Abstract
Distances matrices are traditionally analyzed with statistical methods that represent distances as maps such as Metric Multidimensional Scaling (mds), Generalized Procrustes Analysis (gpa), Individual Differences Scaling (indscal), and distatis. Mds analyzes only one distance matrix at a time while gpa, indscal and distatis extract similarities between several distance matrices. However, none of these methods is predictive. Partial Least Squares Regression (plsr) predicts one matrix from another, but does not analyze distance matrices. We introduce a new statistical method called Distance-based Partial Least Squares Regression (displsr), which predicts one distance matrix from another. We illustrate displsr with data obtained from a neuroimaging experiment, which explored semantic categorization.
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References
H. Abdi, “Metric multidimensional scaling,” in Encyclopedia of Measurement and Statistics, N. J. Salkind, ed., pp. 598–605, Thousand Oaks (CA): Sage, 2007.
W. S. Torgerson, “Multidimensional scaling: I. Theory and method,” Psychometrika 17, pp. 401–419, 1952.
J. Gower and G. Dijksterhuis, Procrustes Problems, New York: Oxford University Press, 2004.
J. D. Carroll and J.-J. Chang, “Analysis of individual differences in multidimensional scaling via an n-way generalization of Eckart-Young decomposition,” Psychometrika 35, pp. 283–319, 1970.
H. Abdi, D. Valentin, A. J. O’Toole, and B. Edelman, “Distatis: The analysis of multiple distance matrices,” in Proceedings of the ieee Computer Society: International Conference on Computer Vision and Pattern Recognition, pp. 43–47, 2005.
H. Abdi, J.P. Dunlop, and L.A. Williams, “How to compute reliability estimates and display confidence and tolerance intervals for pattern classiffiers using the Bootstrap and 3-way multidimensional scaling Distatis,” in NeuroImage 17, pp. 89–95, 2009.
H. Abdi, D. Valentin, S. Chollet, and C. Chrea, “ Analyzing assessors and products in sorting tasks: DISTATIS, theory and applications,” in Food Quality and Preference, 18, pp. 627–640, 2007.
A. Krishnan, L. J. Williams, A. R. McIntosh, and H. Abdi, “Partial least squares (pls) methods for neuroimaging: A tutorial and review,” NeuroImage 56, pp. 455–475, 2011.
L.R., Tucker, “An inter-battery method of factor analysis.” Psychometrika 23, pp. 111–136, 1958.
F.L. Bookstein, P.L. Sampson, A.P. Streissguth, and H.M. Barr, “Exploting redundant measurements of dose and developmental outcome: New methods from the behavioral teratology of alcohol,” Developmental Psychology 32, pp. 404–415, 1996.
P.D. Sampson, A.P. Streissguth, H.M. Barr, and F.S.Bookstein, “Neurobehavioral effect of prenatal alcohol: Part II, partial least square analysis,” Neurotoxicology and Teratology 11, pp. 477–491.
A. Tishler, D. Dvir, A. Shenhar, and S. Lipovetsky, “Identifying critical success factors in defense development projects: A multivariate analysis,” Technological Forecasting and Social Change 51, pp. 151–171, 1996.
A. Tishler, and S. Lipovetsky, “Modelling and forecasting with robust canonical analysis: method and application,” Computers and Operations Research 27, pp. 217–232, 2000.
S. Dolédec, and D. Chessel, “Co-inertia analysis: an alernative methods for studying sepcies-environment relationships.” Fresehwater Biology 31, pp. 277–294.
H. Abdi, “Partial least squares regression and projection on latent structure regression (PLS Regression),” WIREs Computational Statistics 2, pp. 97–106, 2010.
H. Wold, “Soft modelling: The basic design and some extensions,” in Systems under indirect observation: Causality-structure-prediction Part II, K. Jöreskog and H. Wold, eds., pp. 1–54, Amsterdam: North-Holland Publishing Company, 1982.
S. Wold, M. Sjöström, and L. Eriksson, “Pls-regression: A basic tool of chemometrics,” Chemometrics and Intelligent Laboratory Systems 58, pp. 109–130, 2001.
H. Abdi, “Singular value decomposition (svd) and generalized singular value decomposition (gsvd),” in Encyclopedia of Measurement and Statistics, N. Salkind, ed., pp. 907–912, Thousand Oaks (CA): Sage, 2007.
M. Greenacre, Theory and Applications of Correspondence Analysis, Academic Press, London, 1984.
H. Yanai, K. Takeuchi, and Y. Takane, Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition, New York, Springer, 2011.
B. L. Bush and R. B. Nachbar, Jr., “Sample-distance partial least squares: pls optimized for many variables, with application to comfa,” Journal of Computer-aided Molecular Design 7, pp. 587–619, 1993.
Y. C. Martin, C. T. Lin, C. Hetti, and J. DeLazzer, “Pls analysis of distance matrices to detect nonlinear relationships between biological potency and molecular properties,” Journal of Medicinal Chemistry 38, pp. 3009–3015, 1995.
P. Legendre and M. J. Anderson, “Distance-based redundancy analysis: Testing multispecies responses in multifactorial ecological experiments,” Ecological Monographs 69, pp. 1–24, 1999.
M. A. Zapala and N. J. Schork, “Multivariate regression analysis of distance matrices for testing associations between gene expression patterns and related variables,” Proceedings of the National Academy of Sciences 103, pp. 19430–19435, 2006.
S. Rännar, F. Lindgren, P. Geladi, and S. Wold, “A pls kernel algorithm for data sets with many variables and fewer objects. Part I: Theory and algorithm,” Journal of Chemometrics 8, pp. 111–125, 1994.
A. Höskuldsson, “Pls regression methods,” Journal of Chemometrics 2, pp. 211–228, 1988.
H. Abdi, “Congruence: Congruence coefficient, R V coefficient and Mantel coefficient,” in Encyclopedia of Research Design, N. Salkind, D. D.M., and B. Frey, eds., pp. 222–229, Thousand Oaks (CA): Sage, 2010.
H. Abdi, “R V coefficient and congruence coefficient,” in Encyclopedia of Measurement and Statistics, N. Salkind, ed., pp. 849–853, Thousand Oaks (CA): Sage, 2007.
E. J. Dietz, “Permutation tests for association between two distance matrices,” Systematic Zoology 32, pp. 21–26, 1983.
J. Josse, J. Pagès, and F. Husson, “Testing the significance of the R V coefficient,” Computational Statistics & Data Analysis 53, pp. 82–91, 2008.
N. Kriegeskorte, M. Mur, and P. Bandettini, “Representational similarity analysis connecting the branches of systems neuroscience,” Frontiers in Systems Neuroscience 2, p. doi:10.3389/neuro.06.004.2008, 2008.
R. Kiani, H. Esteky, K. Mipour, and K. Tanaka, “Object category structure in response patterns of neuronal population in monkey inferior temporal cortex,” Journal of Neurophysiology 97, pp. 4296–4309, 2007.
J. Daugman, “How iris recognition works,” I eee Transactions on Circuits and Systems for Video Technology 14, pp. 21–30, 2004.
G. Orban, D. van Essen, and W. Vanduffel, “Comparative mapping of higher visual areas in monkeys and humans,” Trends in Cognitive Sciences 8, pp. 315–324, 2004.
B. Efron and R. Tibshirani, “Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy,” Statistical Science 1, pp. 54–77, 1986.
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Krishnan, A., Kriegeskorte, N., Abdi, H. (2013). Distance-Based Partial Least Squares Analysis. In: Abdi, H., Chin, W., Esposito Vinzi, V., Russolillo, G., Trinchera, L. (eds) New Perspectives in Partial Least Squares and Related Methods. Springer Proceedings in Mathematics & Statistics, vol 56. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8283-3_8
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DOI: https://doi.org/10.1007/978-1-4614-8283-3_8
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