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 84.
... method of choice, if there exist no strong arguments for another choice of metrics. This method was applied to many problems, has been transformed and rediscovered several times, and is now known under several names: mostly as PCA or as ...
... methods. Supervised learning algorithms assume that a training set of (input, output) observations is given (e.g., digitized images of characters and their class labels). The goal is then to learn a function that predicts the output for ...
... methods find their origins in MDS in the sense that their goal is to preserve pairwise relationships between data points. LLE conserves local linear patterns whereas ISOMAP applies MDS using the geodesic (manifold) distance approximated ...
... methods can work with branched and disconnected principal components. S. Girard and S. Iovleff introduce autoassociative models, a new tool for building NLPCA methods, and compare it to other modern methods. A. Gorban, N. Sumner, and A ...
... methods and bioinformatics. By means of PCA students discover that the information in the genome is encoded by non-overlapping triplets. Next, they learn to find gene positions. In Appendix the MatLab program listings are presented ...
Saturs
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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 |