Lectures on discrete geometry

By Jirí Matousek. 2002

1,603 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design

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In Computer Graphics and Computer-Aided Design

Citations in the corpus

Analysis of classifiers’ robustness to adversarial perturbations (2015, background): “The following result from Matoušek (2002) precisely bounds the measure of a spherical cap.”
Euclidean embeddings of finite metric spaces (2013, background): “For approximate embeddings, see Chapter 15 of Matoušek’s book [18].”
Information-theoretic lower bounds on the oracle complexity of convex optimization (2009, methodology): “By standard arguments [6], we can construct such a packing set V with cardinality |V| ≥ (2/ √ e).”
Uniform convergence of Vapnik–Chervonenkis classes under ergodic sampling (2010, result): “ of X. The join of A 1,...,Ak is said to be full if it has (maximal) cardinality 2k. The next lemma makes an elementary connection between full joins and the VC dimension. A similar result appears in [9] as Lemma 10.3.4. We include a short proof here for completeness. 8 T. M. ADAMS AND A. B. NOBEL L”
A tight bound on approximating arbitrary metrics by tree metrics (2003, background): “For more details, we point the reader to Chapter 15 in Matousek [38].”
Geometric Approximation Algorithms (2011, background): “Our presentation follows Matoušek [Mat02].”
Universal ε-approximators for integrals (2010, neutral): “In this literature the support of ν is called an ε-net, ε-transversal, ε-sample or ε-approximation [8, 27, 9].”
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions (2011, background): “ view column j of a matrix Γ as deﬁning a linear function in dimension Rd1; for each j = 1,2,...,d1, this deﬁnes a Hilbert space Hj of functions. By known results on metric entropy of Euclidean balls [17], this function class has logarithmic metric entropy, so that part (b) of the above lemma applie”
Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey (2011, background): “, [Mat02] for a background on convex polytopes including cyclic polytopes.”
Counting faces of randomly-projected polytopes when the projection radically lowers dimension (2006, background): “Here the sum covers the external angles between the original polytope Q and its subfaces G, α(G, Q), multiplied by the sum of all internal angles between each particular subface G and its faces F, β(F, G). For definitions of these angles see eg. Gr¨unbaum [18, Chapter 14], or Matousek [ 25 ].”