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Neural Computing and Applications
Published in: Neural Computing and Applications 4/2018

20-10-2017 | Original Article

Smooth statistical modeling of bivariate non-monotonic data by a three-stage LUT neural system

Authors: Simone Fiori, Nicola Fioranelli

Published in: Neural Computing and Applications | Issue 4/2018

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Abstract

The present paper introduces a new statistical data modeling algorithm based on artificial neural systems. This procedure allows abstracting from datasets by working on their probability density functions. The proposed method strives to capture the overall structure of the analyzed data, exhibits competitive computational runtimes and may be applied to non-monotonic real-world data (building on a previously developed isotonic neural modeling algorithm). An outstanding feature of the proposed method is the ability to return a smoother model compared to other modeling algorithms. Smooth models could have applications in the fields of engineering and computer science. In fact, the present research was motivated by an image contour resampling problem that arises in shape analysis. The features of the proposed algorithm are illustrated and compared to the features of existing algorithms by means of numerical tests on shape resampling.
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Appendix
Available only for authorised users
Footnotes
1
It is tacitly assumed that, while the points in the dataset \({{\mathbb {D}}}\) generally are not evenly spaced, the resampled coordinate \(\hat{x}\) is evenly spaced in \({{\mathbb {M}}}\), although such an assumption is not strictly necessary for the discussed modeling algorithm to work.
 
2
The shape contour datasets used within the present paper were drawn from the Surrey fish database described in http://​www.​ee.​surrey.​ac.​uk/​CVSSP/​demos/​css/​demo.​html. Unfortunately, these datasets are no longer available from the server. We can make them available to interested readers upon request.
 
3
The idea behind the RMSR index is as follows. Let us denote by z(x) the profile ordinate of a line parameterized by x. A completely flat (i.e., minimally rough) profile will be characterized by \({\mathrm{d}}z/{\mathrm{d}}x=0\), hence the cumulative quantity \(\int ({\mathrm{d}}z/{\mathrm{d}}x)^2{\mathrm{d}}x=0\). Conversely, the more a profile is uneven/rough, the larger \(({\mathrm{d}}z/{\mathrm{d}}x)^2\) is, the larger \(\int ({\mathrm{d}}z/{\mathrm{d}}x)^2{\mathrm{d}}x\) will result. We took a numerical approximation of this integral as a measure of roughness of a shape, approximated numerically by the sum of terms \((\hat{\xi }_i-\hat{\xi }_{i-1})^2\) and \((\hat{\eta }_i-\hat{\eta }_{i-1})^2\).
 
4
We used the MATLAB function interp1 with the syntax yh = interp1 (x,y,xh,method), where (x,y) is a dataset, yh is the result of interpolation at ‘query points’ xh, and method is either ‘linear’ or ‘spline.’
 
5
The derivative \(\kappa (s)=\theta '(s)\) represents the local curvature of the planar shape described by the orientation function \(\theta (s)\).
 
6
The above procedure takes the same syntax of the \({\hbox {MATLAB}}^{\copyright }\)’s function ‘interp1’.
 
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Metadata
Title
Smooth statistical modeling of bivariate non-monotonic data by a three-stage LUT neural system
Authors
Simone Fiori
Nicola Fioranelli
Publication date
20-10-2017
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 4/2018
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-017-3215-1

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