Goce Trajcevski

Querying and mining of time series data: experimental comparison of representations and distance measures

The last decade has witnessed a tremendous growths of interests in applications that deal with querying and mining of time series data. Numerous representation methods for dimensionality reduction and similarity measures geared towards time series have been introduced. Each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive set of time series experiments re-implementing 8 different representation methods and 9 similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this paper, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. Our experiments have provided both a unified validation of some of the existing achievements, and in some cases, suggested that certain claims in the literature may be unduly optimistic.

Experimental comparison of representation methods and distance measures for time series data

The previous decade has brought a remarkable increase of the interest in applications that deal with querying and mining of time series data. Many of the research efforts in this context have focused on introducing new representation methods for dimensionality reduction or novel similarity measures for the underlying data. In the vast majority of cases, each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive experimental study re-implementing eight different time series representations and nine similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this article, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. In addition to providing a unified validation of some of the existing achievements, our experiments also indicate that, in some cases, certain claims in the literature may be unduly optimistic.

Managing uncertainty in moving objects databases

This article addresses the problem of managing Moving Objects Databases (MODs) which capture the inherent imprecision of the information about the moving objects location at a given time. We deal systematically with the issues of constructing and representing the trajectories of moving objects and querying the MOD. We propose to model an uncertain trajectory as a three-dimensional (3D) cylindrical body and we introduce a set of novel but natural spatio-temporal operators which capture the uncertainty and are used to express spatio-temporal range queries. We devise and analyze algorithms for processing the operators and demonstrate that the model incorporates the uncertainty in a manner which enables efficient querying, thus striking a balance between the modeling power and computational efficiency. We address some implementation aspects which we experienced in our DOMINO project, as a part of which the operators that we introduce have been implemented. We also report on some experimental observations of a practical relevance.

Spatio-temporal data reduction with deterministic error bounds

A common way of storing spatio-temporal information about mobile devices is in the form of a 3D (2D geography + time) trajectory. We argue that when cellular phones and Personal Digital Assistants become location-aware, the size of the spatio-temporal information generated may prohibit efficient processing. We propose to adopt a technique studied in computer graphics, namely line-simplification, as an approximation technique to solve this problem. Line simplification will reduce the size of the trajectories. Line simplification uses a distance function in producing the trajectory approximation. We postulate the desiderata for such a distance-function: it should be sound, namely the error of the answers to spatio-temporal queries must be bounded. We analyze several distance functions, and prove that some are sound in this sense for some types of queries, while others are not. A distance function that is sound for all common spatio-temporal query types is introduced and analyzed. Then we propose an aging mechanism which gradually shrinks the size of the trajectories as time progresses. We also propose to adopt existing linguistic constructs to manage the uncertainty introduced by the trajectory approximation. Finally, we analyze experimentally the effectiveness of line-simplification in reducing the size of a trajectories database.

Probabilistic range queries for uncertain trajectories on road networks

Trajectories representing the motion of moving objects are typically obtained via location sampling, e.g. using GPS or road-side sensors, at discrete time-instants. In-between consecutive samples, nothing is known about the whereabouts of a given moving object. Various models have been proposed (e.g., sheared cylinders; spacetime prisms) to represent the uncertainty of the moving objects both in unconstrained Euclidian space, as well as road networks. In this paper, we focus on representing the uncertainty of the objects moving along road networks as time-dependent probability distribution functions, assuming availability of a maximal speed on each road segment. For these settings, we introduce a novel indexing mechanism -- UTH (Uncertain Trajectories Hierarchy), based upon which efficient algorithms for processing spatio-temporal range queries are proposed. We also present experimental results that demonstrate the benefits of our proposed methodologies.

Continuous probabilistic nearest-neighbor queries for uncertain trajectories

This work addresses the problem of processing continuous nearest neighbor (NN) queries for moving objects trajectories when the exact position of a given object at a particular time instant is not known, but is bounded by an uncertainty region. As has already been observed in the literature, the answers to continuous NN-queries in spatio-temporal settings are time parameterized in the sense that the objects in the answer vary over time. Incorporating uncertainty in the model yields additional attributes that affect the semantics of the answer to this type of queries. In this work, we formalize the impact of uncertainty on the answers to the continuous probabilistic NN-queries, provide a compact structure for their representation and efficient algorithms for constructing that structure. We also identify syntactic constructs for several qualitative variants of continuous probabilistic NN-queries for uncertain trajectories and present efficient algorithms for their processing.

On-line data reduction and the quality of history in moving objects databases

In this work we investigate the quality bounds for the data stored in Moving Objects Databases (MOD) in the settings in which mobile units can perform an on-board data reduction in real time. It has been demonstrated that line simplification techniques, when properly applied to the large volumes of data pertaining to the past trajectories of the moving objects. result in substantial storage savings while guaranteeing deterministic error bounds to the queries posed to the MOD. On the other hand. it has also been demonstrated that if moving objects establish an agreement with the MOD regarding the (im)precision tolerance significant savings can be achieved in transmission when updating the location-in-time information. In this paper we take a first step towards analyzing the quality of the history in making in MOD by correlating the (impact of the) agreement between the server and the moving objects for on-line updates in real time with the error bounds of the data that becomes a representation of the past trajectories as time evolves.

SIDnet-SWANS: a simulator and integrated development platform for sensor networks applications

This work presents the SIDnet, a simulation-based environment for applications development in wireless sensor networks settings. It enables run-time interactions with the network for the purpose of observing the behavior of algorithms protocols in the presence of various conditions such as phenomena fluctuations, or a sudden loss of service both at an individual node, as well as a collection of nodes.

Dynamics-aware similarity of moving objects trajectories

This work addresses the problem of obtaining the degree of similarity between trajectories of moving objects. Typically, a Moving Objects Database (MOD) contains sequences of (location, time) points describing the motion of individual objects, however, they also implicitly storethe velocity -- an important attribute describing the dynamics the motion. Our main goal is to extend the MOD capability with reasoning about how similar are the trajectories of objects, possibly moving along geographically different routes. We use a distance function which balances the lack of temporal-awareness of the Hausdorff distance with the generality (and complexity of calculation) of the Fréchet distance. Based on the observation that in practice the individual segments of trajectories are assumed to have constant speed, we provide efficient algorithms for: (1) optimal matching between trajectories; and (2) approximate matching between trajectories, both under translations and rotations, where the approximate algorithm guarantees a bounded error with respect to the optimal one.

The Geometry of Uncertainty in Moving Objects Databases

This work addresses the problem of querying moving objects databases. which capture the inherent uncertainty associated with the location of moving point objects. We address the issue of modeling, constructing, and querying a trajectories database. We propose to model a trajectory as a 3D cylindrical body. The model incorporates uncertainty in a manner that enables efficient querying. Thus our model strikes a balance between modeling power, and computational efficiency. To demonstrate efficiency, we report on experimental results that relate the length of a trajectory to its size in bytes. The experiments were conducted using a real map of the Chicago Metropolitan area.We introduce a set of novel but natural spatio-temporal operators which capture uncertainty, and are used to express spatio-temporal range queries. We also devise and analyze algorithms to process the operators. The operators have been implemented as a part of our DOMINO project.