We present several applications of non-linear datamodeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are general...
详细信息
We present several applications of non-linear datamodeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen's self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.
We consider principal curves and surfaces in the context of multivariate regression modelling. For predictor spaces featuring complex dependency patterns between the involved variables, the intrinsic dimensionality of...
详细信息
We consider principal curves and surfaces in the context of multivariate regression modelling. For predictor spaces featuring complex dependency patterns between the involved variables, the intrinsic dimensionality of the data tends to be very small due to the high redundancy induced by the dependencies. In situations of this type, it is useful to approximate the high-dimensional predictor space through a low-dimensional manifold (i.e., a curve or a surface), and use the projections onto the manifold as compressed predictors in the regression problem. In the case that the intrinsic dimensionality of the predictor space equals one, we use the local principal curve algorithm for the the compression step. We provide a novel algorithm which extends this idea to local principal surfaces, thus covering cases of an intrinsic dimensionality equal to two, which is in principle extendible to manifolds of arbitrary dimension. We motivate and apply the novel techniques using astrophysical and oceanographic data examples.
Structural Health Monitoring aims to identify damages in engineering structures by monitoring changes in their vibration response. Unsupervised learning algorithms can be used to obtain a model of the undamaged condit...
详细信息
Spherical neutron polarimetry (SNP) is a powerful technique for the determination of magnetic structures which may otherwise be intractable. The complexity of the neutron scattering process and the large number of dif...
详细信息
Spherical neutron polarimetry (SNP) is a powerful technique for the determination of magnetic structures which may otherwise be intractable. The complexity of the neutron scattering process and the large number of different possible trial structures typically leads to refinements based on a simple trial and error generation of possible models and a possible failure to explore valid possible models. The combination of the model symmetry types determined from representational analysis and reverse-Monte Carlo refinement creates a generalized refinement strategy for SNP data that allows refinement in terms of symmetry adapted modes built up from the basis vectors that describe the orientations of the magnetic moments on the different magnetic sites, and those of the different domains that are possible in a sample: spin (S)-domains and K-domains. This methodology typically leads to a large reduction in the number of refined parameters as well as the rigorous inclusion of any symmetry related domains. In combination with reverse-Monte Carlo refinement algorithms a general strategy for refining complex magnetic structures can be created. We present an example of a frustrated magnetic structure that have been determined using this approach Er2Ti2O7. (C) 2009 Elsevier B.V. All rights reserved.
State explosion in model checking continues to be the primary obstacle to widespread use of software model checking. The large input ranges of variables used in software is the main cause of state explosion. As softwa...
详细信息
The proceedings contain 68 papers. The special focus in this conference is on Rough Computing, Rough Set Theory and Its Applications. The topics include: Decision rules, bayes’ rule and rough sets;from computation wi...
ISBN:
(纸本)3540666451
The proceedings contain 68 papers. The special focus in this conference is on Rough Computing, Rough Set Theory and Its Applications. The topics include: Decision rules, bayes’ rule and rough sets;from computation with measurements to computation with perceptions;on text mining techniques for personalization;a road to discovery science;approximate distributed synthesis and granular semantics for computing with words;discovery of rules about complications;rough genetic algorithms;a rough-fuzzy neural computational approach;toward spatial reasoning in the framework of rough mereology;an algorithm for finding equivalence relations from tables with non-deterministic information;on the extension of rough sets under incomplete information;an alternative formulation;formal rough concept analysis;noise reduction in telecommunication channels using rough sets and neural networks;rough set analysis of electrostimilation test database for the prediction of post-operative profits in cochlear implanted patients;a rough set-based approach to text classification;modular rough fuzzy MLP;correspondence and complexity results;handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems;the generic rough set inductive logic programming model and motifs in strings;rough problem settings for inductive logic programming;using rough sets with heuristics to feature selection;the discretization of continuous attributes based on compatibility rough set and genetic algorithm;level cut conditioning approach to the necessity measure specification;four c-regression methods and classification functions and context-free fuzzy sets in data mining context.
暂无评论