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. |
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1.–5. rezultāts no 87.
... Non-linear PCA (NLPCA) extends PCA by replacing the linear encoder and decoder by non-linear functions (for example, feed-forward neural networks [7]), and optimizing them in an auto-encoding setup. The embedded manifold appears only ...
... PCA by explicitly constructing an embedded manifold, and by encoding using standard geometric projection onto the ... non-linear manifold learning algorithms. The SOM algorithm is arguably the torch holder of this batch of nonlinear ...
... PCA and K-Means decipher genome”. This exercise on principal component ... Nonlinear principal component analysis using autoassociative neural networks ... Nonlinear dimensionality reduction by locally linear embedding. Science, 290, 2323 ...
... PCA Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Nonlinearity Test for PCA Models ... Nonlinear Principal Component Analysis – a Review Fig. 1.1. Principle of nonlinearity test.
... . . . . . . . . . . . . . 199 8 Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit Stéphane Girard and Serge Iovleff .................................. 202 8.1 Introduction ...
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 |