Underestimation modification for intrinsic dimension estimation

Qiu, Haiquan; Yang, Youlong; Hua, Peng

doi:10.1016/j.patcog.2023.109580

Cited by 2 publications

(2 citation statements)

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“…An alternative dimensionality measure was introduced by Grassberger and Procaccia (1983) as the correlation dimension, which characterizes the distance between pairs of samples. For a dataset of N samples {V S,i } 1≤i≤N and a given radius r, the correlation dimension (C N (r)) is defined as the ratio of sample pairs (V S,i , V S,j ) i =j being at distance less than r data are scattered" (Qiu et al, 2023), which is likely to be the case in high-dimensional spaces. The correlation dimension of the velocity fields is around 16 (Tab.…”

Section: Correlation Dimensionmentioning

confidence: 99%

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Synthetic ground motions in heterogeneous geologies: the HEMEW-3D dataset for scientific machine learning

Lehmann,

Gatti,

Bertin

et al. 2024

Preprint

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Abstract. The ever-improving performances of physics-based simulations and the rapid developments of deep learning are offering new perspectives to study earthquake-induced ground motion. Due to the large amount of data required to train deep neural networks, applications have so far been limited to recorded data or two-dimensional simulations. To bridge the gap between deep learning and high-fidelity numerical simulations, this work introduces a new database of physics-based earthquake simulations. The HEMEW-3D database comprises 30,000 simulations of elastic wave propagation in three-dimensional (3D) geological domains. Each domain is parametrized by a different geological model built from a random arrangement of layers augmented by random fields that represent heterogeneities. For each simulation, ground motion is synthetized at the surface by a grid of virtual sensors. The high frequency of waveforms (fmax = 5 Hz) allows extensive analyses of surface ground motion. Existing and foreseen applications range from statistic analyses of the ground motion variability and machine learning methods on geological models, to deep learning-based predictions of ground motion depending on 3D heterogeneous geologies.

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Section: Correlation Dimensionmentioning

confidence: 99%

“…Levina and Bickel ( 2004) proposed another approach based on the Maximum Likelihood Estimator (MLE) of the distance to the closest neighbours. Although this method may still underestimate data with high intrinsic dimensionality (Qiu et al, 2023), it provides higher estimates than the correlation dimension (Table 3 and Fig. A3).…”

Section: Mle Intrinsic Dimensionmentioning

confidence: 99%