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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
Euclidean distance is the special case of Minkowski distance when = 2. See also Minkowski distance. Euler number a topological invariant of an object having an orientable surface. Assuming that the surface is endowed with the structure of a graph with vertices, edges, and faces (where two neighboring faces have in common either a vertex or an edge with its two end-vertices, their interiors being disjoint): the Euler number is V - E + F, where V , E, and F are respectively the number of vertices, edges and faces; this number V - E + F does not depend on the choice of the subdivision into vertices, edges, and faces. For a bounded 2-D object in a Euclidean or digital plane, the Euler number is equal to the number of connected components of that object, minus the number of holes in it. For 2-D binary digital figures on a bounded grid, the Euler number can easily be computed by counting the number of occurrences of some local configurations of on and off pixels. Also called genus. eureka in a multiprocessor system, a coordination (synchronization) operation generating a completion signal that is logically ORed among all processors participating in an asynchronously parallel action. The interpretation and name come
k-Nearest Neighbor Classifier and Supervised Clustering
Published in Nong Ye, Data Mining, 2013
and one target variable y whose categorical value needs to be determined, a k-nearest neighbor classifier first locates k data points that are most similar to (i.e., closest to) the data point as the k-nearest neighbors of the data point and then uses the target classes of these k-nearest neighbors to determine the target class of the data point. To determine the k-nearest neighbors of the data point, we need to use a measure of similarity or dissimilarity between data points. Many measures of similarity or dissimilarity exist, including the Euclidean distance, the Minkowski distance, the Hamming distance, Pearson’s correlation coefficient, and cosine similarity, which are described in this section.
Topological Data Analysis of Biomedical Big Data
Published in Ervin Sejdić, Tiago H. Falk, Signal Processing and Machine Learning for Biomedical Big Data, 2018
Angkoon Phinyomark, Esther Ibáñez-Marcelo, Giovanni Petri
A distance matrix is constructed from a given distance function by specifying all pairwise distances between points. Euclidean distance and its variance normalized version are the most common use of distance (e.g., [5,36,37,38]). The original version is suitable for data that is not directly comparable, while the standardized version is able to give better performance when data contains heterogeneous scale variables. Other distance measures, which can be applied to biomedical time-series data, include Manhattan distance, Minkowski distance, and cosine similarity.
Comparative Assessment of Regression Techniques for Wind Power Forecasting
Published in IETE Journal of Research, 2023
Rachna Pathak, Arnav Wadhwa, Poras Khetarpal, Neeraj Kumar
Let: T = {(yi, xi), i = 1, 2, 3, … nT}be a training set of the observed data, where yi{1, 2, 3, … c} denotes class memberships and the vector x’i= (xi1, … xip) represents predictor values. For any new observation (y, x) the nearest neighbor (y1, x1)in the training set is determined by: where d(., .) is the distance function and y’ = y1, the class to which nearest neighbor belongs, is chosen as prediction for y. The notations xj and yj describe the jth nearest neighbor of x and its class membership. Typically, the Euclidean distance is chosen as the distance function, which can be understood as a case of the Minkowski distance having the value of q =2. Using grid search, we experimentally found out that a value of k =5 returned the best results in terms of minimal and close range RMSE values, as compared to other models generated with k = x; where x was in the set {2, 3, 4, 5, 6, 7, 8}. The model had a uniform weight assignment along with Euclidian distance metric and the kd-tree algorithm for optimal spatial data organization.
An assessment of the efficiency of spatial distances in linear object matching on multi-scale, multi-source maps
Published in International Journal of Image and Data Fusion, 2018
Alireza Chehreghan, Rahim Ali Abbaspour
where and are two arbitrary points. When , this distance is called Euclidean distance, and when , it is called Manhattan distance. In this paper, all distances between the points are defined based on Minkowski distance. Major applicable spatial distances used in matching of linear objects are introduced and explained briefly in the following.
Bonferroni Distances and Their Application in Group Decision Making
Published in Cybernetics and Systems, 2020
Fabio Blanco-Mesa, José M. Merigó
The Minkowski distance (Gil-Aluja 1999; Gil-Lafuente 2005) is a distance measure that generalized a wide range of distance such as Hamming distance, Euclidean distance, geometric distance, and harmonic distance. In fuzzy set theory, it can be useful, for example, for the calculation of distances between fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, and interval-valued intuitionistic fuzzy sets, etc. The weight Minkowski distance can be defined as follows.