A qualitative approach to the identification, visualisation and interpretation of repetitive motion patterns in groups of moving point objects

Discovering repetitive patterns is important in a wide range of research areas, such as bioinformatics and human movement analysis. This study puts forward a new methodology to identify, visualise and interpret repetitive motion patterns in groups of Moving Point Objects (MPOs). The methodology consists of three steps. First, motion patterns are qualitatively described using the Qualitative Trajectory Calculus (QTC). Second, a similarity analysis is conducted to compare motion patterns and identify repetitive patterns. Third, repetitive motion patterns are represented and interpreted in a continuous triangular model. As an illustration of the usefulness of combining these hitherto separated methods, a specific movement case is examined: Samba dance, a rhythmical dance will? many repetitive movements. The results show that the presented methodology is able to successfully identify, visualize and interpret the contained repetitive motions

Analysing imperfect temporal information in GIS using the Triangular Model

Rough set and fuzzy set are two frequently used approaches for modelling and reasoning about imperfect time intervals. In this paper, we focus on imperfect time intervals that can be modelled by rough sets and use an innovative graphic model [i.e. the triangular model (TM)] to represent this kind of imperfect time intervals. This work shows that TM is potentially advantageous in visualizing and querying imperfect time intervals, and its analytical power can be better exploited when it is implemented in a computer application with graphical user interfaces and interactive functions. Moreover, a probabilistic framework is proposed to handle the uncertainty issues in temporal queries. We use a case study to illustrate how the unique insights gained by TM can assist a geographical information system for exploratory spatio-temporal analysis

A Priori Error Analysis and Spring Arithmetic

WOSInternational audienceError analysis is defined by the following concern: bounding the output variation of a (nonlinear) function with respect to a given variation of the input variables. This paper investigates this issue in the framework of interval analysis. The classical way of analyzing the error is to linearize the function around the point corresponding to the actual input, but this method is local and not reliable. Both drawbacks can be easily circumvented by a combined use of interval arithmetic and domain splitting. However, because of the underlying linearization, a standard interval algorithm leads to a pessimistic bound, and even simply fails (i.e., returns an infinite error) in case of singularity. We propose an original nonlinear approach where intervals are used in a more sophisticated way through the so-called "springs". This new structure allows to represent an (infinite) set of intervals constrained by their midpoints and their radius. The output error is then calculated with a spring arithmetic in the same way as the image of a function is calculated with interval arithmetic. Our method is illustrated on two examples, including an application of geopositioning

Multi-scale analysis of linear data in a two-dimensional space

Many disciplines are faced with the problem of handling time-series data. This study introduces an innovative visual representation for time series, namely the continuous triangular model. In the continuous triangular model, all subintervals of a time series can be represented in a two-dimensional continuous field, where every point represents a subinterval of the time series, and the value at the point is derived through a certain function (e. g. average or summation) of the time series within the subinterval. The continuous triangular model thus provides an explicit overview of time series at all different scales. In addition to time series, the continuous triangular model can be applied to a broader sense of linear data, such as traffic along a road. This study shows how the continuous triangular model can facilitate the visual analysis of different types of linear data. We also show how the coordinate interval space in the continuous triangular model can support the analysis of multiple time series through spatial analysis methods, including map algebra and cartographic modelling. Real-world datasets and scenarios are employed to demonstrate the usefulness of this approach

Interactive analysis of time intervals in a two-dimensional space

Time intervals are conventionally represented as linear segments in a one-dimensional space. An alternative representation of time intervals is the triangular model (TM), which represents time intervals as points in a two-dimensional space. In this paper, the use of TM in visualising and analysing time intervals is investigated. Not only does this model offer a compact visualisation of the distribution of intervals, it also supports an innovative temporal query mechanism that relies on geometries in the two-dimensional space. This query mechanism has the potential to simplify queries that are difficult to specify using traditional linear temporal query devices. Moreover, a software prototype that implements TM in a geographical information system (GIS) is introduced. This prototype has been applied in a real scenario to analyse time intervals that were detected by a Bluetooth tracking system. This application shows that TM has the potential to support a traditional GIS to analyse interval-based geographical data

Displaying risk in mergers: a diagrammatic approach for exchange ratio determination

This article extends, in a stochastic setting, previous results in the determination of feasible exchange ratios for merging companies. A first outcome is that shareholders of the companies involved in the merging process face both an upper and a lower bounds for acceptable exchange ratios. Secondly, in order for the improved `bargaining region' to be intelligibly displayed, the diagrammatic approach developed by Kulpa is exploited