Adaptive Control Processes: A Guided Tour

By M. Freimer, Richard Bellman. 1961

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Citations in the corpus

Unsupervised Deep Embedding for Clustering Analysis (2015, background): “The dimensionality of Z is typically much smaller than X in order to avoid the “curse of dimensionality” (Bellman, 1961).”
Data dimensionality estimation methods: a survey (2003, background): “Then it can be hard to make reliable classifiers when the dimensionality of input data is high (curse of dimensionality [3]).”
Pattern Recognition and Machine Learning (2006, unknown): “The severe difficulty that can arise in spaces of many dimensions is sometimes called the curse of dimensionality (Bellman, 1961).”
Survey of clustering algorithms (2005, background): “ponential growth of complexity in the case of multivariate function estimation under a high dimensionality situation [28], is generally used to describe the problems accompanying high dimensional spaces [34], [132].”
Combining active learning and reactive control for robot grasping (2010, background): “For high-dimensional domains, such as robot grasping, any discrete segmenting will scale badly due to the curse of dimensionality [4].”
Local structure preserving discriminative projections for RGB-D sensor-based scene classification (2015, background): “However, LDA suffers from the concentration of measure phenomenon [4,12], which is caused by the difference in Euclidean distances and the difficulty in distinguishing between pairs of high-dimensional samples.”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, background): “More generally, we can attribute the inadequacy of product-rules as the dimension s increases to a phenomenon called the curse of dimensionality, which was coined by Richard Bellman [25] to describe the fact that each time s increases by one, the “size” of the space [0, 1)s to be sampled “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].”
Structure of the Hessian matrix and an economical implementation of Newton’s method in the problem of canonical approximation of tensors (2010, unknown): “They make it possible to overcome the “curse of dimensionality” (see [ 1 ]) by using compact representations of multidi� mensional data and the corresponding algorithms for processing them (see [2]).”
Very High Resolution Multiangle Urban Classification Analysis (2012, background): “Classification with this large amount of raw data will most likely be less successful than other techniques due to the curse of dimensionality [51], [52].”
Researchers' perspectives on Industry 4.0: multi-disciplinary analysis and opportunities for operations management (2020, background): “Another series of studies Casti (1979), Barabasi (2005), Ivanov and Sokolov (2010), Basole and Bellamy (2014) offer insights into the structural dynamics of the networks, their connectivity, feedbacks, visibility, coordination, (self)-adaptation and (self)-learning, following the fundamentals (Maruy”
Kernel Methods for Deep Learning (2009, background): “It is possible to expand the input space by adding nonlinear features Φ(x) explicitly and to learn the linear weights for the resulting representation; however, this often increases the input dimensionality too much, leading to a problematic situation known as the curse of dimensionality (Bellman, 1”
Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability (2001, background): “The curse of dimensionality The curse of dimensionality (Bellman 1961) refers to the exponential growth of computation needed for a specific task as a function of the dimensionality of the input space.”