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 84.
... Structure of Bacterial Genomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 9.4.1 Brief Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 9.4.2 ...
... structure that defines the mapping and demapping stages by neural network layers. Tan and Mavrovouniotis [68] pointed out, however, that the 5 layers network topology of autoassociative neural networks may be difficult to train, i.e. ...
... structure [16] may only cover a limited class of nonlinear functions. Hence, the IT network topology [68] may provide a more effective nonlinear compression than the technique by Dong and McAvoy [16]. In addition, Jia et al. [31] ...
... structure within the recorded data is linear or nonlinear. Kruger et al. [38] introduced this nonlinearity test using the principle outlined in Fig.1.1. The left plot in this figure shows that the first principal component describes the ...
... structure: 1 r12 ···r1N r21 1 ···r2N RZZ= ⎡ ⎢ ⎢ ⎢ ⎣ . . . . . . . . . . . . rN1 rN2 ··· 1 ⎤ ⎥ ⎥ ⎥ ⎦ . (1.16) Given that the total number of disjunct regions is m the number of observations used to construct any correlation ...
Saturs
1 | |
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 |