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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We tackle the problem of extracting stay regions from a geospatial trajectory where a user has stayed longer than a certain time threshold. There are four major difficulties with this problem: (1) stay regions are not only point-type ones such as at a bus-stop but large and arbitrary-shaped ones such as at a shopping mall; (2) trajectories contain spatial outliers; (3) there are missing points in trajectories; and (4) trajectories should be analyzed in an online mode. Previous algorithms cannot overcome these difficulties simultaneously. Density-based batch algorithms have advantages over the previous algorithms in discovering of arbitrary-shaped clusters from spatial data containing outliers; however, they do not consider temporal durations and thus have not been used for extracting stay regions. We extended a density-based algorithm so that it would work in a duration-based manner online and have robustness to missing points in stay regions while keeping its advantages. Experiments on real trajectories of 13 users conducting their daily activities for three weeks demonstrated that our algorithm statistically significantly outperformed five state-of-the-art algorithms in terms of F1 score and works well without trajectory preprocessing consisting of filtering, interpolating, and smoothing. In this paper, we introduce a feature-preserving denoising algorithm. It is built on the premise that the underlying surface of a noisy mesh is piecewise smooth, and a sharp feature lies on the intersection of multiple smooth surface regions. A vertex close to a sharp feature is likely to have a neighborhood that includes distinct smooth segments. By defining the consistent subneighborhood as the segment whose geometry and normal orientation most consistent with those of the vertex, we can completely remove the influence from neighbors lying on other segments during denoising. Our method identifies piecewise smooth subneighborhoods using a robust density-based clustering algorithm based on shared nearest neighbors. In our method, we obtain an initial estimate of vertex normals and curvature tensors by robustly fitting a local quadric model. An anisotropic filter based on optimal estimation theory is further applied to smooth the normal field and the curvature tensor field. This is followed by second-order bilateral filtering, which better preserves curvature details and alleviates volume shrinkage during denoising. The support of these filters is defined by the consistent subneighborhood of a vertex. We have applied this algorithm to both generic and CAD models, and sharp features, such as edges and corners, are very well preserved. Finding contours in natural images is a fundamental problem that serves as the basis of many tasks such as image segmentation and object recognition. At the core of contour detection technologies are a set of hand-designed gradient features, used by most approaches including the state-of-the-art Global Pb (gPb) operator. In this work, we show that contour detection accuracy can be significantly improved by computing Sparse Code Gradients (SCG), which measure contrast using patch representations automatically learned through sparse coding. We use K-SVD for dictionary learning and Orthogonal Matching Pursuit for computing sparse codes on oriented local neighborhoods, and apply multi-scale pooling and power transforms before classifying them with linear SVMs. By extracting rich representations from pixels and avoiding collapsing them prematurely, Sparse Code Gradients effectively learn how to measure local contrasts and find contours. We improve the F-measure metric on the BSDS500 benchmark to 0.74 (up from 0.71 of gPb contours). Moreover, our learning approach can easily adapt to novel sensor data such as Kinect-style RGB-D cameras: Sparse Code Gradients on depth maps and surface normals lead to promising contour detection using depth and depth+color, as verified on the NYU Depth Dataset. The Meeting problem for (k 2 ) searchers in a polygon P (possibly with holes) consists in making the searchers move within P, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of P, we minimize the number of searchers k for which the Meeting problem is solvable. Specifically, if P has a rotational symmetry of order ( ) (where ( =1 ) corresponds to no rotational symmetry), we prove that (k= +1 ) searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with (k=2 ) searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look–Compute–Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations (provided that the coordinates of the polygon’s vertices are algebraic real numbers in some global coordinate system), and each searcher can geometrically construct its own destination point at each cycle using only a compass and a straightedge. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.