Understanding (dis)similarity measures

Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial Intelligence. Yet they have many different and often partial definitions or properties, usually restricted to one field of application and thus incompatible with other uses. This paper contributes to the design and understanding of similarity and dissimilarity measures for Artificial Intelligence. A formal dual definition for each concept is proposed, joined with a set of fundamental properties. The behavior of the properties under several transformations is studied and revealed as an important matter to bear in mind. We also develop several practical examples that work out the proposed approach.Postprint (published version

Cluster analysis: Basic Concepts and Algorithms

Cílem práce je uvést čtenáře do problematiky shlukové analýzy s využitím praktických příkladů a ilustrací. První a druhá kapitola jsou zaměřeny na popis a analýzu datového souboru Iris, který bude využíván v průběhu práce. Kapitola věnovaná shlukové analýze začíná formulací úlohy a pokračuje uvedením hierarchických metod shlukování společně s vybranými metodami nehiearchického shlukování (k-means, DBSCAN). Poslední část práce je věnována měření kvality shlukování a její aplikaci při hledání optimálního počtu shluků. Pro lepší pochopení jsou všechny metody nejdříve popsány intuitivně, poté formulovány matematickým aparátem a následně implementovány v jazyce R.The aim of this work is to introduce the reader to the issues of cluster analysis using practical examples and illustrations. The first and second chapters are focused on the description and analysis of the Iris dataset, which will be used during the work. The chapter devoted to cluster analysis begins with the formulation of the task and continues with the introduction of hierarchical clustering methods together with selected methods of non-hierarchical clustering (k-means, DBSCAN). The last part of the work is devoted to the clustering quality measures and application in finding the optimal number of clusters. For a better understanding, all methods are first described intuitively, then formulated with a mathematical apparatus, and then implemented in R.470 - Katedra aplikované matematikyvýborn

Understanding (dis)similarity measures

Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial Intelligence. Yet they have many different and often partial definitions or properties, usually restricted to one field of application and thus incompatible with other uses. This paper contributes to the design and understanding of similarity and dissimilarity measures for Artificial Intelligence. A formal dual definition for each concept is proposed, joined with a set of fundamental properties. The behavior of the properties under several transformations is studied and revealed as an important matter to bear in mind. We also develop several practical examples that work out the proposed approach

Understanding (dis)similarity measures

Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial Intelligence. Yet they have many different and often partial definitions or properties, usually restricted to one field of application and thus incompatible with other uses. This paper contributes to the design and understanding of similarity and dissimilarity measures for Artificial Intelligence. A formal dual definition for each concept is proposed, joined with a set of fundamental properties. The behavior of the properties under several transformations is studied and revealed as an important matter to bear in mind. We also develop several practical examples that work out the proposed approach