LEADER 07597nam 22007455 450 001 9910494563103321 005 20251113195125.0 010 $a3-030-74552-X 024 7 $a10.1007/978-3-030-74552-3 035 $a(CKB)4100000011984528 035 $a(MiAaPQ)EBC6682763 035 $a(Au-PeEL)EBL6682763 035 $a(OCoLC)1261379859 035 $a(PPN)260304484 035 $a(DE-He213)978-3-030-74552-3 035 $a(EXLCZ)994100000011984528 100 $a20210722d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCluster Analysis and Applications /$fby Rudolf Scitovski, Kristian Sabo, Francisco Martínez-Álvarez, ?ime Ungar 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (277 pages) 225 1 $aComputer Science Series 311 08$a3-030-74551-1 320 $aIncludes bibliographical references and index. 327 $a1 -- Introduction. 2 Representatives -- 2.1 Representative of data sets with one feature. 2.1.1. Best LS-representative -- 2.1.2 Best `1-representative -- 2.1.3 Best representative of weighted data -- 2.1.4 Bregman divergences -- 2.2 Representative of data sets with two features -- 2.2.1 Fermat?Torricelli?Weber problem -- 2.2.2 Centroid of a set in the plane -- 2.2.3 Median of a set in the plane -- 2.2.4 Geometric median of a set in the plane -- 2.3 Representative of data sets with several features -- 2.3.1 Representative of weighted data -- 2.4 Representative of periodic data -- 2.4.1 Representative of data on the unit circle -- 2.4.2 Burn diagram -- 3 Data clustering -- 3.1 Optimal k-partition -- 3.1.1 Minimal distance principle and Voronoi diagram -- 3.1.2 k-means algorithm -- 3.2 Clustering data with one feature -- 3.2.1 Application of the LS-distance-like function -- 3.2.2 The dual problem -- 3.2.3 Least absolute deviation principle -- 3.2.4 Clustering weighted data -- 3.3 Clustering data with two or several features -- 3.3.1 Least squares principle -- 3.3.2 The dual problem -- 3.3.3 Least absolute deviation principle -- 3.4 Objective function F(c1, . . . , ck) = Pm i=1 min 1?j?k d(cj , ai) -- 4 Searching for an optimal partition -- 4.1 Solving the global optimization problem directly -- 4.2 k-means algorithm II -- 4.2.1 Objective function F using the membership matrix -- 4.2.2 Coordinate Descent Algorithms -- 4.2.3 Standard k-means algorithm -- 4.2.4 k-means algorithm with multiple activations -- 4.3 Incremental algorithm -- 4.4 Hierarchical algorithms -- 4.4.1 Introduction and motivation -- 4.4.2 Applying the Least Squares Principle. 4.5 DBSCAN method -- 4.5.1 Parameters MinPts and 97 4.5.2 DBSCAN algorithm -- 4.5.3 Numerical examples -- 5 Indexes -- 5.1 Choosing a partition with the most appropriate number of clusters -- 5.1.1 Calinski?Harabasz index -- 5.1.2 Davies?Bouldin index -- 5.1.3 Silhouette Width Criterion -- 5.1.4 Dunn index -- 5.2 Comparing two partitions -- 5.2.1 Rand index of two partitions -- 5.2.2 Application of the Hausdorff distance -- 6 Mahalanobis data clustering -- 6.1 Total least squares line in the plane. 6.2 Mahalanobis distance-like function in the plane -- 6.3 Mahalanobis distance induced by a set in the plane -- 6.3.1 Mahalanobis distance induced by a set of points in R n -- 6.4 Methods to search for optimal partition with ellipsoidal clusters -- 6.4.1 Mahalanobis k-means algorithm 139 CONTENTS v -- 6.4.2 Mahalanobis incremental algorithm -- 6.4.3 Expectation Maximization algorithm for Gaussian mixtures -- 6.4.4 Expectation Maximization algorithm for normalized Gaussian mixtures and Mahalanobis k-means algorithm -- 6.5 Choosing partition with the most appropriate number of ellipsoidal clusters -- 7 Fuzzy clustering problem -- 7.1 Determining membership functions and centers -- 7.1.1 Membership functions. 7.1.2 Centers -- 7.2 Searching for an optimal fuzzy partition with spherical clusters -- 7.2.1 Fuzzy c-means algorithm -- 7.2.2 Fuzzy incremental clustering algorithm (FInc) -- 7.2.3 Choosing the most appropriate number of clusters -- 7.3 Methods to search for an optimal fuzzy partition with ellipsoidal clusters -- 7.3.1 Gustafson?Kessel c-means algorithm -- 7.3.2 Mahalanobis fuzzy incremental algorithm (MFInc) -- 7.3.3 Choosing the most appropriate number of clusters -- 7.4 Fuzzy variant of the Rand index -- 7.4.1 Applications -- 8 Applications -- 8.1 Multiple geometric objects detection problem and applications -- 8.1.1 Multiple circles detection problem -- 8.1.2 Multiple ellipses detection problem -- 8.1.3 Multiple generalized circles detection problem -- 8.1.4 Multiple lines detection problem -- 8.1.5 Solving MGOD-problem by using the RANSAC method -- 8.2 Determining seismic zones in an area -- 8.2.1 Searching for seismic zones -- 8.2.2 The absolute time of an event -- 8.2.3 The analysis of earthquakes in one zone -- 8.2.4 The wider area of the Iberian Peninsula -- 8.2.5 The wider area of the Republic of Croatia -- 8.3 Temperature fluctuations -- 8.3.1 Identifying temperature seasons -- 8.4 Mathematics and politics: How to determine optimal constituencies? -- 8.4.1 Mathematical model and the algorithm -- 8.4.2 Defining constituencies in the Republic of Croatia -- 8.4.3 Optimizing the number of constituencies -- 8.5 Iris -- 8.6 Reproduction of Escherichia coli. 9 Modules and the data sets -- 9.1 Functions -- 9.2 Algorithms -- 9.3 Data generating -- 9.4 Test examples -- 9.5 Data sets -- Bibliography -- Index. 330 $aWith the development of Big Data platforms for managing massive amount of data and wide availability of tools for processing these data, the biggest limitation is the lack of trained experts who are qualified to process and interpret the results. This textbook is intended for graduate students and experts using methods of cluster analysis and applications in various fields. With clear explanations of ideas and precise definitions of notions, accompanied by numerous examples and exercises together with Mathematica programs and modules, Cluster Analysis and Applications is meant for students and researchers in various disciplines, working in data analysis or data science. 410 0$aComputer Science Series 606 $aArtificial intelligence$xData processing 606 $aComputer science 606 $aPattern recognition systems 606 $aArtificial intelligence 606 $aAlgorithms 606 $aMachine learning 606 $aData Science 606 $aTheory and Algorithms for Application Domains 606 $aAutomated Pattern Recognition 606 $aArtificial Intelligence 606 $aDesign and Analysis of Algorithms 606 $aMachine Learning 615 0$aArtificial intelligence$xData processing. 615 0$aComputer science. 615 0$aPattern recognition systems. 615 0$aArtificial intelligence. 615 0$aAlgorithms. 615 0$aMachine learning. 615 14$aData Science. 615 24$aTheory and Algorithms for Application Domains. 615 24$aAutomated Pattern Recognition. 615 24$aArtificial Intelligence. 615 24$aDesign and Analysis of Algorithms. 615 24$aMachine Learning. 676 $a519.53 700 $aScitovski$b Rudolf$0846245 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910494563103321 996 $aCluster analysis and applications$92833847 997 $aUNINA