Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Semiautomatic detection of floor topology from CAD architectural drawings

Abstract: A method for the semiautomatic detection of the topology of building floors represented as CAD drawings stored in vector file format is presented in this paper. This method involves the detection of walls and joint points amid walls and openings, and the search of intersection points amid walls. To give support to the wall detection process, this paper introduces the wall adjacency graph (WAG), a data structure created to detect walls from sets of planar segments contained in architectural floor plans. Wall adjacency graphs allow us to obtain a consistent and exhaustive set of walls very quickly (less than one second for real floor plans). A generalized version of the wall adjacency graph is also presented to deal with some of the limitations of the initial WAG. Algorithms for the detection of joint points and wall intersection points are presented as well, based on the analysis of the geometry from the input CAD drawings. Moreover, all this process works appropriately with both straight and circular segments. The obtained floor topology can later be used as input to generate 3D models of buildings, which are widely used on virtual cities, BIM systems and GIS.

Programming the Hilbert curve

Abstract: The Hilbert curve has previously been constructed recursively, using p levels of recursion of n‐bit Gray codes to attain a precision of p bits in n dimensions. Implementations have reflected the awkwardness of aligning the recursive steps to preserve geometrical adjacency. We point out that a single global Gray code can instead be applied to all np bits of a Hilbert length. Although this “over‐transforms” the length, the excess work can be undone in a single pass over the bits, leading to compact and efficient computer code.

Eigenvalue Outliers of Non-Hermitian Random Matrices with a Local Tree Structure

Abstract: Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical processes. We present a general and exact theory for the eigenvalue outliers of random matrices with a local tree structure. For adjacency and Laplacian matrices of oriented random graphs, we derive analytical expressions for the eigenvalue outliers, the first moments of the distribution of eigenvector elements associated with an outlier, the support of the spectral density, and the spectral gap. We show that these spectral observables obey universal expressions, which hold for a broad class of oriented random matrices.

Partially supervised machine learning of data classification based on local-neighborhood Laplacian Eigenmaps

Abstract: A local-neighborhood Laplacian Eigenmap (LNLE) algorithm is provided for methods and systems for semi-supervised learning on manifolds of data points in a high-dimensional space. In one embodiment, an LNLE based method includes building an adjacency graph over a dataset of labelled and unlabelled points. The adjacency graph is then used for finding a set of local neighbors with respect to an unlabelled data point to be classified. An eigen decomposition of the local subgraph provides a smooth function over the subgraph. The smooth function can be evaluated and based on the function evaluation the unclassified data point can be labelled. In one embodiment, a transductive inference (TI) algorithmic approach is provided. In another embodiment, a semi-supervised inductive inference (SSII) algorithmic approach is provided for classification of subsequent data points. A confidence determination can be provided based on a number of labeled data points within the local neighborhood. Experimental results comparing LNLE and simple LE approaches are presented.