Journal ArticleDOI
Adaptive Principal Surfaces
TLDR
In this paper, a nonlinear generalization of principal components analysis (PCA) is developed for curve and surface reconstruction and to data summarization, and a principal surface of the data is constructed adaptively, using some ideas from the MARS procedure of Friedman.Abstract:
We develop a nonlinear generalization of principal components analysis. A principal surface of the data is constructed adaptively, using some ideas from the MARS procedure of Friedman. We explore applications to curve and surface reconstruction and to data summarization.read more
Citations
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Journal ArticleDOI
GTM: the generative topographic mapping
TL;DR: A form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm, is introduced.
Book
Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning
TL;DR: Techniques covered range from traditional multivariate methods, such as multiple regression, principal components, canonical variates, linear discriminant analysis, factor analysis, clustering, multidimensional scaling, and correspondence analysis, to the newer methods of density estimation, projection pursuit, neural networks, and classification and regression trees.
Journal Article
Locally Defined Principal Curves and Surfaces
Umut Ozertem,Deniz Erdogmus +1 more
TL;DR: A novel theoretical understanding of principal curves and surfaces, practical algorithms as general purpose machine learning tools, and applications of these algorithms to several practical problems are presented.
Journal ArticleDOI
Overview of object oriented data analysis
J. Steve Marron,Andrés M. Alonso +1 more
TL;DR: The notion of object oriented data analysis also impacts data analysis, through providing a framework for discussion of the many choices needed in many modern complex data analyses, especially in interdisciplinary contexts.
Book ChapterDOI
The Self-Organizing Maps: Background, Theories, Extensions and Applications
TL;DR: Among various existing neural network architectures and learning algorithms, Kohonen’s selforganizing map (SOM) is one of the most popular neural network models and can provide topologically preserved mapping from input to output spaces.
References
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Book
Principal Component Analysis
TL;DR: In this article, the authors present a graphical representation of data using Principal Component Analysis (PCA) for time series and other non-independent data, as well as a generalization and adaptation of principal component analysis.
Journal ArticleDOI
Multivariate Adaptive Regression Splines
TL;DR: In this article, a new method is presented for flexible regression modeling of high dimensional data, which takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data.
Proceedings ArticleDOI
Surface reconstruction from unorganized points
TL;DR: A general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points that is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners.
Journal ArticleDOI
An Algorithm for Finding Best Matches in Logarithmic Expected Time
TL;DR: An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record.
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