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 45.
... parameter vector Pg:(Pk1Pk2Pk3-~~Pkj~~pk1v) : N 210% I ||Pk||2 I 1~ (1-7) 3:1 Storing the score variables in a vector tT I (t1 t2 t3 - - - tj - - - tn ), t Q R" has the following first and second order statistics: E{t}I0 E{ttT} :A, (1.8) ...
... parameter vector p 1,, associated with A1,, stores the kth set of coefficients to obtain the kth linear transformation of the original variable set z to produce tk. Furthermore, given that S Z Z is a positive definite or semidefinite ...
... parameter arc-length is regarded as a projection index for each sample in a similar fashion to the score variable that represents the distance of the projected data point from the origin. In this respect, a one-dimensional nonlinear ...
... parameter t ∈ Ξ, that is fT (t) = ( f1 (t) ··· fn (t) ) , where f1 (t) ··· fn (t) are referred to as coordinate functions. Definition 3. For any z ∈ RN, the corresponding projection index tf (z) on the curve f (t) is defined as tf (z) ...
Esat sasniedzis šīs grāmatas aplūkošanas reižu limitu.
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 |