Querying Uncertain Spatio-Temporal Data

Abstract

Abstract-The problem of modeling and managing uncertain data has received a great deal of interest, due to its manifold applications in spatial, temporal, multimedia and sensor databases. There exists a wide range of work covering spatial uncertainty in the static (snapshot) case, where only one point of time is considered. In contrast, the problem of modeling and querying uncertain spatio-temporal data has only been treated as a simple extension of the spatial case, disregarding time dependencies between consecutive timestamps. We present a framework for efficiently modeling and querying uncertain spatio-temporal data. The key idea of our approach is to model possible object trajectories by stochastic processes. This approach has three major advantages over previous work. First it allows answering queries in accordance with the possible worlds model. Second, dependencies between object locations at consecutive points in time are taken into account. And third it is possible to reduce all queries on this model to simple matrix multiplications. Based on these concepts we propose efficient solutions for different probabilistic spatio-temporal queries for a particular stochastic process, the Markov chain. In an experimental evaluation we show that our approaches are several order of magnitudes faster than state-of-the-art competitors.

A temporal-probabilistic database model for information extraction

“…In contrast, valid-time annotations, which we consider, refer to a time interval during which a fact is considered to be valid [24]. Research in uncertain spatio-temporal databases, such as [14], focuses on stochastically modeling trajectories through space and time, rather than utilizing concepts known from PDBs (such as a possible-worlds model with data lineage [35]), as we do. Temporal Information Extraction.…”

Indexing uncertain spatio-temporal data

“…Data: We consider a discrete time and space domain, i.e., the common assumption of many existing works (e.g. [18,1,10,8]), where S = {s1, ...s |S| } ⊆ R D is a finite set of possible locations, which we call states, in a D-dimensional space and T = N + 0 is the time domain. Given this spatio-temporal domain, the (certain) movement of an object o corresponds to a trajectory represented as function o : T → S of time defining the location o(t) ∈ S of o at a certain point of time t ∈ T .…”

“…In particular, assuming a maximum speed in each direction of each dimension, the possible locations that an object can visit between two exact observations is bounded. Recent work [8] follows the pragmatic assumption that the uncertain movement of an object between consecutive observations can be described by a MarkovChain model, which captures the time dependencies between consecutive locations. [8] shows how the space of possible worlds (i.e., trajectories between consecutive observations) can be efficiently analyzed by multiplying Markov-Chain transition matrices and that probabilistic query evaluation can be facilitated by integrating pruning mechanisms into the Markov Chain matrices.…”

“…Recent work [8] follows the pragmatic assumption that the uncertain movement of an object between consecutive observations can be described by a MarkovChain model, which captures the time dependencies between consecutive locations. [8] shows how the space of possible worlds (i.e., trajectories between consecutive observations) can be efficiently analyzed by multiplying Markov-Chain transition matrices and that probabilistic query evaluation can be facilitated by integrating pruning mechanisms into the Markov Chain matrices. All these are sufficient for the case where there are few queried objects, following similar movements; however, if there is a large number of objects in the database, with different movements, evaluating a probabilistic spatio-temporal query directly against each object individually (i.e., a scan-based approach) would be very expensive.…”

Representative clustering of uncertain data

“…In such a scenario, an uncertainty data model is typically used to capture the distribution of the possible object locations. For instance, past observations as well as empirically learned moving patterns of an object can be used to obtain a probability function for the position at a time after the object's last observation [16]. Examples of probability density functions (PDFs) around the observations are shown in the Figure. Object A, for instance, is likely to be moving around the lake (since movement inside the lake is impossible), while the movements of other objects are less constrained.…”