Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

By Francesco Camastra, Alessandro Vinciarelli. 2002

253 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Mathematical Physics, Statistical and Nonlinear Physics, Representation & Self-Supervised Learning

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Mathematical Physics

In Statistical and Nonlinear Physics

In Representation & Self-Supervised Learning

Citations in the corpus

Measuring the Intrinsic Dimension of Objective Landscapes (2018, methodology): “Finally, note that although our approach is related to a rich body of work on estimating the “intrinsic dimension of a dataset” (Camastra & Vinciarelli, 2002; K ´ egl, 2003; Fukunaga & Olsen, 1971; Lev-ina & Bickel, 2005; Tenenbaum et al., 2000), it differs in a few respects.”
Geodesic entropic graphs for dimension and entropy estimation in manifold learning (2004, methodology): “Other methods have been proposed based on local geometric techniques, e.g., estimation of local neighborhoods [6] or fractal dimension [17] and estimating packing numbers [5] of the manifold.”
Data dimensionality estimation methods: a survey (2003, methodology): “Finally heuristic methods [64,65] have been proposed in order to estimate how fractal techniques underestimate the dimensionality of a data set when its cardinality is unadequate.”
Dimensionality of object representations in monkey inferotemporal cortex (2014, methodology): “Although best known for calculating fractal dimensions, it can be used for estimates of intrinsic dimensionality in general (Camastra & Vinciarelli, 2002; Lee & Verleysen, 2007; Martinez, Martinez, & Solka, 2012).”
Intrinsic dimension estimation: Advances and open problems (2016, methodology): “Although empirical solutions [11,14,82] were proposed, the construction of a robust ID estimator w.”
Incremental nonlinear dimensionality reduction by manifold learning (2006, background): “This can be estimated by analyzing either the spectrum of the target inner product matrix or the residue of the low rank approximation as in [46], or by other methods to estimate the intrinsic dimensionality of a manifold [9], [10], [12], [27], [31], [39].”
The vulnerability of learning to adversarial perturbation increases with intrinsic dimensionality (2017, background): “Over the past decades, many characterizations of the ID of sets have been proposed [10], [11], [12], [13], [14], [15], [16], [17], [18], [19].”
Riemannian Manifold Learning (2008, background): “distances [41], [42], [43], [44] or fractal dimensions [45].”
Making machine learning models interpretable (2012, background): “The problem of finding the adequate output dimension for NLDR techniques is an area of research on its own [18].”