Intrinsic dimension estimation: Advances and open problems

Camastra, Francesco; Staiano, Antonino

doi:10.1016/j.ins.2015.08.029

Cited by 143 publications

(134 citation statements)

References 74 publications

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“…In practice, n is approximated by fitting a linear slope of a series of estimates of increasing r and C in logarithmic coordinates. As outlined before [2], an ideal estimator should be robust to noise, high dimensionality and multiscaling, as well as accurate and computationally tractable. Moreover, it should provide a range of values for the input data in which it operates properly.…”

Section: Dimensionalitymentioning

confidence: 99%

Estimating the effective dimension of large biological datasets using Fisher separability analysis

Albergante

Bac

Zinovyev

2019

2019 International Joint Conference on Neural Networks (IJCNN)

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Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a recently introduced dimensionality estimator, based on analysing the separability properties of data points, on several benchmarks and real biological datasets. We show that the introduced measure of ID has performance competitive with state-of-the-art measures, being efficient across a wide range of dimensions and performing better in the case of noisy samples. Moreover, it allows estimating the intrinsic dimension in situations where the intrinsic manifold assumption is not valid.

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Section: Dimensionalitymentioning

confidence: 99%

Estimating the effective dimension of large biological datasets using Fisher separability analysis

Albergante

Bac

Zinovyev

2019

2019 International Joint Conference on Neural Networks (IJCNN)

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“…There is an extensive literature (see e.g. [12,13]) on computing an intrinsic dimension of the sample Ω from a manifold V . The intrinsic dimension of Ω is a positive real number that approximates the Hausdorff dimension of V , a quantity that measures the local dimension of a space using the distances between nearby points.…”

Section: Dimension Diagramsmentioning

confidence: 99%

“…Each connected component is a real manifold of dimension d = dim(V ). The definitions of intrinsic dimension can be grouped into two categories: local methods and global methods [13,34]. Definitions involving information about sample neighborhoods fit into the local category, while those that use the whole dataset are called global.…”

Section: Dimension Diagramsmentioning

confidence: 99%

Learning algebraic varieties from samples

et al. 2018

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“…The minimum number of features necessary to encode this information is called intrinsic dimension (ID). More formally, ID refers to a lower-dimensional submanifold of the embedding space containing all data objects without information loss [8]. Several methods for intrinsic dimension estimation have been proposed (see, for example, Ref.…”

Section: Hubness and Its Reductionmentioning

confidence: 99%

“…Several methods for intrinsic dimension estimation have been proposed (see, for example, Ref. [8] for a recent review). Empirical results suggest that hubness depends on a data set's intrinsic dimension rather than the embedding dimension [44].…”

Section: Hubness and Its Reductionmentioning

confidence: 99%

A comprehensive empirical comparison of hubness reduction in high-dimensional spaces

Feldbauer

Flexer

2018

Knowl Inf Syst

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Hubness is an aspect of the curse of dimensionality related to the distance concentration effect. Hubs occur in high-dimensional data spaces as objects that are particularly often among the nearest neighbors of other objects. Conversely, other data objects become antihubs, which are rarely or never nearest neighbors to other objects. Many machine learning algorithms rely on nearest neighbor search and some form of measuring distances, which are both impaired by high hubness. Degraded performance due to hubness has been reported for various tasks such as classification, clustering, regression, visualization, recommendation, retrieval and outlier detection. Several hubness reduction methods based on different paradigms have previously been developed. Local and global scaling as well as shared neighbors approaches aim at repairing asymmetric neighborhood relations. Global and localized centering try to eliminate spatial centrality, while the related global and local dissimilarity measures are based on density gradient flattening. Additional methods and alternative dissimilarity measures that were argued to mitigate detrimental effects of distance concentration also influence the related hubness phenomenon. In this paper, we present a large-scale empirical evaluation of all available unsupervised hubness reduction methods and dissimilarity measures. We investigate several aspects of hubness reduction as well as its influence on data semantics which we measure via nearest neighbor classification. Scaling and density gradient flattening methods improve evaluation measures such as hubness and classification accuracy consistently for data sets from a wide range of domains, while centering approaches achieve the same only under specific settings.

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Intrinsic dimension estimation: Advances and open problems

Cited by 143 publications

References 74 publications

Estimating the effective dimension of large biological datasets using Fisher separability analysis

Estimating the effective dimension of large biological datasets using Fisher separability analysis

Learning algebraic varieties from samples

A comprehensive empirical comparison of hubness reduction in high-dimensional spaces

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