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Geometric data summarization has become an essential tool in both geometric approximation algorithms and where geometry intersects with big data problems. In linear or near-linear time large data sets can be compressed into a summary, and…
An efficient algorithm for computing the choropleth map classification scheme known as equal area breaks or geographical quantiles is introduced. An equal area breaks classification aims to obtain a coloring for the map such that the area…
Choropleth maps, which utilize color schemes to visualize spatial patterns and trends, are simple yet effective tools for geographic data analysis. As such, color scheme design is a critical aspect of choropleth map creation. The…
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably…
Choropleth maps and graduated symbol maps are often used to visualize quantitative geographic data. However, as the number of classes grows, distinguishing between adjacent classes increasingly becomes challenging. To mitigate this issue,…
Structured representations such as scene graphs serve as an efficient and compact representation that can be used for downstream rendering or retrieval tasks. However, existing efforts to generate realistic images from scene graphs perform…
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
We evaluate several augmentations to the choropleth map to convey additional information, including glyphs, 3D, cartograms, juxtaposed maps, and shading methods. While choropleth maps are a common method used to represent societal data,…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…
Today, one's disposes of large datasets composed of thousands of geographic objects. However, for many processes, which require the appraisal of an expert or much computational time, only a small part of these objects can be taken into…
Systems such as Microsoft Songsmith automatically assign chords and harmony to a melody by minimizing the dissonance across all chord changes. Although this produces harmonious music, it is not what practicing musicians do. In this paper, I…
Humans are remarkably efficient at forming spatial understanding from just a few visual observations. When browsing real estate or navigating unfamiliar spaces, they intuitively select a small set of views that summarize the spatial layout.…
We consider the problem of segmenting dynamic regions in CrowdCam images, where a dynamic region is the projection of a moving 3D object on the image plane. Quite often, these regions are the most interesting parts of an image. CrowdCam…