Výsledky vyhledávání - "Lecture Notes in Computational Science and Enginee"

Principal manifolds for data visualization and dimension reduction Autor Gorban, Alexander N., Kégl, Balázs, Wunsch, Donald C., Zinovyev, Andrei

“…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…”
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Nonlinear Principal Component Analysis: Neural Network Models and Applications Autor Scholz, Matthias, Fraunholz, Martin, Selbig, Joachim

“…Nonlinear principal component analysis (NLPCA) as a nonlinear generalisation of standard principal component analysis (PCA) means to generalise the principal…”
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Diffusion Maps - a Probabilistic Interpretation for Spectral Embedding and Clustering Algorithms Autor Nadler, Boaz, Lafon, Stephane, Coifman, Ronald, Kevrekidis, Ioannis G.

“…Spectral embedding and spectral clustering are common methods for non-linear dimensionality reduction and clustering of complex high dimensional datasets. In…”
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Learning Nonlinear Principal Manifolds by Self-Organising Maps Autor Yin, Hujun

“…This chapter provides an overview on the self-organised map (SOM) in the context of manifold mapping. It first reviews the background of the SOM and issues on…”
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Developments and Applications of Nonlinear Principal Component Analysis – a Review Autor Kruger, Uwe, Zhang, Junping, Xie, Lei

“…Although linear principal component analysis (PCA) originates from the work of Sylvester [67] and Pearson [51], the development of nonlinear counterparts has…”
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Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization Autor Gorban, Alexander N., Zinovyev, Andrei Y.

“…Principal manifolds are defined as lines or surfaces passing through “the middle” of data distribution. Linear principal manifolds (Principal Components…”
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Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes Autor Gorban, Alexander N., Sumner, Neil R., Zinovyev, Andrei Y.

“…Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of…”
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Topology-Preserving Mappings for Data Visualisation Autor Pena, Marian, Barbakh, Wesam, Fyfe, Colin

“…We present a family of topology preserving mappings similar to the Self-Organizing Map (SOM) and the Generative Topographic Map (GTM). These techniques can be…”
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The Iterative Extraction Approach to Clustering Autor Mirkin, Boris

“…The Iterative Extraction approach (ITEX) extends the one-by-one extraction techniques in Principal Component Analysis to other additive data models. We…”
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Representing Complex Data Using Localized Principal Components with Application to Astronomical Data Autor Einbeck, Jochen, Evers, Ludger, Bailer-Jones, Coryn

“…Often the relation between the variables constituting amultivariate data space might be characterized by one or more of the terms: “nonlinear”, “branched”,…”
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Dimensionality Reduction and Microarray Data Autor Elizondo, David A., Passow, Benjamin N., Birkenhead, Ralph, Huemer, Andreas

“…Microarrays are being currently used for the expression levels of thousands of genes simultaneously. They present new analytical challenges because they have a…”
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On Bounds for Diffusion, Discrepancy and Fill Distance Metrics Autor Damelin, Steven B.

“…Criteria for optimally discretizing measurable sets in Euclidean space is a difficult and old problem which relates directly to the problem of good numerical…”
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PCA and K-Means Decipher Genome Autor Gorban, Alexander N., Zinovyev, Andrei Y.

“…In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data…”
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Geometric Optimization Methods for the Analysis of Gene Expression Data Autor Journée, Michel, Teschendorff, Andrew E., Absil, Pierre-Antoine, Tavaré, Simon, Sepulchre, Rodolphe

“…DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful…”
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Auto-Associative Models, Nonlinear Principal Component Analysis, Manifolds and Projection Pursuit Autor Girard, Stéphane, Iovleff, Serge

“…Auto-associative models have been introduced as a new tool for building nonlinear Principal component analysis (PCA) methods. Such models rely on successive…”
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