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 57.
... iterative) manifold learners. The most recent representatives of this approach are Local Linear Embedding (LLE) [9] and ISOMAP [10]. Both methods find their origins in MDS in the sense that their goal is to preserve pairwise ...
... iterative extraction approach to clustering and describes additive models for clustering entity-to-feature and similarity. This approach emerged within the PCA framework by extending the bilinear Singular Value Decomposition model to ...
... . . . . . . 109 4.3.2 Iterative Data Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.4 Principal Manifold as Elastic Membrane . . . . . . . . . . . . . . . . . . . . . . . . 110 4.5 Method Implementation ...
... iterative NIPALS algorithm [78], which was defined similarly by Fisher and MacKenzie earlier in [80], and the singular value decomposition. Good overviews concerning PCA are given in Mardia et al. [45], Joliffe [32], Wold et al. [80] ...
... and (1.10) can be obtained using a singular value decomposition of the data covariance matrix S Z Z or the iterative Power method [22]. 1.3 Nonlinearity Test for PCA Models This section discusses how 1 Nonlinear PCA I a Review 5.
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 |