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Ordinal analysis by transformations
2009
Annals of Pure and Applied Logic
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The technique of using infinitary rules in an ordinal analysis has been one of the most productive developments in ordinal analysis. ...
We apply this to a system of inductive definitions with at least the strength of a recursively inaccessible ordinal. ...
Introduction Infinitary inference rules have been a key tool in ordinal analysis since their introduction by Schütte [14] . ...
doi:10.1016/j.apal.2008.09.011
fatcat:4psauotquvag5ofq74jpazfcwe
Evaluating the Predictive Power of Ordination Methods in Ecological Context
2018
Mathematics
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The combination of methods and data transformations results in 96 alternative solutions for any one data set. These are compared by a graphical display, that is, an ordination of ordinations. ...
The results from two real-world data sets indicate that some ordination methods greatly vary with data transformation. Scores close to a binary scale perform best in almost all ordination methods. ...
Van der Maarel [20] suggested replacing these by a rank scale to simplify transformation and subsequent analysis. ...
doi:10.3390/math6120295
fatcat:rruzw4v6mjhijjgpsam42ospra
Ecologically meaningful transformations for ordination of species data
2001
Oecologia
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This paper examines how to obtain species biplots in unconstrained or constrained ordination without resorting to the Euclidean distance [used in principalcomponent analysis (PCA) and redundancy analysis ...
To achieve this goal, transformations are proposed for species data tables. ...
This research was supported by NSERC grant number OGP7738 to P. Legendre. ...
doi:10.1007/s004420100716
pmid:28547606
fatcat:ras4onns3bhond5jzv4mpv3lf4
Ordinal analysis of time series
2005
Physica A: Statistical Mechanics and its Applications
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The permutation entropy only provides one detail of the ordinal structure of a time series. Here we present a method for extracting the whole ordinal information. ...
In order to develop fast and robust methods for extracting qualitative information from non-linear time series, Bandt and Pompe have proposed to consider time series from the pure ordinal viewpoint. ...
As a base for data analysis on the ordinal level, we have introduced the ordinal transformation. ...
doi:10.1016/j.physa.2005.05.022
fatcat:omcfxpe2onc77bdu2unpzawtfm
Economic explanation, ordinality and the adequacy of analytic specification
2004
Journal of Economic Methodology
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by dint of the ordinality itself. ...
In the case of the efficiency wage model, the only usable transformations of the ordinal effort scale are those which are multiples of each other. ...
by the ordinally equivalent transformed variable T(y), results in the structure h(T(y)) = -λ -2y which has no maximum anywhere. ...
doi:10.1080/1350178042000280621
fatcat:e6wdwqgkhjbmbj2c3zpnuvbkqe
Sensitivity analysis for plane orientation in three-dimensional cephalometric analysis based on superimposition of serial cone beam computed tomography images
2010
Dentomaxillofacial Radiology
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Evaluation of the method to transform the co-ordinate system was first done by comparing interlandmark distances before and after transformations, giving errors in lengths in the order of 10-14% (software ...
A sensitivity evaluation was performed by adding 0.25 mm, 0.5 mm and 1 mm error in one axis of the ELSA. ...
Co-ordinate system transformations were performed in two steps. The co-ordinate system was constructed using two planes defined by anatomical landmarks. ...
doi:10.1259/dmfr/17319459
pmid:20841457
pmcid:PMC3520184
fatcat:i3onldzxvrc53cal733f2yryja
On selecting an appropriate multivariate analysis
2006
Canadian Journal of Plant Science
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analysis of biological data. ...
On selecting an appropriate multivariate analysis. Can. J. Plant Sci. 86: 663-676. ...
ACKNOWLEDGEMENTS This research was supported by the Natural Sciences and Engineering Research Council. ...
doi:10.4141/p05-164
fatcat:vxxx2gcyi5aipmyplwzhfgeddq
Privacy Preserving Data Mining for Ordinal Data using Correlation Based Transformation Strategy (CBTS)
2016
Indian Journal of Science and Technology
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In the proposed work, Correlation Based Transformation Strategy for Privacy Preserving Data Mining is used for ordinal data. ...
Methods/ Statistical Analysis: Though privacy is achieved by hiding the sensitive or private data, it will affect the data mining algorithms in knowledge extraction, so an effective method or strategy ...
Keywords: Correlation Analysis, Nominal Data, Ordinal Data, Privacy Preserving Data Mining, Transformation Strategy Privacy Preserving Data Mining for Ordinal Data using Correlation Based Transformation ...
doi:10.17485/ijst/2016/v9i47/107360
fatcat:abvvcyawkzhnvfe3qzv4f4ttua
Page 82 of American Society of Civil Engineers. Collected Journals Vol. 4, Issue 1
[page]
1999
American Society of Civil Engineers. Collected Journals
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direct runoff; QAt) = ordinate of computed direct runoff at r; T = base period; t = time step; UH(t) = ordinate of unit hydrograph at f; X(t) = ordinate of effective rainfall at ¢ interval; X(z"') = Z-transform ...
The available studies lack, in terms of application, use of the Z-transform technique in storm-runoff analysis, and it is from this perspective this study has been undertaken. ...
A Comparison of Nonmetric Multidimensional Scaling, Principal Components and Reciprocal Averaging for the Ordination of Simulated Coenoclines, and Coenoplanes
1977
Ecology
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The use of nonmetric multidimensional scaling as an ordination method has been studied by the use of simulated coenoclines and coenoplanes. ...
The use of a log transformation of the species values had a marginal effect while the use of a 'Manhattan' distance metric in ordination space produced inferior results. 552 M. ...
The latter method has been used often in the geological sciences for Q analysis (Jdreskog et al.
1976). In both cases, a log transform of the data was made before analysis. ...
doi:10.2307/1939004
fatcat:6vgswlvvrfa55d6c3jd6ffthiq
Page 366 of Behavior Research Methods Vol. 10, Issue 3
[page]
1978
Behavior Research Methods
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366 ANDERSON
Only ordinal or directional relations among the response data may be used in model analysis. The advantage of such tests is that they require only an ordinal or monotone response scale. ...
Within the functional measurement approach, however, a valid error theory for ordinal analysis has been developed. ...
Topics in constrained and unconstrained ordination
2014
Plant Ecology
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We defend detrended correspondence analysis by theoretical arguments and by reanalysing data that previously gave bad results. ...
We show by examples that constrained ordination can yield more informative views on effects of interest compared to unconstrained ordination (where such effects can be invisible) and show how constrained ...
Acknowledgements This paper benefitted from comments by David Warton and Pierre Legendre. The contribution of PS was funded by the Center of Excellence PLADIAS, 14-36079G, Czech Science Foundation. ...
doi:10.1007/s11258-014-0356-5
fatcat:at2c7xeiinarlpvzlzwgke4vda
Ordinal spectrum: a frequency domain characterization of complex time series
[article]
2020
arXiv
pre-print
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Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to characterise the complexity of a time series. ...
Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. ...
In fact, the power spectrum estimated from chaotic sequences can be replicated by a monotonic nonlinear transformation of linearly filtered noise [12] [13] [14] . ...
arXiv:2009.02547v1
fatcat:olcquiaqengthah7iitgu4kenm
From Classical to Canonical Ordination
[chapter]
2012
Developments in Paleoenvironmental Research
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= lines
Canonical
ordination triplot
Daniel Borcard
François Gillet
Pierre Legendre
Principal component analysis (PCA)
Principles of canonical analysis ...
Apply log( y + c ) transformation • Make community composition data suitable for Euclidean-based ordination methods (PCA, RDA) ! ...
doi:10.1007/978-94-007-2745-8_8
fatcat:dlkrkggjbfgvtkmiw7lbwnqkqa
Otolith shape feature extraction oriented to automatic classification with open distributed data
2005
Marine and Freshwater Research
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A new method derived from the Karhunen-Loève transformation was proposed as the main procedure for standardising the codification of the otolith contours. ...
Two types of codification methods (Cartesian and Polar) were evaluated, and the limitations (loss of information) and the benefits (invariance to affine transformations) associated with each method were ...
and Technology and by the IBACS European project. ...
doi:10.1071/mf04163
fatcat:eacetb5ryjgtfifxmfsvr4wkh4
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