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 36.
... Multidimensional Scaling (MDS) [5] also known as Torgerson or Torgerson-Gower scaling. Thus, the basic loop of K-means that alternates between a projection and an optimization step became the algorithmic skeleton of many non-linear ...
... multidimensional scaling, and principal curves are analysed and discussed. A. Gorban and A. Zinovyev developed a general geometric framework for constructing “principal objects” of various dimensions and topologies with the simple ...
... multidimensional data space. B. Nadler, S. Lafon, R. Coifman, and I. G. Kevrekidis provide a diffusion based probabilistic analysis of embedding and clustering algorithms that use the normalized graph Laplacian. They define a random ...
... Multidimensional Scaling and Principal Manifolds . . . . . . . . . 80 3.4.1 Multidimensional Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.4.2 Principal Manifolds ...
... multidimensional extensions to produce principal surfaces or principal manifolds. Another paradigm, which has been proposed by Kramer [37], is related to the construction of an artificial neural network to represent a nonlinear version ...
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 |