The Curse of Dimensionality

By Moshe Sniedovich. 2010

803 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

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In Computational Theory and Mathematics

Citations in the corpus

Hyper-Parameter Optimization: A Review of Algorithms and Applications (2020, methodology): “Of course, methods exist for dimensionality reduction (e.g., PCA), but any method comes with a cost on the robustness of the model (Yiu, 2019).”
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification (2018, background): “In order to construct a surrogate response surface for a multivariate function with a large number of uncertain parameters, one has to overcome the phenomenon known as the curse of dimensionality , a term coined by the mathematician Richard Bellman [22].”
Crystal fingerprint space--a novel paradigm for studying crystal-structure sets. (2010, background): “This phenomenon is very simple to observe experimentally (Köppen, 2000; François et al., 2007).”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, neutral): “Curse of Dimensionality [23,24] The curse of dimensionality is the expression of all phenomena that appears with HDD.”
Structured Pruning for Deep Convolutional Neural Networks: A Survey (2023, background): “Bayesian Optimization helps reduce the “curse of dimensionality problem” [238] encountered while learning the optimal sparse structures.”
Unsupervised Machine Learning for Networking: Techniques, Applications and Research Challenges (2017, background): “dimensions, these phenomena are said to suffer from the curse of dimensionality [134].”
Personalized Cross-Silo Federated Learning on Non-IID Data (2020, background): “In this case, Euclidean distance may not be effective in evaluating the difference between wi and wj anymore due to the curse of dimensionality (Verleysen and François 2005; Wikipedia. 2020).”
Knowledge-based Systems (2009, neutral): “We consider two values: religiosity ( 𝑟𝑙 ) and permissiveness ( 𝑝𝑟 ).”
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, background): “The task of constructing a response surface becomes exponentially difficult as the number of input dimensions increases, a phenomenon widely referred to as the curse of dimensionality [26].”
Detection of Adversarial Training Examples in Poisoning Attacks through Anomaly Detection (2018, background): “This is known as the curse of dimensionality [20].”