Nowadays, spatial data are ubiquitous in various fields of science, such as transportation and the social Web. A recent research direction in analyzing spatial data is to provide means for "exploratory analysis" of such data where analysts are guided towards interesting options in consecutive analysis iterations. Typically, the guidance component learns analyst's preferences using her explicit feedback, e.g., picking a spatial point or selecting a region of interest. However, it is often the case that analysts forget or don't feel necessary to explicitly express their feedback in what they find interesting. Our approach captures implicit feedback on spatial data. The approach consists of observing mouse moves (as a means of analyst's interaction) and also the explicit analyst's interaction with data points in order to discover interesting spatial regions with dense mouse hovers. In this paper, we define, formalize and explore Interesting Dense Regions (IDRs) which capture preferences of analysts, in order to automatically find interesting spatial highlights. Our approach involves a polygon-based abstraction layer for capturing preferences. Using these IDRs, we highlight points to guide analysts in the analysis process. We discuss the efficiency and effectiveness of our approach through realistic examples and experiments on Airbnb and Yelp datasets.
Region Discovery. Our approach finds interesting dense regions (IDRs) in order to derive analyst's implicit preferences. There exist several approaches to infer a spatial region for a given set of points @cite_9 @cite_16 @cite_26 @cite_15 @cite_13 @cite_2 . The common approach is to cluster points in form of concave and convex polygons. @cite_9 , an algorithm is proposed to verify if a given point @math on the surface of a sphere is located inside, outside, or along the border of an arbitrary spherical polygon. In @cite_16 @cite_26 , a non-convex polygon is constructed from a set of input points on a plane. In @cite_15 @cite_13 , imprecise regions are delineated into a convex or concave polygon. In our approach, it is important to discover regions by capturing mouse move points. In case a concave polygon is constructed, the dents'' of such a polygon may entail points which are not necessarily in @math . In the IDR's algorithm, however, we adapt Quickhull @cite_2 , due its simplicity, efficiency and its natural implementation of convex polygons.
@cite_26 @cite_9 @cite_2 @cite_15 @cite_16 @cite_13
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The convex onion-peeling of a set of points is the organization of these points into a sequence of interpolating convex polygons. This method is adequate to detect the shape of the "center" of a set of points when this shape is convex. However it reveals inadequate to detect non-convex shapes. Alternatively, we propose an extension of the convex onion-peeling method. It consists in representing a set of points with a sequence of non-convex polylines which are computed using the A-shape descriptor. This method is applied to robust statistical estimation. It is shown that it makes the estimators robust to the presence of outliers by removing suspect samples from the available population. An algorithm for determining if any given point,P, on the surface of a sphere is located inside, outside, or along the border of an arbitrary spherical polygon,S, is described. The polygon is described by specifying coordinates of its vertices, and coordinates of some pointX which is known to lie withinS. The algorithm is based on the principle that an arc joiningX andP will cross the border ofS an odd number of times ifP lies outsideS, and an even number of times ifP lies withinS. The algorithm has been implemented as a set of FORTRAN subroutines, and a listing is provided. The algorithm and subroutine package can be used with spherical polygons containing holes, or with composited spherical polygons. The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions. This paper describes several steps in the derivation of boundaries of imprecise regions using the Web as the information source. We discuss how to use the Web to obtain locations that are part of and locations that are not part of the region to be delineated, and then we propose methods to compute the region algorithmically. The methods introduced are evaluated to judge the potential of the approach. This paper presents a simple, flexible, and efficient algorithm for constructing a possibly non-convex, simple polygon that characterizes the shape of a set of input points in the plane, termed a characteristic shape. The algorithm is based on the Delaunay triangulation of the points. The shape produced by the algorithm is controlled by a single normalized parameter, which can be used to generate a finite, totally ordered family of related characteristic shapes, varying between the convex hull at one extreme and a uniquely defined shape with minimum area. An optimal O(nlogn) algorithm for computing the shapes is presented. Characteristic shapes possess a number of desirable properties, and the paper includes an empirical investigation of the shapes produced by the algorithm. This investigation provides experimental evidence that with appropriate parameterization the algorithm is able to accurately characterize the shape of a wide range of different point distributions and densities. The experiments detail the effects of changing parameter values and provide an indication of some ''good'' parameter values to use in certain circumstances. There are many situations in GIScience where it would be useful to be able to assign a region to characterize the space occupied by a set of points. Such a region should represent the location or configuration of the points as an aggregate, abstracting away from the individual points themselves. In this paper, we call such a region a ‘footprint' for the points. We investigate and compare a number of methods for producing such footprints, with respect to nine general criteria. The discussion identifies a number of potential choices and avenues for further research. Finally, we contrast the related research already conducted in this area, highlighting differences between these existing constructs and our ‘footprints'.