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Data point

About: Data point is a(n) research topic. Over the lifetime, 4925 publication(s) have been published within this topic receiving 111519 citation(s). The topic is also known as: datapoint & data point. more


Journal ArticleDOI: 10.1126/SCIENCE.1136800
Brendan J. Frey1, Delbert Dueck1Institutions (1)
16 Feb 2007-Science
Abstract: Clustering data by identifying a subset of representative examples is important for processing sensory signals and detecting patterns in data. Such "exemplars" can be found by randomly choosing an initial subset of data points and then iteratively refining it, but this works well only if that initial choice is close to a good solution. We devised a method called "affinity propagation," which takes as input measures of similarity between pairs of data points. Real-valued messages are exchanged between data points until a high-quality set of exemplars and corresponding clusters gradually emerges. We used affinity propagation to cluster images of faces, detect genes in microarray data, identify representative sentences in this manuscript, and identify cities that are efficiently accessed by airline travel. Affinity propagation found clusters with much lower error than other methods, and it did so in less than one-hundredth the amount of time. more

Topics: Affinity propagation (70%), Cluster analysis (57%), Data point (50%)

5,696 Citations

Open accessJournal ArticleDOI: 10.1109/34.400568
Yizong Cheng1Institutions (1)
Abstract: Mean shift, a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper. This generalization makes some k-means like clustering algorithms its special cases. It is shown that mean shift is a mode-seeking process on the surface constructed with a "shadow" kernal. For Gaussian kernels, mean shift is a gradient mapping. Convergence is studied for mean shift iterations. Cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data. Applications in clustering and Hough transform are demonstrated. Mean shift is also considered as an evolutionary strategy that performs multistart global optimization. > more

Topics: k-means clustering (58%), Cluster analysis (57%), Mean-shift (56%) more

3,554 Citations

Proceedings ArticleDOI: 10.1145/800186.810616
01 Jan 1968-
Abstract: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface. These irregularly-spaced locations, hence referred to as “data points,” may have diverse meanings: in meterology, weather observation stations; in geography, surveyed locations; in city and regional planning, centers of data-collection zones; in biology, observation locations. It is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point. In order to display these data in some type of contour map or perspective view, to compare them with data for the same region based on other data points, or to analyze them for extremes, gradients, or other purposes, it is extremely useful, if not essential, to define a continuous function fitting the given values exactly. Interpolated values over a fine grid may then be evaluated. In using such a function it is assumed that the original data are without error, or that compensation for error will be made after interpolation. more

Topics: Interpolation (55%), Data point (54%), Contour line (54%) more

3,433 Citations

Open accessProceedings ArticleDOI: 10.1145/133994.134011
Hugues Hoppe1, Tony DeRose1, Tom Duchamp1, John W. McDonald1  +1 moreInstitutions (1)
01 Jul 1992-
Abstract: This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces. more

  • Figure 3: Reconstruction examples.
    Figure 3: Reconstruction examples.
  • Figure 1: Reconstruction of ray-traced CSG object (simulated multi-view range data).
    Figure 1: Reconstruction of ray-traced CSG object (simulated multi-view range data).
  • Figure 2: Reconstruction of ray-traced CSG object (continued).
    Figure 2: Reconstruction of ray-traced CSG object (continued).
Topics: Subdivision surface (66%), Piecewise (60%), Surface reconstruction (58%) more

2,963 Citations

Journal ArticleDOI: 10.1109/34.192473
Isak Gath1, Amir B. Geva1Institutions (1)
Abstract: This study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set. Assessment of cluster validity is based on performance measures using hypervolume and density criteria. An algorithm is derived from a combination of the fuzzy K-means algorithm and fuzzy maximum-likelihood estimation. The unsupervised fuzzy partition-optimal number of classes algorithm performs well in situations of large variability of cluster shapes, densities, and number of data points in each cluster. The algorithm was tested on different classes of simulated data, and on a real data set derived from sleep EEG signal. > more

Topics: Fuzzy clustering (73%), Fuzzy classification (68%), Defuzzification (63%) more

1,643 Citations

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Topic's top 5 most impactful authors

Akemi Gálvez

10 papers, 357 citations

Andrés Iglesias

10 papers, 357 citations

René Vidal

8 papers, 1.6K citations

Feiping Nie

7 papers, 167 citations

David M. Mount

7 papers, 194 citations

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