Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition

By Thomas M. Cover. 1965

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Citations in the corpus

Re-evaluating circuit mechanisms underlying pattern separation (2019, positive): “Higher dimensional coding subspaces facilitate the separation of overlapping activity patterns by providing a larger activity space in which those representations are embedded, thereby increasing their linear separability (Cover, 1965; Figure 1C).”
Inductive Logic Programming: Theory and Methods (1994, methodology): “• Quadratic Classifiers: is a more general version of the Linear Classifier, used for classification of measurement values of two or more classes of objects or events by a quadric surface[3].”
Capacity and Trainability in Recurrent Neural Networks (2016, background): “ CAPACITY EXPERIMENTS 2.1 PER-PARAMETER CAPACITY A foundational result in machine learning is that a single-layer perceptron with N2 parameters can store at least 2 bits of information per parameter (Cover, 1965; Gardner, 1988; Baldi & Venkatesh, 1987). More precisely, a perceptron can implement”
The Utility of Sparse Representations for Control in Reinforcement Learning (2018, background): “…(Földiák 1990); improved computational efﬁciency for updating weights in the predictor, as only weights corresponding to active features need to be updates; and enabling linear separability in the high-dimensional space (Cover 1965), which facilitates the learning of a simple linear predictor.”
Exponentially vanishing sub-optimal local minima in multilayer neural networks (2017, background): “See (Cover, 1965, Theorem 1) for a proof of the left inequality as equality (the Schläﬂi Theorem) in the case that the columns of X are in “general position” (which holds X -a.e, see deﬁnition in (Cover, 1965)) .”
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors (2011, background): “A bound for is developed in [66] and [67] as”
Fast growing and interpretable oblique trees via logistic regression models (2009, background): “Cover [1965] extended this result to enumerate the number of ways there are to partition points across hyperplanes of the form {x : w · f(x) = 0} for more general functions f .”
Physical Human Activity Recognition Using Wearable Sensors (2015, unknown): “In [71], the authors proposed a classiﬁcation methodology to recognize, using acceleration data, different classes of motions, such as driving a car, being in a train, and walking, by comparing different machine learning techniques (Random Forests, SVM and Naive Bayes).”
Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning (2019, background): “Hence on one hand αVC = 1, on the other hand the Gardner capacity amounts to αc = 2 ([21, 19]).”
Brain Computer Interfaces, a Review (2012, unknown): “The basis of SVM is to map data into a high dimensional space and find a separating hyperplane with the maximal margin [237] according to Cover’s theorem on the separability of patterns [238].”
Large Scale Machine Learning (2004, background): “1, introduced by Cover (1965) which relates the capacity of a Perceptron to the dimension of the data.”
VC dimension of neural networks (1998, background): “The basic technical fact needed arose in 19th century work by L. Schl¨aﬂi, see also Cover (1965).”
Reinforcement learning design for cancer clinical trials (2009, unknown): “The data xi are mapped into a feature space by a nonlinear transformation Φ, which guarantees that any data set becomes arbitrarily separable as the data dimension grows [28], then a hyperplane f(x) is fitted to the mapped data.”