Search results for "Euclidean Distance"

What's So Speciall About Euclidean Distance? A Characterization Result with Applications to Mobility and Spatial Voting

2009

In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly rep- resent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard (“global”) matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known “concordance” ordering. We then provide a characterization of an index of rank mo- bility based on partial matrices and show that, in the standard case of comparing two global matrices, it is equiv…

CUDA-Accelerated Alignment of Subsequences in Streamed Time Series Data

2014

Euclidean Distance (ED) and Dynamic Time Warping (DTW) are cornerstones in the field of time series data mining. Many high-level algorithms like kNN-classification, clustering or anomaly detection make excessive use of these distance measures as subroutines. Furthermore, the vast growth of recorded data produced by automated monitoring systems or integrated sensors establishes the need for efficient implementations. In this paper, we introduce linear memory parallelization schemes for the alignment of a given query Q in a stream of time series data S for both ED and DTW using CUDA-enabled accelerators. The ED parallelization features a log-linear calculation scheme in contrast to the naive …

Some inequalities involving the euclidean condition of a matrix

1960

Mass transport problems for the Euclidean distance obtained as limits of p-Laplacian type problems with obstacles

2014

In this paper we analyze a mass transportation problem that consists in moving optimally (paying a transport cost given by the Euclidean distance) an amount of a commodity larger than or equal to a fixed one to fulfil a demand also larger than or equal to a fixed one, with the obligation of paying an extra cost of −g1(x) for extra production of one unit at location x and an extra cost of g2(y) for creating one unit of demand at y. The extra amounts of mass (commodity/demand) are unknowns of the problem. Our approach to this problem is by taking the limit as p→∞ to a double obstacle problem (with obstacles g1, g2) for the p-Laplacian. In fact, under a certain natural constraint on the extra …

Criminal networks analysis in missing data scenarios through graph distances

2021

Data collected in criminal investigations may suffer from issues like: (i) incompleteness, due to the covert nature of criminal organizations; (ii) incorrectness, caused by either unintentional data collection errors or intentional deception by criminals; (iii) inconsistency, when the same information is collected into law enforcement databases multiple times, or in different formats. In this paper we analyze nine real criminal networks of different nature (i.e., Mafia networks, criminal street gangs and terrorist organizations) in order to quantify the impact of incomplete data, and to determine which network type is most affected by it. The networks are firstly pruned using two specific m…

GEM

2014

The widespread use of digital sensor systems causes a tremendous demand for high-quality time series analysis tools. In this domain the majority of data mining algorithms relies on established distance measures like Dynamic Time Warping (DTW) or Euclidean distance (ED). However, the notion of similarity induced by ED and DTW may lead to unsatisfactory clusterings. In order to address this shortcoming we introduce the Gliding Elastic Match (GEM) algorithm. It determines an optimal local similarity measure of a query time series Q and a subject time series S. The measure is invariant under both local deformation on the measurement-axis and scaling in the time domain. GEM is compared to ED and…

A study on spectral optimisation in partial response CPM signals

1995

An optimisation technique for the minimisation of the effective bandwidth in partial response CPM signals is described. The minimum Euclidean distance is used as optimisation constraint because the bit error probability is a function of this parameter for high values of signal to noise ratio. The procedure has been implemented for a correlation length corresponding to two signalling intervals. The optimisation problem leads to a system of two nonlinear differential equations for the pulse shape, together with some boundary conditions. Numerical solution of the differential equations has been performed; initial conditions have been adjusted, to satisfy the boundary conditions using an iterat…

Data Mining Algorithms for Knowledge Extraction

2020

In this paper, we study the methods, techniques, and algorithms used in data mining, and from the studied algorithms, we emphasized the clustering algorithms, more precisely on the K-means algorithm. This algorithm was first studied using the Euclidean distance, then modifying the distance between the clusters using the distances Mahalanobis and Canberra. After implementing the algorithms in C/C++, we compared the clustering of the three algorithms, after which we modified them and studied the distance between the clusters.

G. Herglotz’ Behandlung von Beschleunigungswellen in seiner Vorlesung «Mechanik der Kontinua» angewandt auf die Stosswellen von Christoffel

1981

Following a lecture delivered by Herglotz in 1925/26 we briefly treat acceleration waves in hyperelastic materials. Our main result is a divergence equation for the squared Euclidean norm of the so-called ‘wave vector’. We then apply Herglotz’ method (devised for acceleration waves) to the propagation of such first order discontinuities in elastic bodies as were treated by Christoffel in [1].

Modeling the Mechanical Behavior of the Breast Tissues Under Compression in Real Time

2017

This work presents a data-driven model to simulate the mechanical behavior of the breast tissues in real time. The aim of this model is to speed up some multimodal registration algorithms, as well as some image-guided interventions. Ten virtual breast phantoms were used in this work. Their deformation during a mammography was performed off-line using the finite element method. Three machine learning models were trained with the data from those simulations. Then, they were used to predict the deformation of the breast tissues. The models were a decision tree and two ensemble methods (extremely randomized trees and random forest). Four experiments were designed to assess the performance of th…