# Algorithms for Estimating Intrinsic Dimensions. This package is used for estimating intrinsic dimension of a given dataset. package ## Details 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 `corint,convU,lbmle,nni,pack` for estimating global intrinsic dimensions, and `mada,side` for estimating local intrinsic dimensions. A data generator `gendata` is included in the packege. ## Examples ```r ## Not run: ## 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 ## End(Not run) ``` ## References P. Grassberger and I. Procaccia. Measuring the strangeness of strange attractors. Physica, 1983. E. Levina and P. J. Bickel. Maximum likelihood estimation of intrinsic dimension. Advances in Neural Information Processing Systems 17, 2005. D. MacKay and Z. Ghahramani. [http://www.inference.org.uk/mackay/dimension/](http://www.inference.org.uk/mackay/dimension/) K. W. Pettis et al. An intrinsic dimensionality estimator from near neighbor information. IEEE transactions on pattern recognition and machine intelligence, 1979. M. Hein and J-Y. Audibert. Intrinsic dimensionality estimation of submanifolds in Rd. International Conference on Machine Learning, 2005. B. Kegl. Intrinsic dimension estimation using packing numbers. Advances in Neural Information Processing Systems 15, 2002. B. Eriksson and M. Crovella. Estimating intrinsic dimension via clustering. IEEE Statistical Signal Processing Workshop, 2012. H. Hino, J. Fujiki, S. Akaho, and N. Murata, 'Local Intrinsic Dimension Estimation by Generalized Linear Modeling', Neural Computation, 2017 ## Author(s) Hideitsu Hino hideitsu.hino@gmail.com

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