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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1.–5. rezultāts no 82.
... . Griebel D. E. Keyes Alexander N. Gorban Balázs Kégl Donald C. Wunsch Andrei Zinovyev Editors R. M. Nieminen D. Roose T. Schlick Principal Manifolds for Data Visualization and Dimension Reduction Springer 2.4 Circular PCA . 51. Front ...
... Principal Manifolds for Data Visualization and Dimension Reduction With 82 Figures and 22 Tables Springer Editors Alexander N. Gorban Department of Mathematics University of Leicester.
... principal component), then by a plane, etc. What was invented in the data approximation during the century? First of all, the approximation by linear manifolds (lines, planes, ...) was supple- mented by a rich choice of the approximate ...
... encoding setup . The embedded manifold appears only implicitly as the decoded image of the input space , and the geometric notion of projection does not apply . Principal curves and manifolds [8], on the other hand, extend VIII Preface.
... Principal curves and manifolds [8], on the other hand, extend the geometric interpretation of PCA by explicitly constructing an embedded manifold, and by encoding using standard geometric projection onto the manifold. How to define the ...
Saturs
1 | |
References | 39 |
References | 65 |
References | 91 |
References | 127 |
98 | 146 |
The Iterative Extraction Approach to Clustering | 151 |
100 | 159 |
References | 216 |
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 |
References | 174 |
Components | 192 |
References | 199 |
PCA and KMeans Decipher Genome | 309 |
Color Plates | 325 |
Citi izdevumi - Skatīt visu
Principal Manifolds for Data Visualization and Dimension Reduction Alexander N. Gorban 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 |