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 51.
... techniques even today. An important improvement of SOM came with the introduction of the Generative Topographic Mapping (GTM) [6], establishing a probabilistic framework and a well-defined objective function. The generative ...
... techniques: PCA, K-means, and Multidimensional Scaling (MDS) [5] also known as Torgerson or Torgerson-Gower scaling. Thus, the basic loop of K-means that alternates between a projection and an optimization step became the algorithmic ...
... techniques can be considered as a non-linear projection from input or data space to the output or latent space. B. Mirkin develops the iterative extraction approach to clustering and describes additive models for clustering entity-to ...
... Techniques . 5.2.1 5.2.2 K - Means .. K - Harmonic Means . 5.2.3 Neural Gas .. 5.2.4 Weighted K - Means . 5.2.5 The Inverse Weighted K - Means 5.3 Topology Preserving Mappings 131 131 . 132 132 133 . 135 136 137 138 5.3.1 Generative ...
... technique that relies on a simple transformation of recorded observation, stored in a vector z ∈ RN, to produce statistically independent score variables, stored in t ∈ Rn, n ≤ N: t = PTz . (1.1) Here, P is a transformation matrix ...
Saturs
1 | |
References | 39 |
References | 65 |
References | 91 |
References | 127 |
98 | 146 |
The Iterative Extraction Approach to Clustering | 151 |
100 | 159 |
References | 216 |
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 |
References | 174 |
Components | 192 |
References | 199 |
PCA and KMeans Decipher Genome | 309 |
Color Plates | 325 |
Citi izdevumi - Skatīt visu
Principal Manifolds for Data Visualization and Dimension Reduction Alexander N. Gorban 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 |