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 40.
... eigenvalue decomposition of a data covariance, or correlation matrix and numerical algorithms to obtain this decomposition include the iterative NIPALS algorithm [78], which was defined similarly by Fisher and MacKenzie earlier in [80] ...
... eigenvalues are positive and real and the eigenvectors are mutually orthonormal. The solution of Equation (1.14) also implies that the score variables are statistically independent, as defined in (1.10), which follows from: A 1 ATA AAAT ...
... eigenvalues in that region. 4. PCA models are determined for the remaining disjunct regions. 5. The PCA models for each region include the same number of retained principal components. 1.3.2 Disjunct Regions Here, we investigate how to ...
... eigenvalues A1, h h A2, . . ., AN depend on the elements in the correlation matrix RZZ. According to (1.18) and (1.19), however, these values are calculated within a confidence limits obtained for a significance level a. This, in turn ...
... eigenvalues is then benchmarked against these limits to examine whether they fall inside or at least one residual variance value is outside. The test is completed if accuracy bounds have been computed for each of the disjunct regions ...
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 |