Short note: Method of Dimensionality Reduction for compressible viscoelastic media. I. Frictionless normal contact of a Kelvin-Voigt solid

2017 ◽  
Vol 98 (2) ◽  
pp. 306-311 ◽  
Author(s):  
E. Willert ◽  
V. L. Popov
Keyword(s):  
Dimensionality Reduction ◽  
Short Note ◽  
Normal Contact ◽  
Viscoelastic Media ◽  
Method Of Dimensionality Reduction

scholarly journals A Review of the Method of Dimensionality Reduction in Contact Mechanics: Applications for Structural Damping, Wear and Adhesion

2015 ◽  
Author(s):  
V.L. Popov ◽  
M. Heß ◽  
M. Popov
Keyword(s):  
Dimensionality Reduction ◽  
Three Dimensional ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Tangential Direction ◽  
Fretting Wear ◽  
Normal Contact ◽  
Method Of Dimensionality Reduction ◽  
Frictional Damping ◽  
Arbitrary Axis

In the method of dimensionality reduction (MDR), contacts of three-dimensional bodies are mapped to the contact problem with a one-dimensional elastic or viscoelastic foundation. This is valid for the normal contact, the tangential contact and the normal contact of viscoelastic bodies. For the above classes of contact problems, several examples are considered and discussed in detail. This includes: (a) Fretting wear for arbitrary histories of loading (for simultaneous oscillations both in normal and horizontal directions); (b) Frictional damping under the influence of oscillations in normal and tangential direction as well as normal and torsional loading; (c) Adhesion of bodies of arbitrary axis-symmetric shape with extension to the adhesive contact of elastomers.

A Simplified Version of Persson's Multiscale Theory for Rubber Friction Due to Viscoelastic Losses

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
M. Ciavarella
Keyword(s):  
Dimensionality Reduction ◽  
Free Parameter ◽  
Fractal Dimensions ◽  
Scale Model ◽  
Entire Spectrum ◽  
Method Of Dimensionality Reduction ◽  
Single Scale ◽  
Rubber Friction ◽  
Exact Calculations ◽  
Best Fit

We show that the full multiscale Persson's theory for rubber friction due to viscoelastic losses can be approximated extremely closely to simpler models, like that suggested by Persson in 1998 and similarly by Popov in his 2010 book (but notice that we do not make any use of the so-called “Method of Dimensionality Reduction” (MDR)), so it is essentially a single scale model at the so-called large wavevector cutoff. The dependence on the entire spectrum of roughness is therefore only confusing, at least for range of fractal dimensions of interest D≃2.2, and we confirm this with actual exact calculations and reference to recent data of Lorenz et al. Moreover, we discuss the critical assumption of the choice of the “free parameter” best fit truncation cutoff.

scholarly journals A method of dimensionality reduction by selection of components in principal component analysis for text classification

Filomat ◽  
2018 ◽  
Vol 32 (5) ◽  
pp. 1499-1506 ◽  
Author(s):  
Yangwu Zhang ◽  
Guohe Li ◽  
Heng Zong
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Dimensionality Reduction ◽  
Principal Components Analysis ◽  
Text Classification ◽  
Principal Components ◽  
Principal Component ◽  
Method Of Dimensionality Reduction ◽  
Components Analysis ◽  
Selection Of

Dimensionality reduction, including feature extraction and selection, is one of the key points for text classification. In this paper, we propose a mixed method of dimensionality reduction constructed by principal components analysis and the selection of components. Principal components analysis is a method of feature extraction. Not all of the components in principal component analysis contribute to classification, because PCA objective is not a form of discriminant analysis (see, e.g. Jolliffe, 2002). In this context, we present a function of components selection, which returns the useful components for classification by the indicators of the performances on the different subsets of the components. Compared to traditional methods of feature selection, SVM classifiers trained on selected components show improved classification performance and a reduction in computational overhead.

Text Categorisation Through Dimensionality Reduction Using Wavelet Transform

2020 ◽  
Vol 19 (04) ◽  
pp. 2050039
Author(s):  
Jorge Chamorro-Padial ◽  
Rosa Rodríguez-Sánchez
Keyword(s):  
Wavelet Transform ◽  
Dimensionality Reduction ◽  
Text Classification ◽  
High Energy ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Vertical Orientation ◽  
Method Of Dimensionality Reduction ◽  
Horizontal Orientation ◽  
Relevant Level

This paper proposes a new method of dimensionality reduction when performing Text Classification, by applying the discrete wavelet transform to the document-term frequencies matrix. We analyse the features provided by the wavelet coefficients from the different orientations: (1) The high energy coefficients in the horizontal orientation correspond to relevant terms in a single document. (2) The high energy coefficients in the vertical orientation correspond to relevant terms for a single document, but not for the others. (3) The high energy coefficients in the diagonal orientation correspond to relevant terms in a document in comparison to other terms. If we filter using the wavelet coefficients and fulfil these three conditions simultaneously, we can obtain a reduced vocabulary of the corpus, with less dimensions than in the original one. To test the success of the reduced vocabulary, we recoded the corpus with the new reduced vocabulary and we obtained a statistically relevant level of accuracy for document classification.

Sign in / Sign up

Export Citation Format

Share Document