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Record Nr. |
UNISA996464419303316 |
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Autore |
Scitovski Rudolf |
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Titolo |
Cluster analysis and applications / / Rudolf Scitovski [and three others] |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2021] |
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©2021 |
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ISBN |
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Descrizione fisica |
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1 online resource (277 pages) |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- 1 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 I -- 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)=i=1m min1≤j≤kd(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 |
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Introduction and Motivation -- 4.4.2 Applying the Least Squares Principle -- 4.5 DBSCAN Method -- 4.5.1 Parameters MinPts and ε -- 4.5.2 DBSCAN Algorithm -- Main DBSCAN Algorithm -- 4.5.3 Numerical Examples -- 5 Indexes. |
5.1 Choosing a Partition with the Most Appropriate Numberof 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 Rn -- 6.4 Methods to Search for Optimal Partition with Ellipsoidal Clusters -- 6.4.1 Mahalanobis k-Means Algorithm -- 6.4.2 Mahalanobis Incremental Algorithm -- 6.4.3 Expectation Maximization Algorithm for GaussianMixtures -- 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 The Number of Geometric Objects Is Known in Advance -- 8.1.2 The Number of Geometric Objects Is Not Known in Advance. |
8.1.3 Searching for MAPart and Recognizing GeometricObjects -- 8.1.4 Multiple Circles Detection Problem -- Circle as the Representative of a Data Set -- Artificial Data Set Originating from a Single Circle -- The Best Representative -- Multiple Circles Detection Problem in the Plane -- The Number of Circles Is Known -- KCC Algorithm -- The Number of Circles Is Not Known -- Real-World Images -- 8.1.5 Multiple Ellipses Detection Problem -- A Single Ellipse as the Representative of a Data Set -- Artificial Data Set Originating from a Single Ellipse -- The Best Representative -- Multiple Ellipses Detection Problem -- The Number of Ellipses Is Known in Advance -- KCE Algorithm -- The Number of Ellipses Is Not Known in Advance -- Real-World Images -- 8.1.6 Multiple Generalized Circles Detection Problem -- Real-World Images -- 8.1.7 Multiple Lines Detection Problem -- A Line as Representative of a Data Set -- The Best TLS-Line in Hesse Normal Form -- The Best Representative -- Multiple Lines Detection Problem in the Plane -- The Number of Lines Is Known in Advance -- KCL Algorithm -- The Number of Lines Is Not Known in Advance -- Real-World Images -- 8.1.8 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? -- -- Defining the Problem -- 8.4.1 Mathematical Model and the Algorithm -- Integer Approach -- Linear Relaxation |
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Approach -- 8.4.2 Defining Constituencies in the Republic of Croatia. |
Applying the Linear Relaxation Approach to the Model with 10 Constituencies -- Applying the Integer Approach to the Model with 10 Constituencies -- 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. |
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