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 38.
... equations are treated as the independent, those on the left as the dependent variables. The result of this treatment is that we get one straight line or plane if we treat some one variable as independent, and a quite different one if we ...
... Equation (1.14) also implies that the score variables are statistically independent, as defined in (1.10), which ... Equations (1.9) and (1.10) can be obtained using a singular value decomposition of the data covariance matrix S Z Z or ...
... Equation (1.18) is shown below R(h)ZZL ≤ R(h)ZZ ≤ R(h)ZZU (1.19) which is valid elementwise. Here, R(h)ZZL and R(h)ZZU are matrices storing the lower confidence limits and the upper confidence limits of the nondiagonal elements ...
... Equations (1.20) and (1.22) utilize a singular value decomposition of Z, and reconstructs the discarded components, that is E, I U}; [Am/I? I 1 PZT I TjgPgT. A 0 PT Since Rglg I [Ph P2] [ 0” A,.] [PJLT ], the discarded eigenvalues A1 ...
... Equations (1.17) and (1.18)); 7. Solve Equations (1.24) and (1.25) to compute accuracy bounds σhmax and σhmin ; 8. Obtain correlation/covariance matrices for each disjunct region (scaled with respect to the variance of the observations ...
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 |