Topic
Adjacency list
About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.
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TL;DR: It is argued that a common principle of processing efficiency explains both: the more syntactic and semantic relations whose processing domains are minimized, and the greater the minimization preference in the processing of each relation, the more adjacency the authors find.
Abstract: This paper presents patterns of adjacency in performance data and in cross-linguistic grammatical conventions. It is argued that a common principle of processing efficiency explains both: the more syntactic and semantic relations whose processing domains are minimized, and the greater the minimization preference in the processing of each relation, the more adjacency we find. The preferences of performance are quite systematic and it is suggested that they are ultimately motivated by reductions in simultaneous processing demands in working memory. The correlations with patterns of grammatical variation exist because grammars have conventionalized the adjacency preferences of performance.
97 citations
23 Sep 2013
TL;DR: In this paper, a variety of graph-based semi-supervised learning (SSL) algorithms and graph construction methods have been evaluated empirically on a number of benchmark data sets widely used in the SSL literature.
Abstract: A variety of graph-based semi-supervised learning (SSL) algorithms and graph construction methods have been proposed in the last few years. Despite their apparent empirical success, the field of SSL lacks a detailed study that empirically evaluates the influence of graph construction on SSL. In this paper we provide such an experimental study. We combine a variety of graph construction methods as well as a variety of graph-based SSL algorithms and empirically compare them on a number of benchmark data sets widely used in the SSL literature. The empirical evaluation proposed in this paper is subdivided into four parts: (1) best case analysis; (2) classifiers' stability evaluation; (3) influence of graph construction; and (4) influence of regularization parameters. The purpose of our experiments is to evaluate the trade-off between classification performance and stability of the SSL algorithms on a variety of graph construction methods and parameter values. The obtained results show that the mutual k-nearest neighbors (mutKNN) graph may be the best choice for adjacency graph construction while the RBF kernel may be the best choice for weighted matrix generation. In addition, mutKNN tends to generate smoother error surfaces than other adjacency graph construction methods. However, mutKNN is unstable for a relatively small value of k. Our results indicate that the classification performance of the graph-based SSL algorithms are heavily influenced by the parameters setting and we found no evident explorable pattern to relay to future practitioners. We discuss the consequences of such instability in research and practice.
97 citations
TL;DR: This work presents a new approach for automatic hexahedral meshing, based on the embedded Voronoi graph, which provides complete information regarding proximity and adjacency relationships between the entities of the volume.
Abstract: This work presents a new approach for automatic hexahedral meshing, based on the embedded Voronoi graph. The embedded Voronoi graph contains the full symbolic information of the Voronoi diagram and the medial axis of the object, and a geometric approximation to the real geometry. The embedded Voronoi graph is used for decomposing the object, with the guiding principle that resulting sub-volumes are sweepable. Sub-volumes are meshed independently, and the resulting meshes are easily combined and smoothed to yield the final mesh. The approach presented here is general and automatic. It handles any volume, even if its medial axis is degenerate. The embedded Voronoi graph provides complete information regarding proximity and adjacency relationships between the entities of the volume. Hence, decomposition faces are determined unambiguously, without any further geometric computations. The sub-volumes computed by the algorithm are guaranteed to be well-defined and disjoint. The size of the decomposition is relatively small, since every sub-volume contains a different Voronoi face. Mesh quality seems high since the decomposition avoids generation of sharp angles, and sweep and other basic methods are used to mesh the sub-volumes.
95 citations
TL;DR: A more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs.
94 citations
TL;DR: In this paper, the convergence of the integrated densities of states of finite box Hamiltonians to the one on the whole space holds even at the points of discontinuity, where the integrated density of states has discontinuities precisely at this set of energies.
Abstract: We study the family of Hamiltonians which corresponds to the adjacency operators on a percolation graph. We characterise the set of energies which are almost surely eigenvalues with finitely supported eigenfunctions. This set of energies is a dense subset of the algebraic integers. The integrated density of states has discontinuities precisely at this set of energies. We show that the convergence of the integrated densities of states of finite box Hamiltonians to the one on the whole space holds even at the points of discontinuity. For this we use an equicontinuity-from-the-right argument. The same statements hold for the restriction of the Hamiltonian to the infinite cluster. In this case we prove that the integrated density of states can be constructed using local data only. Finally we study some mixed Anderson-Quantum percolation models and establish results in the spirit of Wegner, and Delyon and Souillard.
93 citations