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Ordinal analysis by transformations

Henry Towsner
2009 Annals of Pure and Applied Logic  
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

Otto Wildi
2018 Mathematics  
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

Pierre Legendre, Eugene D. Gallagher
2001 Oecologia  
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

K. Keller, M. Sinn
2005 Physica A: Statistical Mechanics and its Applications  
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

Donald W. Katzner, Peter Skott
2004 Journal of Economic Methodology  
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

M O Lagravère, P W Major, J Carey
2010 Dentomaxillofacial Radiology  
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

N. C. Kenkel
2006 Canadian Journal of Plant Science  
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)

N. P. Nethravathi, Prasanth G. Rao, Chaitra C. Vaidya, S. Geethanjali, P. Madhura, K. Neha Nandan, P. Deepa Shenoy, M. Indiramma, K. R. Venugopal
2016 Indian Journal of Science and Technology  
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  
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

M. J. R. Fasham
1977 Ecology  
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  
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

Cajo J. F. ter Braak, Petr Šmilauer
2014 Plant Ecology  
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]

Mario Chavez, Johann H. Martinez
2020 arXiv   pre-print
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]

Pierre Legendre, H. John B. Birks
2012 Developments in Paleoenvironmental Research  
= 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

J. Piera, V. Parisi-Baradad, E. García-Ladona, A. Lombarte, L. Recasens, J. Cabestany
2005 Marine and Freshwater Research  
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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