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Error Matrix (error + matrix)

Distribution by Scientific Domains

Mathematics and Statistics	50%

Selected Abstracts

An Adaptive Sampling Scheme for Out-of-Core Simplification

COMPUTER GRAPHICS FORUM, Issue 2 2002
Guangzheng Fei
Current out-of-core simplification algorithms can efficiently simplify large models that are too complex to be loaded in to the main memory at one time. However, these algorithms do not preserve surface details well since adaptive sampling, a typical strategy for detail preservation, remains to be an open issue for out-of-core simplification. In this paper, we present an adaptive sampling scheme, called the balanced retriangulation (BR), for out-of-core simplification. A key idea behind BR is that we can use Garland's quadric error matrix to analyze the global distribution of surface details. Based on this analysis, a local retriangulation achieves adaptive sampling by restoring detailed areas with cell split operations while further simplifying smooth areas with edge collapse operations. For a given triangle budget, BR preserves surface details significantly better than uniform sampling algorithms such as uniform clustering. Like uniform clustering, our algorithm has linear running time and small memory requirement. [source]

Modifiable low-rank approximation to a matrix

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 10 2009
Jesse L. Barlow
Abstract A truncated ULV decomposition (TULVD) of an m×n matrix X of rank k is a decomposition of the form X = ULVT+E, where U and V are left orthogonal matrices, L is a k×k non-singular lower triangular matrix, and E is an error matrix. Only U,V, L, and ,E,F are stored, but E is not stored. We propose algorithms for updating and downdating the TULVD. To construct these modification algorithms, we also use a refinement algorithm based upon that in (SIAM J. Matrix Anal. Appl. 2005; 27(1):198,211) that reduces ,E,F, detects rank degeneracy, corrects it, and sharpens the approximation. Copyright © 2009 John Wiley & Sons, Ltd. [source]

for misspecified regression models

THE CANADIAN JOURNAL OF STATISTICS, Issue 4 2003
Peilin Shi
Abstract The authors propose minimax robust designs for regression models whose response function is possibly misspecified. These designs, which minimize the maximum of the mean squared error matrix, can control the bias caused by model misspecification and provide the desired efficiency through one parameter. The authors call on a nonsmooth optimization technique to derive these designs analytically. Their results extend those of Heo, Schmuland & Wiens (2001). The authors also discuss several examples for approximately polynomial regression. Les auteurs proposent des plans minimax robustes pour des modèles de régression dont la fonction réponse pourrait ,tre mal spécifiée. Ces plans, qui minimisent le maximum de la matrice des erreurs quadratiques, permettent de contr,ler le biais d, à une mauvaise spécification du modèle tout en garantissant l'efficacité désirée au moyen d'un paramètre. Les auteurs se servent d'une technique d'optimisation non lisse pour préciser la forme analytique de ces plans. Leurs résultats généralisent ceux de Heo, Schmuland & Wiens (2001). Les auteurs présentent en outre plusieurs exemples touchant la régression approximativement polynomiale. [source]

Combining land cover mapping of coastal dunes with vegetation analysis

APPLIED VEGETATION SCIENCE, Issue 2 2005
A. Acosta
Abstract Question: Coastal dune systems are characterized by a natural mosaic that promotes species diversity. This heterogeneity often represents a severe problem for traditional mapping or ground survey techniques. The work presented here proposes to apply a very detailed CORINE land cover map as baseline information for plant community sampling and analysis in a coastal dune landscape. Location: Molise coast, Central Italy. Method: We analysed through an error matrix the coherence between land cover classes and vegetation types identified through a field survey. The CORINE land cover map (scale 1: 5000) of the Molise coast was used with the CORINE legend expanded to a fourth level of detail for natural and semi-natural areas. Vegetation data were collected following a random stratified sampling design using the CORINE land cover classes as strata. An error matrix was used to compare, on a category-by-category basis, the relationship between vegetation types (obtained by cluster analyses of sampling plots) and land cover classes of the same area. Results: The coincidence between both classification approaches is quite good. Only one land cover class shows a very weak agreement with its corresponding vegetation type; this result was interpreted as being related to human disturbance. Conclusions: Since it is based on a standard land cover classification, the proposal has a potential for application to most European coastal systems. This method could represent a first step in the environmental planning of coastal systems. [source]