R/ider.R

In ider: Various Methods for Estimating Intrinsic Dimension

#' This package is used for estimating intrinsic dimension of a given dataset.
#' 
#' In common data analysis situations, an observed datum is expressed by a 
#' p-dimensional vector. In general, the apparent data dimension p and its 
#' intrinsic dimension d are different. A basic assumption in many data analysis
#'  and machine learning methods is that the intrinsic dimension is low 
#'  even when the apparent dimension is high and the data distribution is 
#'  constrained onto a low dimensional manifold. 
#'  Examples of such methods include manifold learning, subspace methods, and 
#'  visualization and dimensionality reduction methods.
#'  The key to the success of dimensionality reduction, manifold learning and
#'  latent variable analysis lies in the accurate estimation of the
#'  intrinsic dimension of the dataset at hand.
#'  This package implements a number of intrinsic dimension estimation methods.
#'  Some functions are for estimating the global intrinsic dimension while others
#'  are capable of estimating both local and global intrinsic dimension.
#'  
#'  The package has functions \code{corint,convU,lbmle,nni,pack} for estimating global
#'  intrinsic dimensions, and \code{mada,side} for estimating local intrinsic dimensions. 
#'  A data generator \code{gendata} is included in the packege.
#'   
#' 
#' 
#' 
#' @docType package
#' @name ider-package
#' @title Algorithms for Estimating Intrinsic Dimensions.
#' @aliases ider
#' @author Hideitsu Hino \email{hideitsu.hino@@gmail.com}
#' @references P. Grassberger and I. Procaccia. Measuring the strangeness of strange attractors. 
#' Physica, 1983.
#' @references E. Levina and P. J. Bickel. Maximum likelihood estimation of 
#' intrinsic dimension. Advances in Neural Information Processing Systems 17, 2005.
#' @references D. MacKay and Z. Ghahramani. \url{http://www.inference.org.uk/mackay/dimension/}
#' @references K. W. Pettis et al. An intrinsic dimensionality estimator from near
#' neighbor information. IEEE transactions on pattern recognition and machine intelligence, 1979.
#' @references M. Hein and J-Y. Audibert. Intrinsic dimensionality estimation of
#' submanifolds in Rd. International Conference on Machine Learning, 2005.
#' @references B. Kegl. Intrinsic dimension estimation using packing numbers.
#'  Advances in Neural Information Processing Systems 15, 2002.
#' @references B. Eriksson and M. Crovella. Estimating intrinsic dimension via clustering.
#' IEEE Statistical Signal Processing Workshop, 2012.
#' @references H. Hino, J. Fujiki, S. Akaho, and N. Murata, 'Local Intrinsic Dimension Estimation by Generalized Linear Modeling', Neural Computation, 2017
#' 
#' @examples 
#' \dontrun{
#'  ## global intrinsic dimension estimate
#'  x <- gendata(DataName='SwissRoll',n=300)
#'  
#'  x <- gendata(DataName='SwissRoll',n=300,p=3,q=2)
#'  estcorint <- corint(x=x,k1=5,k2=10)
#'  print(estcorint)
#'  
#'  estmle <- lbmle(x=x,k1=3,k2=5)  ## estimation by mle
#'  print(estmle) 
#'  
#'  estnii <- nni(x=x) ## estimation by nearest neighbor information
#'  print(estnni)
#'  
#'  estconvU <- convU(x=x)  ## estimation by convergence property of U-stats
#'  print(estconvU)
#'  
#' estpackG <- pack(x=x,greedy=TRUE)  ## estimation by the packing number method with greedy algorithm
#' print(estpackG)
#' estpackC <- pack(x=x,greedy=FALSE) ## estimation by the packing number method by clutering
#' print(estpackC)
#' 
#'  ## local intrinsic dimension estimate
#'  tmp <- gendata(DataName='ldbl',n=300)
#' x <- tmp$x
#' estmada <- mada(x=x,local=TRUE)
#' head(estmada)  ## estimated local intrinsic dimensions by mada
#' head(tmp$tDim) ## true local intrinsic dimensions
#' estside <- side(x=x,local=TRUE)
#' head(estside) ## estimated local intrinsic dimensions by side
#' 
#' }
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