Principal Manifolds for Data Visualization and Dimension ReductionAlexander N. Gorban, Balázs Kégl, Donald C. Wunsch, Andrei Zinovyev Springer Science & Business Media, 2007. gada 11. sept. - 340 lappuses In 1901, Karl Pearson invented Principal Component Analysis (PCA). Since then, PCA serves as a prototype for many other tools of data analysis, visualization and dimension reduction: Independent Component Analysis (ICA), Multidimensional Scaling (MDS), Nonlinear PCA (NLPCA), Self Organizing Maps (SOM), etc. The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described as well. Presentation of algorithms is supplemented by case studies, from engineering to astronomy, but mostly of biological data: analysis of microarray and metabolite data. The volume ends with a tutorial "PCA and K-means decipher genome". The book is meant to be useful for practitioners in applied data analysis in life sciences, engineering, physics and chemistry; it will also be valuable to PhD students and researchers in computer sciences, applied mathematics and statistics. |
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Alexander N. Gorban, Balázs Kégl, Donald C. Wunsch, Andrei Zinovyev. game Notes in Computational Science and Engineering Alexander N. Gorban Balazs Kégl Donald C. Wunsch Andrei Zinovyev Editors Principal Manifolds for Data Visualization ...
... Lecture Notes in Computational Science and Engineering 58 Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick Alexander N. Gorban Balázs Kégl Donald C. Wunsch Andrei Zinovyev.
Alexander N. Gorban, Balázs Kégl, Donald C. Wunsch, Andrei Zinovyev. Alexander N. Gorban Balázs Kégl Donald C. Wunsch Andrei Zinovyev (Eds.) Principal Manifolds for Data Visualization and Dimension Reduction With 82 Figures and 22 Tables ...
... Zinovyev. Institut Curie Service Bioinformatique rue d'Ulm 26, 75248 Paris, France email: andrei.zinovyev@curie.fr Library of Congress Control Number: 2007932175 Mathematics Subject Classification: 62H25, 62H30, 62P10, 62P35, 68Q85 ...
... Zinovyev developed a general geometric framework for constructing “principal objects” of various dimensions and topologies with the simple quadratic form of the smoothness penalty. The approach was proposed in the middle of 1990s. It is ...
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References | 39 |
References | 65 |
References | 91 |
References | 127 |
The Iterative Extraction Approach to Clustering | 151 |
References | 174 |
Components | 192 |
Principal Trees | 219 |
of Bacterial Genomes | 229 |
Diffusion Maps a Probabilistic Interpretation for Spectral | 238 |
On Bounds for Diffusion Discrepancy and Fill Distance | 261 |
References | 269 |
Dimensionality Reduction and Microarray Data | 293 |
References | 307 |
PCA and KMeans Decipher Genome | 309 |
Citi izdevumi - Skatīt visu
Principal Manifolds for Data Visualization and Dimension Reduction Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev Ierobežota priekšskatīšana - 2007 |
Principal Manifolds for Data Visualization and Dimension Reduction Alexander N. Gorban,Balázs Kégl,Donald C. Wunsch,Andrei Zinovyev Priekšskatījums nav pieejams - 2009 |