Robust cluster analysis and variable selection. (2014)

• Record Type: Book
• Further Information: Note: Gunter Ritter.
• Authors: Ritter, Gunter
• Contents: Introduction ; ; Mixture and classification models and their likelihood estimators; General consistency and asymptotic normality; Local likelihood estimates; Maximum likelihood estimates; Notes; Mixture models and their likelihood estimators; Latent distributions; Finite mixture models; Identifiable mixture models; Asymptotic properties of local likelihood maxima; Asymptotic properties of the MLE: constrained nonparametric mixture models; Asymptotic properties of the MLE: constrained parametric mixture models; Notes; Classification models and their criteria; Probabilistic criteria for general populations; Admissibility and size constraints; Steady partitions; Elliptical models; Normal models; Geometric considerations; Consistency of the MAP criterion; Notes; ; Robustification by trimming; Outliers and measures of robustness; Outliers; The sensitivities; Sensitivity of ML estimates of mixture models; Breakdown points; Trimming the mixture model; Trimmed likelihood function of the mixture model; Normal components; Universal breakdown points of covariance matrices, mixing rates, and means; Restricted breakdown point of mixing rates and means; Notes; Trimming the classification model – the TDC; Trimmed MAP classification model; Normal case – the Trimmed Determinant Criterion, TDC; Breakdown robustness of the constrained TDC; Universal breakdown point of covariance matrices and means; Restricted breakdown point of the means; Notes; ; Algorithms; EM algorithm for mixtures; General mixtures; Normal mixtures; Mixtures of multivariate t-distributions; Trimming – the EMT algorithm; Order of Convergence; Acceleration of the mixture EM; Notes; k -Parameters algorithms; General and elliptically symmetric models; Steady solutions and trimming; Using combinatorial optimization; Overall algorithms; Notes; Hierarchical methods for initial solutions; ; Favorite solutions and cluster validation; Scale balance and Pareto solutions; Number of components of uncontaminated data; Likelihood–ratio tests; Using cluster criteria as test statistics; Model selection criteria; Ridgeline manifold; Number of components and outliers; Classification trimmed likelihood curves; Trimmed BIC; Adjusted BIC; Cluster validation; Separation indices; Normality and related tests; Visualization; Measures of agreement of partitions; Stability; Notes; ; Variable selection in clustering; Irrelevance; Definition and general properties; The normal case; Filters; Univariate filters; Multivariate filters; Wrappers; Using the likelihood ratio test; Using Bayes factors and their BIC approximations; Maximum likelihood subset selection; Consistency of the MAP cluster criterion with variable selection; Practical guidelines; Notes; ; Applications; Miscellaneous data sets; IRIS data; SWISS BILLS; STONE FLAKES; Gene expression data; Supervised and unsupervised methods; Combining gene selection and profile clustering; Application to the LEUKEMIA data; Notes; ; Appendix A: Geometry and linear algebra; Appendix B: Topology; Appendix C: Analysis; Appendix D: Measures and probabilities; Appendix E: Probability; Appendix F: Statistics; Appendix G: Optimization;
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2014
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 519.53; Cluster analysis
• Languages: English
• ISBNs: 9781439857977
• Related ISBNs: 9781439857960
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.