Classification of maps on a finite set under permutation

2020 ◽  
Author(s):  
Juan Luis García Zapata ◽  
Juan‐Antonio Rico‐Gallego
Keyword(s):  
Finite Set ◽  
Classification Of Maps

Analysis of statistical coefficients and autoregressive parameters over intrinsic mode functions (IMFs) for epileptic seizure detection

2020 ◽  
Vol 65 (6) ◽  
pp. 693-704
Author(s):  
Rafik Djemili
Keyword(s):  
Involuntary Movement ◽  
Epileptic Seizures ◽  
Intrinsic Mode Functions ◽  
Eeg Signals ◽  
Time Segment ◽  
Feature Extraction Method ◽  
Mode Decomposition ◽  
Finite Set ◽  
Student’S T

AbstractEpilepsy is a persistent neurological disorder impacting over 50 million people around the world. It is characterized by repeated seizures defined as brief episodes of involuntary movement that might entail the human body. Electroencephalography (EEG) signals are usually used for the detection of epileptic seizures. This paper introduces a new feature extraction method for the classification of seizure and seizure-free EEG time segments. The proposed method relies on the empirical mode decomposition (EMD), statistics and autoregressive (AR) parameters. The EMD method decomposes an EEG time segment into a finite set of intrinsic mode functions (IMFs) from which statistical coefficients and autoregressive parameters are computed. Nevertheless, the calculated features could be of high dimension as the number of IMFs increases, the Student’s t-test and the Mann–Whitney U test were thus employed for features ranking in order to withdraw lower significant features. The obtained features have been used for the classification of seizure and seizure-free EEG signals by the application of a feed-forward multilayer perceptron neural network (MLPNN) classifier. Experimental results carried out on the EEG database provided by the University of Bonn, Germany, demonstrated the effectiveness of the proposed method which performance assessed by the classification accuracy (CA) is compared to other existing performances reported in the literature.

Classification of Encryption Algorithms using Fisher’s Discriminant Analysis

2016 ◽  
Vol 67 (1) ◽  
pp. 59 ◽  
Author(s):  
Prabhat Kumar Ray ◽  
Shrikant Ojha ◽  
Bimal Kumar Roy ◽  
Ayanendranath Basu
Keyword(s):  
Machine Learning ◽  
Discriminant Analysis ◽  
Block Cipher ◽  
Good Classification ◽  
Finite Set ◽  
Encryption Algorithms ◽  
Fisher’S Discriminant Analysis

<p>Fisher’s Discriminant Analysis (FDA) is a method used in statistics and machine learning which can often lead to good classification between several populations by maximizing the separation between the populations. We will present some applications of FDA that discriminate between cipher texts in terms of a finite set of encryption algorithms. Specifically, we use ten algorithms, five each of stream and block cipher types. Our results display good classification with some of the features. In the present case we have little in terms of an existing standard; however, our limited study clearly shows that further exploration of this issue could be worthwhile.</p>

Application of optimization tasks in cluster analysis

10.12737/7483 ◽  
2014 ◽  
Vol 8 (7) ◽  
pp. 0-0
Author(s):  
Олег Сдвижков ◽  
Oleg Sdvizhkov
Keyword(s):  
Cluster Analysis ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Clustering Algorithms ◽  
Clustering Methods ◽  
Number Of Clusters ◽  
Homogeneous Groups ◽  
Finite Set ◽  
Minimum Number

Cluster analysis [3] is a relatively new branch of mathematics that studies the methods partitioning a set of objects, given a finite set of attributes into homogeneous groups (clusters). Cluster analysis is widely used in psychology, sociology, economics (market segmentation), and many other areas in which there is a problem of classification of objects according to their characteristics. Clustering methods implemented in a package STATISTICA [1] and SPSS [2], they return the partitioning into clusters, clustering and dispersion statistics dendrogram of hierarchical clustering algorithms. MS Excel Macros for main clustering methods and application examples are given in the monograph [5]. One of the central problems of cluster analysis is to define some criteria for the number of clusters, we denote this number by K, into which separated are a given set of objects. There are several dozen approaches [4] to determine the number K. In particular, according to [6], the number of clusters K - minimum number which satisfies where - the minimum value of total dispersion for partitioning into K clusters, N - number of objects. Among the clusters automatically causes the consistent application of abnormal clusters [4]. In 2010, proposed and experimentally validated was a method for obtaining the number of K by applying the density function [4]. The article offers two simple approaches to determining K, where each cluster has at least two objects. In the first number K is determined by the shortest Hamiltonian cycles in the second - through the minimum spanning tree. The examples of clustering with detailed step by step solutions and graphic illustrations are suggested. Shown is the use of macro VBA Excel, which returns the minimum spanning tree to the problems of clustering. The article contains a macro code, with commentaries to the main unit.

Cartography and GIS

2019 ◽  
Author(s):  
Вячеслав Раклов ◽  
Vyacheslav Raklov
Keyword(s):  
Real Estate ◽  
Land Management ◽  
Geographical Information Systems ◽  
Geographical Information ◽  
Gis Mapping ◽  
History Of ◽  
Gis Environment ◽  
Composition Structure ◽  
Classification Of Maps

The textbook considers the basic concepts of cartography, the history of its development, as well as the classification of maps and the main elements of the map, the issues of mathematical cartography, the main stages of creating maps, the factors, types and methods of cartographic generalization. Separate sections of the manual are devoted to cartographic signs and methods of image on maps of thematic content, the development of cartographic scales and methods of use of maps in land management and cadastre. Separately, the issues of the functioning of geographical information systems (GIS): their composition, structure, technology for creating thematic maps in the GIS environment. The manual concludes with a section on GIS mapping for real estate cadastre, environmental protection and land monitoring, as well as recommendations on the choice of GIS and requirements for cartographic documentation of real estate cadastre. Recommended for students studying in the field of "land Management", "Land cadastre", "Urban cadastre".

scholarly journals The classification of maps of surfaces

1987 ◽  
Vol 90 (2) ◽  
pp. 219-242 ◽  
Author(s):  
David Gabai ◽  
William H. Kazez
Keyword(s):  
Classification Of Maps

scholarly journals On the Number of Similar Instances of a Pattern in a Finite Set

10.37236/4972 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Bernardo M. Ábrego ◽  
Silvia Fernández-Merchant ◽  
Daniel J. Katz ◽  
Levon Kolesnikov
Keyword(s):  
Arithmetic Progression ◽  
Finite Subset ◽  
Upper Bound ◽  
Point Subset ◽  
Finite Set ◽  
Equilateral Triangles ◽  
Optimal Configurations ◽  
Full Classification ◽  
General Method

New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose vertices all lie within an $n$-point subset of the plane is shown to be no more than $\lfloor{(4 n-1)(n-1)/18}\rfloor$. The number of $k$-term arithmetic progressions that lie within an $n$-point subset of the line is shown to be at most $(n-r)(n+r-k+1)/(2 k-2)$, where $r$ is the remainder when $n$ is divided by $k-1$. This upper bound is achieved when the $n$ points themselves form an arithmetic progression, but for some values of $k$ and $n$, it can also be achieved for other configurations of the $n$ points, and a full classification of such optimal configurations is given. These results are achieved using a new general method based on ordering relations.

scholarly journals Measuring the Significance of Policy Outputs with Positive Unlabeled Learning

2020 ◽  
pp. 1-8
Author(s):  
RADOSLAW ZUBEK ◽  
ABHISHEK DASGUPTA ◽  
DAVID DOYLE
Keyword(s):  
United Kingdom ◽  
Construct Validity ◽  
Government Regulations ◽  
New Approach ◽  
The United Kingdom ◽  
Novel Approach ◽  
Pu Learning ◽  
Finite Set ◽  
Small Set

Identifying important policy outputs has long been of interest to political scientists. In this work, we propose a novel approach to the classification of policies. Instead of obtaining and aggregating expert evaluations of significance for a finite set of policy outputs, we use experts to identify a small set of significant outputs and then employ positive unlabeled (PU) learning to search for other similar examples in a large unlabeled set. We further propose to automate the first step by harvesting “seed” sets of significant outputs from web data. We offer an application of the new approach by classifying over 9,000 government regulations in the United Kingdom. The obtained estimates are successfully validated against human experts, by forecasting web citations, and with a construct validity test.

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