ide: Intrinsic Dimension Estimation

In intrinsicDimension: Intrinsic Dimension Estimation

Description

Intrinsic dimension estimation with method given as parameter.

Usage

localIntrinsicDimension(.data, .method, ...)
globalIntrinsicDimension(.data, .method, ...)
pointwiseIntrinsicDimension(.data, .method, ...)

Arguments

.data	Data set for which dimension should be estimated.
.method	For local.dimension.estimation, one of 'essLocalDimEst', 'dancoDimEst', 'pcaLocalDimEst', 'maxLikLocalDimEst', 'knnDimEst'. For global.dimension.estimation, one of 'dancoDimEst', 'maxLikGlobalDimEst', 'knnDimEst'. For pointwise.dimension.estimation, 'pcaOtpmLocalDimEst' or 'maxLikPointwiseDimEst'.
...	arguments passed to intrinsic dimension estimator.

Details

For the localIntrinsicDimension function, .data should be a local data set, i.e. a piece of a data set that is well approximated by a hyperplane (meaning that the curvature should be low in the local data set).

The function pointwiseIntrinsicDimension estimates local dimension around each data point in the data set.

Value

For localIntrinsicDimension and globalIntrinsicDimension, a DimEst object with the slot dim.est containing the dimension estimate and possibly additional slots containing additional information about the estimation process. For pointwiseIntrinsicDimension, a DimEstPointwise object, inheriting data.frame, with one slot dim.est containing the dimension estimates and possibly additional slots containing additional information about the estimation process.

Author(s)

Kerstin Johnsson, Lund University

References

Johnsson, K (2016). Structures in high-dimensional data: Intrinsic dimension and cluster analysis. PhD thesis. Lund University.

Johnsson, K., Soneson, C. and Fontes, M. (2015). Low Bias Local Intrinsic Dimension Estimation from Expected Simplex Skewness. IEEE Trans. Pattern Anal. Mach. Intell., 37(1), 196-202.

Ceruti, C. et al. (2012). DANCo: Dimensionality from Angle and Norm Concentration. arXiv preprint 1206.3881.

Rozza, A et al. (2012). Novel high intrinsic dimensionality estimators. Machine learning 89, 37-65.

Fukunaga, K. and Olsen, D. R. (1971). An algorithm for finding intrinsic dimensionality of data. IEEE Trans. Comput., c-20(2):176-183.

Fan, M. et al. (2010). Intrinsic dimension estimation of data by principal component analysis. arXiv preprint 1002.2050.

Bruske, J. and Sommer, G. (1998) Intrinsic dimensionality estimation with optimally topology preserving maps. IEEE Trans. on Pattern Anal. and Mach. Intell., 20(5), 572-575.

Haro, G., Randall, G. and Sapiro, G. (2008) Translated Poisson Mixture Model for Stratification Learning. Int. J. Comput. Vis., 80, 358-374.

Hill, B. M. (1975) A simple general approach to inference about the tail of a distribution. Ann. Stat., 3(5) 1163-1174.

Levina, E. and Bickel., P. J. (2005) Maximum likelihood estimation of intrinsic dimension. Advances in Neural Information Processing Systems 17, 777-784. MIT Press.

Carter, K.M., Raich, R. and Hero, A.O. (2010) On local intrinsic dimension estimation and its applications. IEEE Trans. on Sig. Proc., 58(2), 650-663.

See Also

essLocalDimEst, dancoDimEst, pcaLocalDimEst, knnDimEst pcaOtpmPointwiseDimEst, maxLikGlobalDimEst, maxLikLocalDimEst, maxLikPointwiseDimEst

Examples

data <- hyperBall(100, 4, 15, .05)
localIntrinsicDimension(data, .method='essLocalDimEst', ver = 'a', d = 1)
globalIntrinsicDimension(data, 'dancoDimEst', k = 8, D = 20)
pointwiseIntrinsicDimension(data, .method='maxLikPointwiseDimEst', k = 8, dnoise = NULL)

intrinsicDimension documentation built on June 7, 2019, 5:02 p.m.