A Problem of Dimensionality: A Simple Example

By G. Trunk. 1979

How researchers see this paper

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

Deep double descent: where bigger models and more data hurt (2019, background): “Mei & Montanari (2019): This work provides asymptotic analysis for ridge regression over random features Similar double descent behavior, in restricted settings, was investigated in Trunk (1979); Opper (1995; 2001); Skurichina & Duin (2002).”
Statistical Pattern Recognition: A Review (2000, background): “As expected, the quality of the selected feature subset for small training sets is poor, but improves as the training set size increases.”
A review of feature selection methods based on mutual information (2013, methodology): “Therefore, this procedure is subject to the curse of dimensionality [7, 57].”
Simultaneous feature selection and clustering using mixture models (2004, methodology): “In the second experiment, we consider the Trunk data [24], [57]: two 20-dimensional Gaussians Nðm1; IÞ and Nðm2; IÞ, wherem1 1⁄4 ð1; 1ffiffi 2 p ; .”
Information-Theoretic Feature Selection in Microarray Data Using Variable Complementarity (2008, background): “b) Optimal feature set selection: The potential difficulties of performing feature selection in small sample size situations, due to the curse of dimensionality, have been first raised in [40] and later discussed in [19].”