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Title:

Intrinsic Dimensionality Estimation for High-dimensional Data Sets: New Approaches for the Computation of Correlation Dimension

Description:

The analysis of high–dimensional data is usually challenging since many standard modelling approaches tend to break down due to the so–called “curse of dimensionality”. Dimension reduction techniques, which reduce the data set (explicitly or implicitly) to a smaller number of variables, make the data analysis more efficient and are furthermore u...

The analysis of high–dimensional data is usually challenging since many standard modelling approaches tend to break down due to the so–called “curse of dimensionality”. Dimension reduction techniques, which reduce the data set (explicitly or implicitly) to a smaller number of variables, make the data analysis more efficient and are furthermore useful for visualization purposes. However, most dimension reduction techniques require fixing the intrinsic dimension of the low-dimensional subspace in advance. The intrinsic dimension can be estimated by fractal dimension estimation methods, which exploit the intrinsic geometry of a data set. The most popular concept from this family of methods is the correlation dimension, which requires estimation of the correlation integral for a ball of radius tending to 0. In this paper we propose approaches to approximate the correlation integral in this limit. Experimental results on real world and simulated data are used to demonstrate the algorithms and compare to other methodology. A simulation study which verifies the effectiveness of the proposed methods is also provided. Minimize

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ACADEMY PUBLISHER

Year of Publication:

2013-05-01T00:00:00Z

Source:

Journal of Emerging Technologies in Web Intelligence, Vol 5, Iss 2, Pp 91-97 (2013)

Journal of Emerging Technologies in Web Intelligence, Vol 5, Iss 2, Pp 91-97 (2013) Minimize

Document Type:

article

Language:

English

Subjects:

intrinsic dimensionality ; fractal-based methods ; correlation dimension ; LCC:Science (General) ; LCC:Q1-390 ; LCC:Science ; LCC:Q

intrinsic dimensionality ; fractal-based methods ; correlation dimension ; LCC:Science (General) ; LCC:Q1-390 ; LCC:Science ; LCC:Q Minimize

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310 Collections of general statistics *(computed)*

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Title:

Modelling beyond regression functions: an application of multimodal regression to speed-flow data

Description:

For speed-flow data, which are intensively discussed in transportation science, common nonparametric regression models of the type "y"="m"("x")+noise turn out to be inadequate since simple functional models cannot capture the essential relationship between the predictor and response. Instead a more general setting is required, allowing for multi...

For speed-flow data, which are intensively discussed in transportation science, common nonparametric regression models of the type "y"="m"("x")+noise turn out to be inadequate since simple functional models cannot capture the essential relationship between the predictor and response. Instead a more general setting is required, allowing for multifunctions rather than functions. The tool proposed is conditional modes estimation which, in the form of local modes, yields several branches that correspond to the local modes. A simple algorithm for computing the branches is derived. This is based on a conditional mean shift algorithm and is shown to work well in the application that is considered. Copyright 2006 Royal Statistical Society. Minimize

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article

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Title:

ON DESIGN-WEIGHTED LOCAL FITTING AND ITS RELATION TO THE HORVITZ-THOMPSON ESTIMATOR

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Abstract: Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze design-weighted versions of the well-known local polynomial regression estimators, derive their asymptotic bias and variance, and observe that the asymptotically optimal wei...

Abstract: Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze design-weighted versions of the well-known local polynomial regression estimators, derive their asymptotic bias and variance, and observe that the asymptotically optimal weights are in conflict with (practically motivated) weighting schemes previously proposed in the literature. We investigate this conflict using theory and simulation, and find that the problem has a surprising counterpart in sampling theory, leading us back to the discussion on the Horvitz-Thompson estimator and Basu’s (1971) elephants. In this light one might consider our results as an asymptotic and nonparametric version of the Horvitz-Thompson theorem. The crucial point is that bias-minimizing weights can make estimators extremely vulnerable to outliers in the design space and have therefore to be used with particular care. Key words and phrases: Bias reduction, Horvitz-Thompson estimator, kernel smoothing, leverage values, local polynomial modelling, nonparametric smoothing, stratification. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-13

Source:

http://www.maths.dur.ac.uk/~dma0je/Preprints/dwlf4.pdf

http://www.maths.dur.ac.uk/~dma0je/Preprints/dwlf4.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

LOCAL FITTING WITH A POWER BASIS Authors:

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Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method ...

Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem, we derive asymptotic expressions for bias and variance of this estimator. We apply this method to a simulated data set for various basis functions and discuss situations where the fit can be improved by using a suitable basis. Finally, some remarks about bandwidth selection are given and the method is applied to real data. Key-Words: local polynomial fitting; Taylor expansion; power basis; bias reduction. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-20

Source:

http://www.ine.pt/revstat/pdf/rs040201.pdf

http://www.ine.pt/revstat/pdf/rs040201.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Representing Complex Data Using Localized Principal Components with Application to Astronomical Data

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Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: “nonlinear”, “branched”, “disconnected”, “bended”, “curved”, “heterogeneous”, or, more general, “complex”. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. ...

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: “nonlinear”, “branched”, “disconnected”, “bended”, “curved”, “heterogeneous”, or, more general, “complex”. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-02-28

Source:

http://pca.narod.ru/7MainGorbanKeglWunschZin.pdf

http://pca.narod.ru/7MainGorbanKeglWunschZin.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Modelling beyond Regression Functions: an Application of Multimodal Regression to Speed-Flow Data

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An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y = m(x) + noise. In many situations this simple functional model does not capture adequately the essential relation between pr...

An enormous amount of publications deals with smoothing in the sense of nonparametric regression. However, nearly all of the literature treats the case where predictors and response are related in the form of a function y = m(x) + noise. In many situations this simple functional model does not capture adequately the essential relation between predictor and response. We show by means of speed-flow diagrams, that a more general setting may be required, allowing for multifunctions instead of only functions. It turns out that in this case the conditional modes are more appropriate for the estimation of the underlying relation than the commonly used mean or the median. Estimation is achieved using a conditional mean-shift procedure, which is adapted to the present situation. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-12

Source:

http://www.stat.uni-muenchen.de/sfb386/papers/dsp/paper395.pdf

http://www.stat.uni-muenchen.de/sfb386/papers/dsp/paper395.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Key Words ; Mean shift ; Conditional density ; Conditional mode ; Speed-flow curves

Key Words ; Mean shift ; Conditional density ; Conditional mode ; Speed-flow curves Minimize

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Title:

astronomical

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Representing complex data using localized

Representing complex data using localized Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-17

Source:

http://www.stats.gla.ac.uk/~levers/publications/lpc_gaia.pdf

http://www.stats.gla.ac.uk/~levers/publications/lpc_gaia.pdf Minimize

Document Type:

text

Language:

en

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Title:

quadrature for overdispersed generalized linear models and variance component models License GPL (> = 2) Repository CRAN

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R topics documented: npmlreg-package. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 irlsuicide. 15 missouri. 16 1 2 npmlreg-package plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20 summary.glmmNPML. 22 tolfind. 24 weightslogl.calc.w. 26 Index 28 npmlreg-package Nonparametric maximum likelihood estimation for random effect...

R topics documented: npmlreg-package. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 irlsuicide. 15 missouri. 16 1 2 npmlreg-package plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20 summary.glmmNPML. 22 tolfind. 24 weightslogl.calc.w. 26 Index 28 npmlreg-package Nonparametric maximum likelihood estimation for random effect models Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-24

Source:

http://cran.at.r-project.org/web/packages/npmlreg/npmlreg.pdf

http://cran.at.r-project.org/web/packages/npmlreg/npmlreg.pdf Minimize

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text

Language:

en

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License GPL (> = 2)

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Description Fitting multivariate data patterns with local principal curves; including simple tools for data compression (projection), bandwidth selection, and measuring goodness-of-fit.

Description Fitting multivariate data patterns with local principal curves; including simple tools for data compression (projection), bandwidth selection, and measuring goodness-of-fit. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-11-13

Source:

http://cran.at.r-project.org/web/packages/LPCM/LPCM.pdf

http://cran.at.r-project.org/web/packages/LPCM/LPCM.pdf Minimize

Document Type:

text

Language:

en

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Repository CRAN

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R topics documented: npmlreg-package. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 1 2 npmlreg-package irlsuicide. 15 missouri. 16 plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20

R topics documented: npmlreg-package. 2 alldist. 3 dkern. 10 fabric. 11 family.glmmNPML. 12 gqz. 13 hosp. 14 1 2 npmlreg-package irlsuicide. 15 missouri. 16 plot.glmmNPML. 17 post. 19 predict.glmmNPML. 20 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2014-12-05

Source:

http://cran.us.r-project.org/web/packages/npmlreg/npmlreg.pdf

http://cran.us.r-project.org/web/packages/npmlreg/npmlreg.pdf Minimize

Document Type:

text

Language:

en

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This program is free software ; you can redistribute it and/or mo

This program is free software ; you can redistribute it and/or mo Minimize

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