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Classification Techniques
Published in Harry G. Perros, An Introduction to IoT Analytics, 2021
To use the Voronoi diagram for 1-NN, we need to be able to determine which cell a new data point falls in. This is a special case of the point location problem, a fundamental topic of computational geometry. Higher order Voronoi diagrams are used for k-NN classification with k > 1. In general, Voronoi diagrams are computationally intensive.
Grid k-d tree approach for point location in polyhedral data sets – application to explicit MPC
Published in International Journal of Control, 2020
All approaches reported in literature for the point location problem involve two basic steps: (1) construct the data structure to store the polyhedral regions and the corresponding affine control laws offline and (2) locate the state point in some polyhedron through the online searching algorithm. Many methods have been proposed to reduce the storage requirement so as to improve the point location efficiency. The most efficient solution procedures to date can broadly be classified into two approaches: (1) merge the polyhedral regions according to the convexity of polytopes and the corresponding affine control laws and (2) employ separating functions to avoid storing all polyhedral regions (Baotic, Borrelli, Bemporad, & Morari, 2008; Geyer, Torrisi, & Morari, 2008; Kvasnica, Hledik, Rauova, & Fikar, 2013; Spjotvold, Rakovic, Tondel, & Johansen, 2006; Stevek, Kvasnica, & Fikar, 2013).
Structural optimization with explicit geometric constraints using a B-spline representation
Published in Mechanics Based Design of Structures and Machines, 2022
Yosef M. Yoely, Iddo Hanniel, Oded Amir
The first step in converting the spline-based geometry into fixed grid densities is to determine whether the elements’ nodes are inside, on, or outside curve. The point-in-curve is a special case of point location problem which is a fundamental topic of computational geometry. It finds applications in areas that deal with processing geometrical data: computer graphics, CAD, geographic information systems (GIS), motion planning, robotics and fixed-grid finite element analysis (FG-FEA). In its most general form, the problem is, given a partition of the space into disjoint regions, to determine the region where a query point lies.