Optimized intrinsic dimension estimator using nearest neighbor graphs

Sricharan, Kumar; Raich, Raviv; Hero, Alfred O.

doi:10.1109/icassp.2010.5494931

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…The authors evaluate the performance of their methods on synthetic datasets, some of which have been used by similar studies in the literature [79], while the others (challenging ones) are proposed by the authors to have manifolds with nonconstant curvature. The comparison of the achieved results with those obtained by the estimators proposed in [27,33,112,118] has led to the conclusion that none of the methods has a good performance on all the tested datasets. However, graph theoretic approaches would appear to behave better when manifolds of nonconstant curvature are processed.…”

Section: Nearestmentioning

confidence: 88%

Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework

Campadelli

Casiraghi

Ceruti

et al. 2015

Mathematical Problems in Engineering

112

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When dealing with datasets comprising high-dimensional points, it is usually advantageous to discover some data structure. A fundamental information needed to this aim is the minimum number of parameters required to describe the data while minimizing the information loss. This number, usually called intrinsic dimension, can be interpreted as the dimension of the manifold from which the input data are supposed to be drawn. Due to its usefulness in many theoretical and practical problems, in the last decades the concept of intrinsic dimension has gained considerable attention in the scientific community, motivating the large number of intrinsic dimensionality estimators proposed in the literature. However, the problem is still open since most techniques cannot efficiently deal with datasets drawn from manifolds of high intrinsic dimension and nonlinearly embedded in higher dimensional spaces. This paper surveys some of the most interesting, widespread used, and advanced state-of-the-art methodologies. Unfortunately, since no benchmark database exists in this research field, an objective comparison among different techniques is not possible. Consequently, we suggest a benchmark framework and apply it to comparatively evaluate relevant stateof-the-art estimators.

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Section: Nearestmentioning

confidence: 88%

Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework

Campadelli

Casiraghi

Ceruti

et al. 2015

Mathematical Problems in Engineering

112

View full text Add to dashboard Cite

show abstract

“…Furthermore, the bounded support of a random variable as a source of k-NN estimator bias was already identified in papers by Sricharan et al [8,20]. The authors estimated the bias using Taylor expansion of pdf p(x), as:…”

Section: Theorem 1 (Lebesguementioning

confidence: 99%

Improvement of the k-nn Entropy Estimator with Applications in Systems Biology

Charzyńska¹,

Gambin

2015

Entropy

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Abstract:In this paper, we investigate efficient estimation of differential entropy for multivariate random variables. We propose bias correction for the nearest neighbor estimator, which yields more accurate results in higher dimensions. In order to demonstrate the accuracy of the improvement, we calculated the corrected estimator for several families of random variables. For multivariate distributions, we considered the case of independent marginals and the dependence structure between the marginal distributions described by Gaussian copula. The presented solution may be particularly useful for high dimensional data, like those analyzed in the systems biology field. To illustrate such an application, we exploit differential entropy to define the robustness of biochemical kinetic models.

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“…The utility of these expressions is that they can be used to optimize over tuning parameters of the fusion criterion, thereby circumventing the need for manual parameter tuning. This theory has been applied to non-parametric estimation of the mutual information [8] and estimation of intrinsic dimension [9].…”

Section: Technical Accomplishmentsmentioning

confidence: 99%

“…This has led to the fastest and most reliable anomaly detection method to date and can be applicable to large datasets with millions of samples. The asymptotic theory was applied to intrinsic dimension estimation in [9], which was implemented for fusion and segmentation of hyperspectral imagery in [15]. The theory was also applied to high dimension correlation screening [17].…”

Section: Expressions For Divergence Estimator Bias Variance and A Cltmentioning

confidence: 99%

Performance-driven Multimodality Sensor Fusion

Hero¹,

Raich²

2012

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Optimized intrinsic dimension estimator using nearest neighbor graphs

Cited by 5 publications

References 6 publications

Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework

Intrinsic Dimension Estimation: Relevant Techniques and a Benchmark Framework

Improvement of the k-nn Entropy Estimator with Applications in Systems Biology

Performance-driven Multimodality Sensor Fusion

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