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 12.
... . . . . . 7 1.3.3 Confidence Limits for Correlation Matrix . . . . . . . . . . . . . . . . . 8 1.3.4 Accuracy Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.5 Summary of the Nonlinearity Test ...
... accuracy bounds that are based on the residual variance are obtained for one of the PCA models, for example that of disjunct region I, and the residual variance of the remaining PCA models (for disjunct regions II and III) are ...
... accuracy bounds are to be determined. 2. Each disjunct region has the same number of observations. 3. A PCA model is determined for one region where the the accuracy bounds describe the variation for the sum of the discarded eigenvalues ...
... accuracy bounds. Intuitively, one could consider the most centered region for this purpose or alternatively, a ... accuracy bounds of that region. Then, benchmark the residual variance of the remaining PCA models against this set of ...
... bound, is further defined by R (h) ZZ . Whilst the diagonal elements of this matrix are equal to one, the nondiagonal elements represent correlation ... Accuracy Bounds Finally, (1.19) can now be taken advantage. 1 Nonlinear PCA – a Review 9.
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 |