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 17.
... Component Analysis (PCA). Why and when do we need to solve the data approximation problem instead of regression? Let ... independent, those on the left as the dependent variables. The result of this treatment is that we get one straight line ...
... independent variables are supposed to be accurately known, and the probable value of the dependent variable is ascertained. (2) In many cases of physics and biology, however, the “independent ... Principal Component Analysis –. VI Preface.
... independent variables”, and it appears better to approximate data points than the regression ... component), then by a plane, etc. What was invented in the data ... analysis techniques even today. An important improvement of SOM came with ...
... Principal Component Analysis – a Review Uwe Kruger1, Junping Zhang2, and ... independent score variables, stored in t ∈ Rn, n ≤ N: t = PTz . (1.1) Here ... Component Analysis – a Review Uwe Kruger, Junping Zhang, and Lei Xie Introduction.
... principal directions and the variance along the principal directions of data, respectively. Applying the above analysis to the first principal component ... independent noise, i.e. E {e} = 0, E{ee} = δI, E { etT } = 0 with δ being the noise ...
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 |