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. |
No grāmatas satura
1.–5. rezultāts no 28.
... PCA Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 ... Kernel PCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.5 Analysis of Existing ...
... (PCA) originates from the work of Sylvester [67] and Pearson [51], the ... kernel approaches or the combination of these approaches. This article ... PCA is a data analysis technique that relies on a simple transformation of recorded ...
... PCA first, which is followed by the application of the IT algorithm using the scaled linear principal components. More recently, Kernel PCA (KPCA) has been proposed by Schölkopf [56,57]. KPCA first maps the original variable set z onto ...
... Kernel functions, such as radial basis functions, polynomial or sigmoid kernels, conceptually and computationally efficient NLPCA algorithms can be constructed. This approach, referred to as Kernel PCA, is reviewed in Subsect. 4.3. 1.4 ...
Esat sasniedzis šīs grāmatas aplūkošanas reižu limitu.
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 |