High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality

By David L. Donoho, A. Averbuch, Trevor J. Hastie, I. Johnstone, A. Owen, D. Scott, Bob Stine, Robert Tibshirani, Stanford University, Walter Willinger and 14 more. 2000

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Citations in the corpus

Reinforcement learning in robotics: A survey (2013, background): “Bellman originally coined the term in the context of optimization, but it also applies to function approximation and numerical integration (Donoho, 2000).”
Capsule Networks for Hyperspectral Image Classification (2019, background): “Despite all the extensive research work conducted in the aforementioned areas, the complex nature of HSI data still makes the classification problem a very challenging one and also motivates the development of more powerful and accurate classification schemes [17].”
Nonconcave penalized likelihood with a diverging number of parameters (2004, background): “To select a good penalty function, Fan and Li (2001) proposed three principles that a good penalty function should satisfy: unbiasedness, in which there is no overpenalization of large parameters to avoid unnecessary modeling biases; sparsity, as the resulting penalized likelihood estimators should ”
Local structure preserving discriminative projections for RGB-D sensor-based scene classification (2015, background): “However, due to the concentration of measure phenomenon [12], LDA performance decreases drastically under these circumstances.”
Dimension reduction in multivariate extreme value analysis (2015, background): “These results are not surprising and illustrate a typical phenomenon called the blessing of dimensionality (Donoho, 2000); as d increases, observations occur in relatively small subsets of the original space and are therefore easier to detect and separate.”
Sure independence screening for ultrahigh dimensional feature space (2006, methodology): “Problem (13) is a convex problem and can be solved by LARS and other algorithm such as the one in Meier, van der Geer and Bühlmann (2008).”
Data streams: algorithms and applications (2005, background): “Ther e is an inspiring article by Donoho [52] which is a treasure-tove of statistical analyses of interest with ma ssive data.”
A comprehensive survey of anomaly detection techniques for high dimensional big data (2020, methodology): “Furthermore, traditional methods become less meaningful with increasing dimensionality, as they use strategies that make certain assumptions about the comparatively low dimensionality of the data [29].”
A Survey of Deep Active Learning (2020, unknown): “In addition, density-based methods [192] are susceptible to p-norm limitations when applied to high-dimensional data, resulting in calculation distances that are too concentrated [54].”
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization (2009, methodology): “These approaches include influence function techniques [Huber 1981; Torre and Black 2003], multivariate trimming [Gnanadesikan and Kettenring 1972], alternating minimization [Ke and Kanade 2005], and random sampling techniques [Fischler and Bolles 1981].”
Spectral-Spatial Classification of Hyperspectral Imagery with 3D Convolutional Neural Network (2017, unknown): “This unbalance between the high dimensionality of spectral bands and the limited number of training samples is known as the Hughes phenomenon [8].”
A new embedding quality assessment method for manifold learning (2011, background): “The key problem is caused by “the curse of dimensionality” [1], that is, in handling with such data the computational complexities of algorithms often go up exponentially with the dimension.”
Machine learning and genomics: precision medicine versus patient privacy (2018, background): “In this setting, with many more variables than samples, statistical difficulties arise [3].”
Fusing Multiple Features for Depth-Based Action Recognition (2015, background): “feature normalization and feature selection or transformation because of the relationship between different feature sets and the curse of dimensionality [Donoho et al. 2000].”
A Unified Feature Selection Framework for Graph Embedding on High Dimensional Data (2015, background): “HIGH dimensional data is ubiquitous in many real world applications, especially in this era of data [1], [2].”
The intrinsic dimensionality of plant traits and its relevance to community assembly (2014, background): “Given the vast diversity of life on Earth, ecologists are no strangers to the ‘curse of dimensionality’, which is the general difficulty of navigating high-dimensional spaces (Bellman 1961; Donoho 2000).”