Principal Manifolds for Data Visualization and Dimension Reduction

Pirmais vāks
Alexander N. Gorban
Springer Science & Business Media, 2007 - 334 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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Contents
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

References
199
References
216
Color Plates
325
Autortiesības

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

Bieži izmantoti vārdi un frāzes

accuracy bounds algorithm applications approach approximation auto-associative models biological centroids classification complex construction convergence corresponding cost function covariance data points data set data space defined denote diffusion map dimension reduction dimensionality reduction disjunct regions distance distribution eigenvalues eigenvectors elastic maps embedding Equation error estimation Euclidean example extraction fragments Gaussian gene expression genome Gorban graph grid hyperplane IEEE independent component analysis input iteration ITEX K-Means kernel PCA layer learning linear PCA linear principal LTSA matrix metabolite methods microarray data minimization multidimensional Neural Computation neural networks node nonlinear dimensionality reduction nonlinear PCA one-dimensional optimization orthogonal parameters partition PCA model perceptron principal component analysis principal curves principal manifolds problem projection projection pursuit proposed prototypes random regression residual variance samples score variables Self-Organizing Map similarity spectral clustering statistical step structure subspace techniques topology triplet unsupervised learning vector ViSOM visualisation visualization weights Zinovyev

Bibliogrāfiskā informācija

NosaukumsPrincipal Manifolds for Data Visualization and Dimension Reduction
Grāmatas Lecture Notes in Computational Science and Engineering 58. sējums. sējums, ISSN 1439-7358
RedaktorsAlexander N. Gorban
Izdevums:ilustrēts
IzdevējsSpringer Science & Business Media, 2007
ISBN3540737499, 9783540737490
Apjoms334 lappuses
  
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