moving objects, on the basis of the combination of user-defined statistical distributions and driving movement behaviours. Such synthetic trajectories, at this stage, are collections of precise positions of objects (Instances) representing their evolution in space and time. The second step transforms synthetic trajectories into Logs simulating the detection action performed by a specific network of antennas. It is worth noticing that the Log generation process typically produces a loss of information compared to the original position of points, as they are approximated with the antenna covered area (the cell, possibly also with the distance from the antenna position). Obviously, points not covered by any of the antennas will be lost since no Log is generated. As a final step towards providing synthetic data ready to use by data mining algorithms, CENTRE provides a trajectory reconstruction module, where original trajectories are approximated starting from generated Logs. The system presented in this paper is a workbench to experiment and validate data mining algorithms on mobile telephone data. Its architecture has been modelled to combine user preferences, domain semantics and random generation. It is composed by the following main components: The synthetic trajectories generation module is based on an extension of GSTD algorithm (Generate Spatio Temporal Data [13, 9]). The extension is mainly concerned with the capability to drive the generation process with different group behaviour defined by the user. Each group defines typical aspects of a moving object, such as velocity, direction, agility, by using several probability distributions. We can also define, for each group, an infrastructure, a collection of rectangles, that must be avoided by group objects, during generation process. Here we have defined the possibility for object to change group during the evolution as the moving behaviour of a person may change during the day (we refer to different moving characters of cars, bicycles or pedestrians). Each group is characterised by a parameter setting used for several probability distributions representing typical aspects of a moving behaviour, such as speed, direction etc.. These distributions are then combined to generate typical trajectories. Then the groups themselves may be fatherly combined as the moving behaviour of a person may change in time. The Log generation module takes a set of synthetic trajectories represented as a collection of points and a topology of a network of antennas, named antenna cover map, and returns a set of antenna detection logs. In fact, each point of the trajectory is transformed according to its intersection with the detection area of one or more antennas. The user may define his own antenna cover map through a Geographic Information System so that she/he may generate different simulation scenarios. It could be interesting for example for the analyst to evaluate the effects of different antennas distribution on the Log generation by playing with different antenna cover maps over the same set of synthetic trajectories. Once the Logs of mobile data are available, either synthetically generated or as real data provided by the telecom operator, data has to be prepared for the analysis algorithms. The trajectory reconstruction module takes as input the set of Logs and an antenna cover map and tries to reconstruct the original (synthetic or not) trajectories. Reconstructed trajectories are, typically, an approximation of the original ones, due to the information loss of the Log generation step. This additional functionality provides a minimal kernel of the system where experiments may really be carried on. The plan of the paper follows. In section 2 we introduce the basic concepts on cellular networks and some related work on spatiotemporal data generators. Section 3 presents the architecture of the system and a detailed description of the three main components: Synthetic trajectory generation, Log generation and Trajectory reconstruction. Section 4 presents a running example of Synthetic trajectories generation with two behaviour groups and Trajectories reconstruction. Section 5 is demanded to conclusions and future works. 2. FUNDAMENTAL CONCEPTS In this section we briefly recall some useful concepts about wireless telecommunication and spatio-temporal synthetic data generation. 2.1 Location Management in Cellular Networks Two of the most used worldwide telecommunication protocols for mobile telephones are GSM and UMTS protocols [7]. These protocols are based on a network architecture called cellular. We will give here a common positioning model for both GSM and UMTS protocols, that have similar characteristics concerning positioning data. In general, in a cellular architecture a covered geographical area is disseminated by a number of antennas (or base stations, BTS) emitting a signal to be received by mobile devices. Each antenna covers an area called cell. In this way, the covered area is partitioned in a number of, possibly overlapping, cells uniquely identified by the antenna Id. In urban areas, cells are close to each other and small in area (pico-cells) whose diameter can be down to hundred meters. In rural areas the diameter of a cell can reach kilometres. Typically, UMTS cells are smaller than GSM ones. The presence of a device in a cell is detected by the system periodically for idle devices and continuously for in conversation devices, to maintain correctness and validity of the location information subsystem. Actual position data is maintained in GSM/UMTS location databases called VLR and HLR (Visitor/Home Location Register) [6]. These registers maintain position information of each mobile registered in the network. The VLR controls a Location Area (a quite great region) and stores information about changes of position that occur between substructure (cells and group of cells) of the interested area. The HLR, a global register, stores information about position changes of mobiles between different location area, therefore between different VLR. Beside these registers, that are necessary for the correct operation of the GSM/UMTS system, position retrieval information can be obtained with mobile location solution developed by Ericsson, that exploits a specific server called Mobile Positioning Center (MPC) to supply Location Based Services [5]. There are also many different techniques to discover the position of a mobile inside the network. Some of these techniques use information deriving by antennas close to the mobile device (for example TOA, TDOA, UL-TOA and E-OTD), other are GPS-assisted (A-GPS). Details on such techniques can be found in [5] and [12] Due to the complexity of the domain and considering it is out of the scope of our work to simulate the GSM/UMTS protocol in details, we defined a simplified model of the network structure. In this model, we suppose to use a circular area to represent a cell (compared with sectorial antennas that cover a cone-shaped area). Furthermore, we assume to have a fixed-frequency system to detect the presence of a device inside the network. Like in UL-TOA tech-

3 nique [12], in our model each detection produces a spatio-temporal information that can be summarised by the quadruple (ob j id,ant id,t,d) (1) called Log, where ob j id uniquely identifies the detected device, ant id uniquely identifies the detecting antenna, t is time of detection, d is distance of the device from the antenna. This Log is a simplified model of data that can be physically obtained with different techniques from GSM/UMTS networks. Typically, Logs are not always stored by the telecommunication company, unless they need them for specific tasks, due to the high costs in terms of memory space and network bandwidth. 2.2 Spatio-Temporal Data Generators A moving object is an object evolving in space and time. Examples of moving objects come from everyday life and from several applications fields, from meteorology, to environmental science, to people moving in cities or animals moving in their habitat. A moving object can be modelled as a moving region when it changes its extend and/or shape and its position, over time. When the object is modelled as a point, there is no shape or extent that changes over time, therefore only its spatial localisation characterise its evolution. The spatio-temporal movements of a moving point is named trajectory and it is usually represented as a set of localisation points connected by a polyline. As we have pointed out in the previous section, there are many reasons to generate synthetic datasets. When dealing with spatiotemporal data, such generators should produce a number of spatio-temporal objects that evolve in space over time. Indeed, the evolution of generated objects is usually controlled by user settings. In the field of spatio-temporal databases a few data generators have been proposed in the literature. The Generator for Spatio-Temporal Data (GSTD) [9, 13] is one of the most well known in the literature and, as we will see later, it has been taken as the kernel of our system. GSTD can be seen as a general synthetic spatio temporal data generator since it is not directed to a particular application field and it aims at representing object general movements behaviours. Objects can be points or rectangles moving on positive cartesian plain R 2 + (called workspace), and on the temporal interval [0,1]. Since we are interested in generating mobile telephones movements, that can be abstracted as points, from now on we will focus only on generating moving points. The main idea of GSTD is to generate, for each object o id, a finite number of tuples of the kind (o id, t, s), called Instances of object o id, where t is the timestamp and s the spacestamp. Therefore, an Instance of object o id is a point, generated by the algorithm, with a spatial and temporal localisation. Instances, that are temporally consecutive, represent the evolution of the object. In particular the algorithm considers a sampling of the evolution by taking a user-defined number of snapshots, saving only relative instances. The snapshot concept is in some sense quite similar to a sampling task where positions of the moving object are taken at fixed interval time. Global input parameters control initial placement and subsequent evolution of objects by setting random distributions parameters. These random distributions are exploited to compute spatio-temporal evolution properties like temporal increment interval t and spatial increment c[ ]. Using these values, the algorithm computes the next instance of the object, given the current one: NewSpaceStamp = OldSpaceStamp + c[] NewTimeStamp = OldTimeStamp + t (2) The setting of these parameters allows the user to define dynamic properties of the moving object, like velocity, agility and direction. For example, agility denotes how often an object change direction and can be controlled by setting the change frequency of c[]. Direction and velocity depend directly from both values c[] t. The sequence of all Instances of an object represents its trajectory. Other approaches to spatio temporal data generation include Generator for Time-Evolving Regional Data - G-TERD - proposed in [14] that focuses on generating evolving regions. Compared with GSTD, it allows a much larger number of parameters to be set by the user, it also supports the traditional statistical distributions supported by GSTD and a few additional ones. The Oporto generator [11] is designed for a very specific scenario: fishing at sea. Compared with GSTD and G-TERD, Oporto offers a more limited set of features, although it allows modelling the notion of notion of attraction and repulsion between objects, eg. ships/fish are attracted by fish/plankton), whereas storm areas repel the ships. The Network-based data generator proposed in [1] focuses on networkbased moving objects. The driving application is traffic telematics. Important concepts of the generator are the maximum speed and the maximum edge capacity, the maximum speed of the object classes, the interaction between objects. Our choice in CENTRE has been to rely our system on GSTD and extending it in order to meet some further requirements. The reason of such choice relies on the fact that GSTD is a general spatio-temporal data generator, therefore more suitable for further extensions. Indeed, G-TERD focuses on moving region whereas we are interested in generating moving points. Oporto is specialised for an application field we are not interested in modelling, besides the idea of repulsion and attraction could be exploited in future versions of CENTRE. Analogously, the Network-based generator focuses on network movements, whereas we are interested in generating also free movements. 3. CENTRE: ARCHITECTURE OF THE SYSTEM The aim of the CENTRE system is to randomly generate movement data simulating different users behaviour moving through a cellular network. In order to generate semantics-driven positioning data, a number of synthetic trajectories simulating predefined users movements is produced. The general architecture is shown in Figure 1, that reflects the two step moving data generation process, from Synthetic Trajectories to Log Generation. Eventually, an Approximated Trajectories Reconstruction process takes place. This two step generation process presents several advantages: Exploitation of an existing semantic-based spatio-temporal data generator to obtain realistic people movements scenario. High flexibility in Log Generation obtained by exploiting a parametric user-defined antennas cover map representing different technological and geographical contexts. The possibility to validate and test both trajectories reconstruction techniques and data mining algorithms. The modularity of the system allows to exploit the Trajectory Reconstruction module, possibly, with a collection of real positioning data. Moreover, the other modules can be easily improved or modified independently one from the others, making the CENTRE architecture suitable for further improvements. The CENTRE architecture is characterised by three main components: Synthetic Trajectory Generator, Log Generator, Trajec-

4 a time interval for idle devices localisation, that can vary from few minutes to few hours. We suppose here to have a quite frequent localisation. In the next paragraphs we will give some details of each component of the system. 3.1 Synthetic Trajectory Generator The synthetic generation of mobile telephones movements through the cellular network has been realised by extending the GSTD spatio-temporal data generator on three directions: Figure 1: CENTRE: General Architecture tory Reconstruction module (Figure 1), whose details will be given in following paragraphs. The Synthetic Trajectories generator is based on the spatio-temporal data generator GSTD. Starting from a set of configuration parameters, it generates spatio-temporal Instances representing mobile phone user movements over the network. Log Generator takes Instances, produced on snapshot times, of generated data and an antennas cover map to compute Logs entries. Trajectory Reconstruction takes as input Logs and reconstructs Approximated Trajectories, storing them in a database and thus making them available for further analysis. GIS software (JUMP [10]) and a DBMS (MySQL [3]) provide support for the tasks performed by CENTRE modules. In particular, the GIS software supports the user in creating the antennas cover map, the underlying obstacles infrastructure and in the visualisation of the resulting trajectories. The DBMS allows the storage of computed Logs and Approximated Reconstructed Trajectories. JUMP is an open-source GIS software written in Java that includes a set of exportable libraries that has been employed in CENTRE for Log Generation and Trajectories Reconstruction modules. Furthermore, in CENTRE we have exploited the JUMP feature that allows the import/export of data in GML. In the Log production process a number of assumptions has been done. First of all, we choose here to consider only circular antennas, although usually sectorial antennas are employed in cellular networks. The second assumption concerns the mobile telephone state, since we assume that all telephones are in the idle state (not in conversation). Another assumption we did here is that we do not deal with disconnections (e.g. modelling telephones that are turned off and on during data generation). It is worth noticing here that these assumptions does not determine a significant limitation of the generated Logs. Indeed, sectorial antennas are more complex to model as a polygon in the antennas cover map, however they lead to a better approximation of cellular position. Taking into account only idle devices can be a good approximation when dealing with aggregated data since we assume that idle telephones are much more than on conversation or turned off telephones. Idle assumption is related to the hypothesis that telephone detections occur at regular interval time (that depends on the number of snapshots set in Trajectory Generator module). Indeed this is not far from reality since telecommunication companies usually establish Input & Output. In CENTRE we improved GSTD input data by the use of a configuration file that contains both group behaviour and global parameters. Furthermore, input format has been modified exploiting GML [8] format, a standard interoperable OpenGIS [2] specification for geographic data. GML format allows the user to import customised vectorbased geographic data, such as background infrastructures and antennas cover map. Additionally, the output format has been transformed to GML that allows a better visualisation of results by means of a GIS system. Group Movements. The definition of groups of objects evolving in a similar way can be obtained in original GSTD by distinct run of the algorithm on different input parameters and different object identifiers. This feature has been improved in CENTRE by defining a new group behaviour that allows to evolve objects with different spatio-temporal behaviours during generation time, thus providing the generation of different groups of objects in a single run. In particular, we focused on two aspects: first of all, we implemented a better parameter management definition of a group, that describes characteristics of a moving object with a precise spatio-temporal behaviour. Then, we added the possibility, for each moving object, to change group during its evolution, changing therefore its own behaviour (here called fickleness). Definition of an underlying obstacles infrastructure to limit object movements. Inside workspace R 2 + the GSTD original algorithm generates random rectangles representing obstacles that objects must avoid in their movements. In CEN- TRE, this feature has been modified in order to allow the user to define off-line, possibly with the support of a GIS tool, its own infrastructure to be taken as input in data generation. Indeed, the infrastructure can be seen as an abstraction of the cartography representing, for example, roads, buildings, rivers and so on Input Parameters The input for Trajectory Generator module is organised in a file divided into two main categories: global parameters and group parameters. Global parameters define inputs that are constants during all generation process, for all objects. We can see in Table 1 that we can define the number of objects to be generated, number of group behaviours, a file containing antennas cover map and some other minor options. As we can see in Table 2, group parameters define local properties of all objects that belong to a specific group during the generation process.

5 Parameter NUM GROUPS FILENAME COVERFILE N OBJECT STARTING ID N SNAPSHOT SEED Parameter N INIT NUM N USE FRAMEWORK N FMW FILENAME N MAXGROUPSHIFT N DISTR GROUP N DISTR INIT N INIT MIN X N INIT MAX X N INIT MIN Y N INIT MAX Y N DISTR T N MIN T N MAX T N DISTR DT N MIN DT N MAX DT N DISTR C N MIN C X N MAX C X N MIN C Y N MAX C Y Meaning Total Number of Groups Points Generated File Cover Input File Total Number of Objects Object Starting ID Number of Snapshots Random Parameter Table 1: Global input parameters Meaning Initial number of objects Use of Infrastructure Infrastructure input file Max number of change Group Changing distribution Initial Distribution of Placement Initial Placement Bounding Box Distribution Time(t) Time interval t Distribution of dt Interval of dt Distribution of c[] Interval of c[] Table 2: Input parameters to be set for each group. For each group, user has to specify: Initial number of objects. This is valid only for the initial snapshot of objects in groups. During the generation objects are subject to group changing as we will see later. To limit objects movements we can choose to use an infrastructure specifying its file name (N USE FRAMEWORK and N FWK FILENAME). N DISTR GROUP, specifies the distribution probability that the group uses to acquire objects during generation. N MAXGROUPSHIFT, specifies the maximum number of group change an object can do: objects inherits from group this feature only at initial placement, and not at successive changes because it become a property of the object. Distributions inherited by GSTD and used to calculate spatiotemporal evolution (N DISTR T, N DISTR C) and agility (N DISTR DT) of objects. It is worth noticing that these parameters can be set independently for each group thus allowing to generate, within the same algorithm run, objects with different and independent behaviour that changes over time Changing Objects Behaviour To model a form of fickleness of users during their movement (the intuitive meaning is how often they change behaviour over time), we have realised a new group change behaviour. Indeed, each user can belong to only one group at each time instant, but it can change group over time, thus globally belonging to two or more groups during the entire generation. As a similarity with some realistic scenario we imagine people walking then taking theirs car, or people travelling by bus then start walking and so on. Algorithm 1 Group Change Input: ε, Instance, GROUPS // ε is a threshold for testing object receiving probability // Instance is the current instance of the evolving object // GROUPS is the group collection Output: change 1: if (Instance.canchange()) then 2: change f alse; 3: min MAXINT // init to a big value 4: for (i 0;i < GROUPS.length;i + +) do 5: di f f Instance.Time (GROUPS[i].distr GRP) 6: if (di f f < ε) then 7: if (di f f < min) then 8: min di f f 9: Instance.Group GROUPS[i] 10: change true The group changing method (Algorithm 1) is called by Trajectory Generator module algorithm at each Instance computation of object o id. The algorithm takes as input the object Instance, a threshold ε and specifies a method to determine the most likely group for an object migration. The value provided by the probability distribution N DISTR - GROUP associated to each group is the time instant of maximum receptivity of the group itself. In other words, it is the time instant when the group is more willing to receive objects from other groups. At line 5 in the algorithm, notice that we check the current timestamp and the distribution value (GROUPS[i].distr GRP). When they differ for less than ε (meaning that they are very close), than the current group becomes a candidate to receive the object. Among all candidates, we choose the one for which the difference is the lowest. When no candidates are generated, no group changing is performed. As an example, consider a gaussian distribution set for N DISTR GROUP, we have that the group have its maximum receptivity at all time instants very close to the gaussian media value. 3.2 Log Generator Recall from previous sections that a Log entry represents a spatiotemporal estimation of the device position inside the GSM network and can be modelled as a quadruple (ob j id,t,id ant,d) where obj id represents the mobile telephone unique identifier, t represents the time of localisation, id ant represents the antenna unique identifier and d represents an estimation of the distance of the mobile device from the antenna that detected it. It is worth noticing that this representation produces an information loss compared to the original synthetic generated trajectories. Now, each localisation point is approximated with the entire cell. Let us consider the following example. Let p 1,..., p 5 the original trajectory snapshots. The following Logs will be generated by the Log Generation module:

6 Figure 2: Example of positions detected by three antennas Logs detected by antenna BT S 1 p2: (Obj 1, tt1, BT S 1, d 12 ) p3: (Obj 1, tt2, BT S 1, d 13 ) Logs detected by antenna BT S 2 p3: (Obj 1, tt2, BT S 2, d 23 ) p4: (Obj 1, tt3, BT S 2, d 24 ) Logs detected by antenna BT S 3 p3: (Obj 1, tt2, BT S 3, d 33 ) p5: (Obj 1, tt4,bt S 3, d 35 ) In cellular networks there are several ways to estimate the distance d of the tracked device from the antenna. Some techniques uses the signal power (the less power has the signal the more is the distance), others compute the time elapsed by a bit request to come back from the device. However, the distance d in CENTRE has been simulated by computing the distance from antenna s center to the considered spacestamp of the synthetic trajectory. In order to understand how Log generator works, it is useful to briefly recall how original synthetic trajectories are generated. We have shown in the previous sections that GSTD generates a new Instance object at each time interval. Such Instance represents an object movement. All Instances of object o id represent the evolution of the object, that is, its trajectory. Only Instances corresponding to Snapshots are actually stored. At each Snapshot generated, all associated Logs are computed by the Log Generator module taking as input the antennas cover map as shown in algorithm 2: Algorithm 2 Generate Log Input: Instance, BT S // Instance is the current obj instance // BT S is the collection of antennas shapes Output: LOGS[] // LOGS[] is an array containing results logs 1: for all b BT S do 2: if (Instance.SpaceStamp intersect b) then 3: d distance(b.centre, Instance.SpaceStamp) 4: LOGS.add(b.id, b.centre, Instance.TimeStamp, d) The Log Generation algorithm takes as input an Instance (relative to a snapshot) of moving object and checks, for each cell on the coverage, which one has non-empty intersection with Instance. Then, an estimation of the distance d is then computed. A Log entry is then generated and stored in the database. It is worth noticing that when a device is located in an overlapping area, there will be as many log entries, referred to the same Instance, as many cells covering the spacestamp. The Algorithm has a complexity of O(m n o), where m is the number of objects, n is the number of snapshots, o is the number of antennas. We can reduce this complexity only reducing the factor of the antennas. In fact while number of snapshots and number of objects cannot be reduced, we can reduce the factor o using plane sweep or divide et impera techniques. Instead of checking overlaps between a spatio-temporal point and all the antennas, we can divide the spaces into subparts till we have the minimal portion of region containing that point: so we can check intersections with only the subcollection of antennas regarding this portion of region. By the use of this technique, we can reduce the number of checks up to a logo. This will be task for future improvements. 3.3 Trajectories Reconstruction Logs position data determine the spatio-temporal position of the moving objects with a coarse granularity. Indeed, each Log represents the position of the device that, in the worst case, can be the entire cell, that can be even kilometres of diameter. Therefore, we have an information loss compared with original trajectories. However, unless mobile devices are equipped with GPS positioning system, the topology of cellular network only allows approximated positioning. In order to allow the analysis of the trajectories of objects given their Logs localisation, a trajectory reconstruction process takes place. Indeed, each Log represent an - uncertain - localisation of a mobile object. This uncertainty is essentially a granularity error in space. We assume here that there is no error in the temporal dimension. We have pointed out above that approximating the device position with the detecting cell is a coarse approximation since cells can reach kilometres of diameter. A better approximation is possible when the device position has been detected by two or more antennas, that is the device is located in an overlap area, and multiple Logs have been generated. Therefore, the smaller is the overlap area, the better is the approximation. This observation has been exploited when trying to approximate device position. Indeed, we approximate the cellular position to be in the cell centre (the antenna location in circular cells) when no overlap occurs, whereas we estimate the cellular position to be in the centre of the polygon representing the overlapping area when two or more cells overlap. After that, a linear interpolation between these approximated location points are computed. In this module we implemented a first - quite trivial - attempt of trajectories reconstruction process from Logs. Several improvements to this techniques will be done, defining more sophisticated heuristics and taking into account the estimated distance d stored in Logs. However, even this preliminary attempt shows that when the antenna coverage presents small cells and several overlap, this can be a good approximation of the original trajectories. Figure 3 shows an example of trajectory reconstruction. 4. EXAMPLES In this section we run through the data generation and trajectories reconstruction processes by the means of a driving example showing both the parameters settings and some screenshots of the resulting trajectories. As an example of the data generation process with CENTRE, consider the simulation of a simple, but typical scenario where mobile telephone users, moving around the city, show two different movement behaviour. The first kind of user behaviour represents

7 Group A values Group B values N USE FRAMEWORK = yes N USE FRAMEWORK = no DISTR DT = gaussian DISTR DT = gaussian media = 0.2, variance = 0 media = 0.1, variance = 0 DISTR C: gaussian DISTR C: gaussian media x = 4, variance x = 2 media x = 0, variance x = 1.2 media y = 2, variance y = 2 media y = 0, variance y = 0.8 DISTR T = gaussian DISTR T = gaussian media = 0.1, variance = 0.01 media = 0.1, variance = 0.01 Table 3: Parameters settings for two groups movements screenshot of Figure 4 Figure 3: Trajectory Reconstruction Example people walking, whereas the other one represents a people moving on vehicles. Typically, people walking are characterised by a slow movement and do not necessarily follow streets (since they can walk inside buildings). On the other hand, people moving on vehicles move faster and follow roads. It is also quite usual for people to change behaviour over time, for example changing transportation mean. This two groups scenario can be modelled in CENTRE by defining, at the synthetic trajectories generation step, two groups of moving objects. The first group modelling people walking has been configured to have a slow motion and no obstacles infrastructure, whereas the second one, modelling people on vehicles has been configured to have a faster motion and movements constrained by an obstacles infrastructure, representing buildings. Furthermore, these two groups have been configured to perform a group change that simulates a change in their behaviour. Examples: First Scenario The screenshot of Figure 4 show the synthetic generated trajectories of the two groups. Notice how some trajectories follow a upright direction and avoid obstacles (people on vehicles), whereas other trajectories at the bottom have a higher agility and are not limited by obstacles (people walking). Group A values Group B values MAXGROUPSHIFT = 1 MAXGROUPSHIFT = 1 DISTR GROUP = gaussian DISTR GROUP = gaussian media = 0.5, variance = 0.1 media = 0.5, variance = 0.1 Table 4: Parameters settings for group change screenshot the agility of elements. In other words, objects in group B change direction two times more often than objects in group A. Another difference is the parameter DISTR C that affects the speed and direction of objects. Indeed, group A shows fixed direction and speed, whereas group B moves with no fixed direction (this can obtained setting the Media value to 0 and Variance to a non-zero value) and lower speed than group A. Examples: Second Scenario Figure 5 shows an example of group changing on two single trajectories, for the sake of readability. Figure 5: Group change Figure 4: Two movement groups, one group with obstacles infrastructure (group A) representing for example cars, the other one with lower speed representing pedestrian (group B) Table 3 shows the most relevant parameters settings for CEN- TRE data generation of this scenario. As we can see from Figure 4, the main difference between group A and group B is determined by parameter DISTR DT that drives Table 4 shows relevant parameters settings for group changing on two objects, relative to this screenshot. In particular, distribution function DISTR GROUP provides a value for computing the temporal instant when objects can change their group. Notice that in this case the Media value of 0.5 indicates that objects will possibly change group around the half of generation process. Finally, MAX- GROUPSHIFT parameter indicates the limit of group changes of the object. Examples: Third Scenario Figure 6 shows an example of both data generation and trajectories reconstruction on two single objects. The black solid line represents the original generated trajectory, whereas the red solid line shows the reconstructed trajectory. Here Logs have been computed using the antennas cover map, visible in the background.

8 improved adding more semantics and heuristics to the reconstruction process, for example taking into account the obstacles, such as buildings and roads. Figure 6: An example of trajectory reconstruction We can see how smaller and denser antennas typically produce a better approximation of original trajectories. Examples: Fourth Scenario Finally, this last scenario shows how a suitable definition of the obstacles infrastructure can better represent streets and pedestrian area, as shown in Figure 7. Figure 7: Scenario with vehicles and pedestrians Figure 8: A reconstruction example with uniform antennas coverage The trajectory reconstruction process, shown in Figure 8, gives a quite good approximation of the synthetic trajectories. However, it also introduces some significant errors, since the reconstructed trajectory does not avoid obstacles as the original one did. This can be 5. CONCLUSIONS AND FUTURE WORK The system presented in this paper provides a synthetic spatiotemporal data generator particularly suited for validate and test data mining algorithms. We focus here on defining an abstract model of telecommunication companies positioning data coming from mobile telephones moving through a cellular network. Indeed, positioning data of people moving in a cellular covered region provide the raw data from which to abstract common movement patterns, that can be exploited in several application fields: from traffic management, to service accessibility, to network bandwidth optimisation. However, some difficulties arise when asking for real positioning data from telecommunication companies, mainly due to both technical and privacy issues. Therefore, in order to develop analysis algorithms and test applications, it can be extremely useful to generate, in a synthetic way, spatio-temporal testbeds representing positioning data inside cellular network. Furthermore, having configurable and predictable testbed has the other great advantage of allowing to test and validate analysis algorithm, such as spatio-temporal data mining techniques. For these reasons, we realised CENTRE, a system to produce predictable and configurable datasets of mobile telephone positions, here called Logs. CENTRE is characterised by three main modules. The first one, Synthetic Trajectories Generator is based on GSTD spatio-temporal data generator and produces moving points evolution simulating people movements. The second module, Log Generator, simulates the telephone detection by the network, thus producing the position Logs. Eventually, starting from Logs, an Approximated Trajectories Reconstruction process can take place. The objective of this module is to exploit some heuristics to infer the possible uncertain trajectories of moving people. Obviously, the trajectory reconstruction module is tested and validated on synthetic data, whereas it can be fully exploited whenever real data becomes available. Ongoing work on CENTRE focuses on tailoring the system for data mining algorithms. As an example, group movements and group changing is a typical clustering pattern, as evidenced [4], where CENTRE has been employed to validate and test a spatiotemporal density-based clustering method. Other data mining patterns are interesting for spatio-temporal data, such as sequential and frequent patterns, or decision trees. To this end, we are currently extending CENTRE towards a more data mining-oriented tool, where the user is able to define both the high level patterns hidden in generated data, in addition to some more fine-grained parameters that control specific object movements. Due to the extremely complex scenario of telecommunication protocols and network topologies, a number of assumptions has been done here. As future work, we aim at improving the system to better represent the GSM/UMTS scenario and to represent obstacles infrastructure directly as cartography. Naturally, the trajectory reconstruction process poses new challenges on the uncertain management of moving objects and in the definition of more sophisticated trajectories reconstruction heuristics. CENTRE software is freely available at the URL: 6. ACKNOWLEDGEMENTS This work has been supported by MIUR PRIN Project GeoP- KDD, We wish to thank the anonymous referees for helpful comments and suggestions.

9 7. REFERENCES [1] Thomas Brinkhoff. A framework for generating network-based moving objects. GeoInformatica, 6(2): , [2] OpenGIS Consortium. [3] MySQL database. [4] Margherita D Auria, Mirco Nanni, and Dino Pedreschi. Time-focused density-based clustering of trajectories of moving objects. Submitted for publication, [5] Ericsson. Ericsson mobile location solution. review/ /93.shtml. [6] ETSI/GSM. Home location register/visitor location register - report [7]. [7] ETSI/GSM. Technical reports list. list=y. [8] GML Geographic Markup Language. [9] Dieter Pfoser and Yannis Theodoridis. Generating semantics-based trajectories of moving objects. Intl. J. of Computers, Environment and Urban Systems, 27(3): , [10] JUMP: Java Unified Mapping Platform. [11] Jean-Marc Saglio and Jose Moreira. Oporto: A realistic scenario generator for moving objects. GeoInformatica, 5(1):71 93, [12] Jochen Schiller and Agne s Voisard. Location-Based Services. Morgan Kaufmann, [13] Yannis Theodoridis, Jefferson R. O. Silva, and Mario A. Nascimento. On the generation of spatiotemporal datasets. Lecture Notes Computer Science, 1651, [14] T. Tzouramanis, M. Vassilakopoulos, and Y. Manolopoulos. On the generation of time-evolving regional data. Geoinformatica, 6(3): , 2002.