References.bib

@article{GDI,
  title={The Gait Deviation Index: a new comprehensive index of gait pathology},
  author={Schwartz, Michael H and Rozumalski, Adam},
  journal={Gait \& posture},
  volume={28},
  number={3},
  pages={351--357},
  year={2008},
  publisher={Elsevier}
}

@article{GPS,
  title={The gait profile score and movement analysis profile},
  author={Baker, Richard and McGinley, Jennifer L and Schwartz, Michael H and Beynon, Sarah and Rozumalski, Adam and Graham, H Kerr and Tirosh, Oren},
  journal={Gait \& posture},
  volume={30},
  number={3},
  pages={265--269},
  year={2009},
  publisher={Elsevier}
}

@article{GGI,
  title={An index for quantifying deviations from normal gait},
  author={Schutte, LM and Narayanan, U and Stout, JL and Selber, P and Gage, JR and Schwartz, MH},
  journal={Gait \& posture},
  volume={11},
  number={1},
  pages={25--31},
  year={2000},
  publisher={Elsevier}
}

@article{mahalanobis,
  title={On the generalised distance in statistics},
  author={Mahalanobis, Prasanta Chandra},
  journal={Proceedings of the National Institute of Sciences of India, 1936},
  pages={49--55},
  year={1936}
}


@article{FG_Test,
author = {Farrar, Donald E. and Glaubner, Robert R.},
journal = {The Review of Economics and Statistics},
pages = {92-107},
title = {{Multicollinearity in Regression Analysis: The Problem Revisited}},
volume = {49},
year = {1967},
}


@book{Geometry,
  TITLE = {The Geometry of Multivariate Statistics},
  AUTHOR = {Wickens, Thomas D.},
  YEAR = {1995},
  PUBLISHER = {Psychology Press},
}

@book{GaitCycle,
  TITLE = {Clinical Biomechanics},
  AUTHOR = {Schafer, Richard C.},
  YEAR = {1987},
  PUBLISHER = {Williams & Wilkins},
}

@book{RStats,
  TITLE = {Basics of Matrix Algebra for Statistics with R},
  AUTHOR = {Fieller, Nick},
  YEAR = {2016},
  PUBLISHER = {CRC Press},
}

@book{HD_Spaces,
  TITLE = {Understanding High Dimensional Spaces},
  AUTHOR = {Skillicorn, David B.},
  YEAR = {2012},
  PUBLISHER = {Springer},
}


@inproceedings{Surprising_Behavior,
  title={On the surprising behavior of distance metrics in high dimensional space},
  author={Aggarwal, Charu C and Hinneburg, Alexander and Keim, Daniel A},
  booktitle={International conference on database theory},
  pages={420--434},
  year={2001},
  organization={Springer}
}

@incollection{PCA_Anomaly,
  title={Principal component-based anomaly detection scheme},
  author={Shyu, Mei-Ling and Chen, Shu-Ching and Sarinnapakorn, Kanoksri and Chang, LiWu},
  booktitle={Foundations and Novel Approaches in Data Mining},
  pages={311--329},
  year={2006},
  publisher={Springer}
}


@inproceedings{OutRank,
  title={OutRank: ranking outliers in high dimensional data},
  author={Muller, Emmanuel and Assent, Ira and Steinhausen, Uwe and Seidl, Thomas},
  booktitle={Data Engineering Workshop, 2008. ICDEW 2008. IEEE 24th International Conference on},
  pages={600--603},
  year={2008},
  organization={IEEE}
}

@article {Outlier_Review,
author = {Zimek, Arthur and Schubert, Erich and Kriegel, Hans-Peter},
title = {A survey on unsupervised outlier detection in high-dimensional numerical data},
journal = {Statistical Analysis and Data Mining},
volume = {5},
number = {5},
publisher = {Wiley Subscription Services, Inc., A Wiley Company},
issn = {1932-1872},
url = {http://dx.doi.org/10.1002/sam.11161},
doi = {10.1002/sam.11161},
pages = {363--387},
keywords = {curse of dimensionality, anomalies in high-dimensional data, outlier detection in high-dimensional data, approximate outlier detection, subspace outlier detection, correlation outlier detection},
year = {2012},
}

@inproceedings{Outlier_HDD,
  title={Outlier detection for high dimensional data},
  author={Aggarwal, Charu C and Yu, Philip S},
  booktitle={ACM Sigmod Record},
  volume={30},
  number={2},
  pages={37--46},
  year={2001},
  organization={ACM}
}

@Inbook{Curse_Of_Dimensionality,
  author="Verleysen, Michel
  and Fran{\c{c}}ois, Damien",
  editor="Cabestany, Joan
  and Prieto, Alberto
  and Sandoval, Francisco",
  title="The Curse of Dimensionality in Data Mining and Time Series Prediction",
  bookTitle="Computational Intelligence and Bioinspired Systems: 8th International Work-Conference on Artificial Neural Networks, IWANN 2005, Vilanova i la Geltr{\'u}, Barcelona, Spain, June 8-10, 2005. Proceedings",
  year="2005",
  publisher="Springer Berlin Heidelberg",
  address="Berlin, Heidelberg",
  pages="758--770",
  abstract="Modern data analysis tools have to work on high-dimensional data, whose components are not independently distributed. High-dimensional spaces show surprising, counter-intuitive geometrical properties that have a large influence on the performances of data analysis tools. Among these properties, the concentration of the norm phenomenon results in the fact that Euclidean norms and Gaussian kernels, both commonly used in models, become inappropriate in high-dimensional spaces. This papers presents alternative distance measures and kernels, together with geometrical methods to decrease the dimension of the space. The methodology is applied to a typical time series prediction example.",
  isbn="978-3-540-32106-4",
  doi="10.1007/11494669_93",
  url="https://doi.org/10.1007/11494669_93"
}

@article{jackson1993stopping,
  title={Stopping rules in principal components analysis: a comparison of heuristical and statistical approaches},
  author={Jackson, Donald A},
  journal={Ecology},
  volume={74},
  number={8},
  pages={2204--2214},
  year={1993},
  publisher={Wiley Online Library}
}

@article{peres2005many,
  title={How many principal components? Stopping rules for determining the number of non-trivial axes revisited},
  author={Peres-Neto, Pedro R and Jackson, Donald A and Somers, Keith M},
  journal={Computational Statistics \& Data Analysis},
  volume={49},
  number={4},
  pages={974--997},
  year={2005},
  publisher={Elsevier}
}

@article{ferre1995selection,
  title={Selection of components in principal component analysis: a comparison of methods},
  author={Ferr{\'e}, Louis},
  journal={Computational Statistics \& Data Analysis},
  volume={19},
  number={6},
  pages={669--682},
  year={1995},
  publisher={Elsevier}
}

@article{dray2008number,
  title={On the number of principal components: A test of dimensionality based on measurements of similarity between matrices},
  author={Dray, St{\'e}phane},
  journal={Computational Statistics \& Data Analysis},
  volume={52},
  number={4},
  pages={2228--2237},
  year={2008},
  publisher={Elsevier}
}

@article{guttman1954,
  title={Some necessary conditions for common-factor analysis},
  author={Guttman, Louis},
  journal={Psychometrika},
  volume={19},
  number={2},
  pages={149--161},
  year={1954},
  publisher={Springer}
}

@article{kaiser1960,
  title={The application of electronic computers to factor analysis},
  author={Kaiser, Henry F},
  journal={Educational and psychological measurement},
  volume={20},
  number={1},
  pages={141--151},
  year={1960},
  publisher={Sage Publications Sage CA: Thousand Oaks, CA}
}

@article{frontier1976brokenstick,
  title={Decrease of eigenvalues in principal component analysis-comparison with broken stick model},
  author={Frontier, S},
  journal={Journal of Experimental Marine Biology and Ecology},
  volume={25},
  number={1},
  pages={67--75},
  year={1976},
  publisher={ELSEVIER SCIENCE BV PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
}

@article{horn1965,
  title={A rationale and test for the number of factors in factor analysis},
  author={Horn, John L},
  journal={Psychometrika},
  volume={30},
  number={2},
  pages={179--185},
  year={1965},
  publisher={Springer}
}

@article{peres2003giving,
  title={Giving meaningful interpretation to ordination axes: assessing loading significance in principal component analysis},
  author={Peres-Neto, Pedro R and Jackson, Donald A and Somers, Keith M},
  journal={Ecology},
  volume={84},
  number={9},
  pages={2347--2363},
  year={2003},
  publisher={Wiley Online Library}
}


@Book{MASS_package,
    title = {Modern Applied Statistics with S},
    author = {W. N. Venables and B. D. Ripley},
    publisher = {Springer},
    edition = {Fourth},
    address = {New York},
    year = {2002},
    note = {ISBN 0-387-95457-0},
    url = {http://www.stats.ox.ac.uk/pub/MASS4},
  }
  
  
@article{johnstone2009consistency,
  title={On consistency and sparsity for principal components analysis in high dimensions},
  author={Johnstone, Iain M and Lu, Arthur Yu},
  journal={Journal of the American Statistical Association},
  volume={104},
  number={486},
  pages={682--693},
  year={2009},
  publisher={Taylor \& Francis}
}

@article{shapiro1965analysis,
  title={An analysis of variance test for normality (complete samples)},
  author={Shapiro, Samuel Sanford and Wilk, Martin B},
  journal={Biometrika},
  volume={52},
  number={3/4},
  pages={591--611},
  year={1965},
  publisher={JSTOR}
}
  
  
@article{mcginley2012single,
  title={Single-event multilevel surgery for children with cerebral palsy: a systematic review},
  author={McGinley, Jennifer L and Dobson, Fiona and Ganeshalingam, Rekha and Shore, Benjamin J and Rutz, Erich and Graham, H Kerr},
  journal={Developmental Medicine \& Child Neurology},
  volume={54},
  number={2},
  pages={117--128},
  year={2012},
  publisher={Wiley Online Library}
}

@article{thomason2011single,
  title={Single-event multilevel surgery in children with spastic diplegia: a pilot randomized controlled trial},
  author={Thomason, Pamela and Baker, Richard and Dodd, Karen and Taylor, Nicholas and Selber, Paulo and Wolfe, Rory and Graham, H Kerr},
  journal={JBJS},
  volume={93},
  number={5},
  pages={451--460},
  year={2011},
  publisher={LWW}
}

@article{molloy2010further,
  title={Further evidence of validity of the Gait Deviation Index},
  author={Molloy, M and McDowell, BC and Kerr, Claire and Cosgrove, AP},
  journal={Gait \& posture},
  volume={31},
  number={4},
  pages={479--482},
  year={2010},
  publisher={Elsevier}
}

@article{cimolin2011use,
  title={Use of the Gait Deviation Index for the assessment of gastrocnemius fascia lengthening in children with Cerebral Palsy},
  author={Cimolin, Veronica and Galli, Manuela and Vimercati, Sara Laura and Albertini, Giorgio},
  journal={Research in developmental disabilities},
  volume={32},
  number={1},
  pages={377--381},
  year={2011},
  publisher={Elsevier}
}

@article{esbjornsson2014quantifying,
  title={Quantifying gait deviations in individuals with rheumatoid arthritis using the Gait Deviation Index},
  author={Esbj{\"o}rnsson, AC and Rozumalski, A and Iversen, MD and Schwartz, MH and Wretenberg, P and Brostr{\"o}m, EW},
  journal={Scandinavian journal of rheumatology},
  volume={43},
  number={2},
  pages={124--131},
  year={2014},
  publisher={Taylor \& Francis}
}

@article{celletti2013use,
  title={Use of the Gait Profile Score for the evaluation of patients with joint hypermobility syndrome/Ehlers--Danlos syndrome hypermobility type},
  author={Celletti, Claudia and Galli, Manuela and Cimolin, Veronica and Castori, Marco and Tenore, Nunzio and Albertini, Giorgio and Camerota, Filippo},
  journal={Research in developmental disabilities},
  volume={34},
  number={11},
  pages={4280--4285},
  year={2013},
  publisher={Elsevier}
}

@article{pau2014novel,
  title={Novel characterization of gait impairments in people with multiple sclerosis by means of the gait profile score},
  author={Pau, Massimiliano and Coghe, Giancarlo and Atzeni, Claudia and Corona, Federica and Pilloni, Giuseppina and Marrosu, Maria Giovanna and Cocco, Eleonora and Galli, Manuela},
  journal={Journal of the neurological sciences},
  volume={345},
  number={1},
  pages={159--163},
  year={2014},
  publisher={Elsevier}
}
  
  
@article{filzmoser2008outlier,
  title={Outlier identification in high dimensions},
  author={Filzmoser, Peter and Maronna, Ricardo and Werner, Mark},
  journal={Computational Statistics \& Data Analysis},
  volume={52},
  number={3},
  pages={1694--1711},
  year={2008},
  publisher={Elsevier}
}

@article{de2000mahalanobis,
  title={The mahalanobis distance},
  author={De Maesschalck, Roy and Jouan-Rimbaud, Delphine and Massart, D{\'e}sir{\'e} L},
  journal={Chemometrics and intelligent laboratory systems},
  volume={50},
  number={1},
  pages={1--18},
  year={2000},
  publisher={Elsevier}
}

@Manual{RMarkdown,
  title = {rmarkdown: Dynamic Documents for R},
  author = {JJ Allaire and Joe Cheng and Yihui Xie and Jonathan McPherson and Winston Chang and Jeff Allen and Hadley Wickham and Aron Atkins and Rob Hyndman and Ruben Arslan},
  year = {2017},
  note = {R package version 1.6},
  url = {https://CRAN.R-project.org/package=rmarkdown},
}


@Manual{pca3d,
  title = {pca3d: Three Dimensional PCA Plots},
  author = {January Weiner},
  year = {2017},
  note = {R package version 0.10},
  url = {https://CRAN.R-project.org/package=pca3d},
}

@Manual{nFactors,
  title = {an R package for parallel analysis and non graphical solutions to the Cattell scree test},
  author = {Gilles Raiche},
  year = {2010},
  note = {R package version 2.3.3.},
  url = {http://CRAN.R-project.org/package=nFactors},
}

@Manual{R,
  title = {R: A Language and Environment for Statistical Computing},
  author = {{R Core Team}},
  organization = {R Foundation for Statistical Computing},
  address = {Vienna, Austria},
  year = {2013},
  url = {http://www.R-project.org/},
}
  
@Manual{RStudio, 
  title = {RStudio: Integrated Development Environment for R},
  author = {{RStudio Team}},
  organization = {RStudio, Inc.},
  address = {Boston, MA}, year = {2015},
  url = {http://www.rstudio.com/}, 
}