Abstract: A computer-implemented method, computerized apparatus and computer program product for efficient solution of nearest object problems. A set of objects having non-point shapes representable by one or more geometric elements are obtained. For each object in the set the one or more geometric elements are sampled to obtain a set of points representing the set of objects. A Voronoi diagram is constructed for the set of points, whereby a subdivision of a space accommodating the set of objects into a plurality of cells, each cell containing a single point of the set of points and defining a region of closest neighbors of the point, is obtained. Cells containing points representing the same object are aggregated into a unified cell defining an estimated region of closest neighbors of the object.

Abstract: A computer-implemented method, computerized apparatus and computer program product for efficient solution of nearest object problems. A set of objects having non-point shapes representable by one or more geometric elements are obtained. For each object in the set the one or more geometric elements are sampled to obtain a set of points representing the set of objects. A Voronoi diagram is constructed for the set of points, whereby a subdivision of a space accommodating the set of objects into a plurality of cells, each cell containing a single point of the set of points and defining a region of closest neighbors of the point, is obtained. Cells containing points representing the same object are aggregated into a unified cell defining an estimated region of closest neighbors of the object.

Abstract: A computer-implemented method, computerized apparatus and computer program product for efficient solution of nearest object problems. A set of objects having non-point shapes representable by one or more geometric elements are obtained. For each object in the set the one or more geometric elements are sampled to obtain a set of points representing the set of objects. A Voronoi diagram is constructed for the set of points, whereby a subdivision of a space accommodating the set of objects into a plurality of cells, each cell containing a single point of the set of points and defining a region of closest neighbors of the point, is obtained. Cells containing points representing the same object are aggregated into a unified cell defining an estimated region of closest neighbors of the object.

Abstract: A method, apparatus and computer program product for Functional Space-Time Trajectory Clustering. The method comprises receiving collections of data structures comprising location and time descriptors. The method further comprises estimating functional curves from the collections of data structures. The method further comprises reducing dimensions of the functional curves; and clustering the functional curves into clusters.

Abstract: A computerized method of improving position measurement of an indoor positioning system (IPS), comprising: gathering a plurality of position samples of a mobile device measured by an indoor wireless device, each of the position samples is indicative of a measured position and a measurement time; receiving a current position sample of the mobile device; for each of the plurality of position samples and the current position sample, determining a time weight, the time weight is higher for samples measured at a later time; for each of the plurality of position samples and the current position sample, determining a signal weight, the signal weight is higher for measured with stronger signal; and estimating a current position of the mobile device by weighting at least some of the position samples with the respective weights.

Abstract: A computerized method of improving position measurement of an indoor positioning system (IPS), comprising: gathering a plurality of position samples of a mobile device measured by an indoor wireless device, each of the position samples is indicative of a measured position and a measurement time; receiving a current position sample of the mobile device; for each of the plurality of position samples and the current position sample, determining a time weight, the time weight is higher for samples measured at a later time; for each of the plurality of position samples and the current position sample, determining a signal weight, the signal weight is higher for measured with stronger signal; and estimating a current position of the mobile device by weighting at least some of the position samples with the respective weights.

Abstract: A computer-implemented method, computerized apparatus and computer program product for efficient solution of nearest object problems. A set of objects having non-point shapes representable by one or more geometric elements are obtained. For each object in the set the one or more geometric elements are sampled to obtain a set of points representing the set of objects. A Voronoi diagram is constructed for the set of points, whereby a subdivision of a space accommodating the set of objects into a plurality of cells, each cell containing a single point of the set of points and defining a region of closest neighbors of the point, is obtained. Cells containing points representing the same object are aggregated into a unified cell defining an estimated region of closest neighbors of the object.

Abstract: Visual construction of spatial or spatio-temporal relationships is disclosed. A method according to the disclosed subject matter may comprise receiving a visual representation of rule, the visual representation comprising two or more objects. A spatial relationship appearing in the visual representation may be analyzed and multiple alternative textual representations for the spatial relationship may be determined. A user selection between the multiple alternative textual representations of the spatial relationship may be received, whereby obtaining a selected verbalization of the relationship. A verbalization of the rule, which comprises the verbalization of the relationship, may be generated.

Abstract: A method, apparatus and computer program product for Functional Space-Time Trajectory Clustering. The method comprises receiving collections of data structures comprising location and time descriptors. The method further comprises estimating functional curves from the collections of data structures. The method further comprises reducing dimensions of the functional curves; and clustering the functional curves into clusters.

Abstract: A computerized clustering method. The method comprises receiving a spatial point dataset comprising a plurality of spatial points in a space, heuristically calculating, using a processor, a plurality of ?-shape based segmentations such that each of the plurality of ?-shape based segmentations defines a plurality of polygonal areas that cluster the plurality of spatial points in a plurality of clusters which collectively bounds the plurality of spatial points, presenting to an operator in each sequential iteration of a plurality of sequential iterations another of the plurality of ?-shape based segmentations, and selecting by the operator one or more of the plurality of ?-shape based segmentations.

Abstract: A computerized visualization method for illustrating multi-dimensional data, comprising: receiving a plurality of location data points, each location data point having a plurality of measured features; choosing at least one location dimension from received said plurality of dimensions; grouping said plurality of location data points into a plurality of location groups according to chosen said at least one location dimension; plotting, by a processor, said plurality of location groups as a plurality of flower charts, each said plurality of flower charts, having a plurality of pie sectors, illustrates remaining said plurality of measured features subsequent to said choosing at least one location dimension; and positioning each said plurality of flower charts, in a visual representation, according to chosen said plurality of location dimensions.

Abstract: A computerized clustering method. The method comprises receiving a spatial point dataset comprising a plurality of spatial points in a space, heuristically calculating, using a processor, a plurality of ?-shape based segmentations such that each of the plurality of ?-shape based segmentations defines a plurality of polygonal areas that cluster the plurality of spatial points in a plurality of clusters which collectively bounds the plurality of spatial points, presenting to an operator in each sequential iteration of a plurality of sequential iterations another of the plurality of ?-shape based segmentations, and selecting by the operator one or more of the plurality of ?-shape based segmentations.

Abstract: A computerized visualization method for illustrating multi-dimensional data, comprising: receiving a plurality of location data points, each location data point having a plurality of measured features; choosing at least one location dimension from received said plurality of dimensions; grouping said plurality of location data points into a plurality of location groups according to chosen said at least one location dimension; plotting, by a processor, said plurality of location groups as a plurality of flower charts, each said plurality of flower charts, having a plurality of pie sectors, illustrates remaining said plurality of measured features subsequent to said choosing at least one location dimension; and positioning each said plurality of flower charts, in a visual representation, according to chosen said plurality of location dimensions.