Functional Additive Models on Manifolds of Planar Shapes and Forms

References

• Adams, D., Rohlf, F., and Slice, D. (2013), “A Field Comes of Age: Geometric Morphometrics in the 21st Century,” Hystrix, the Italian Journal of Mammalogy, 24, 7–14.
   Web of Science ®Google Scholar
• Backenroth, D., Goldsmith, J., Harran, M. D., Cortes, J. C., Krakauer, J. W., and Kitago, T. (2018), “Modeling Motor Learning Using Heteroscedastic Functional Principal Components Analysis,” Journal of the American Statistical Association, 113, 1003–1015.
   PubMed Web of Science ®Google Scholar
• Baranyi, P., Yam, Y., and Várlaki, P. (2013), Tensor Product Model Transformation in Polytopic Model-based Control, Boca Raton, FL: CRC Press.
   Google Scholar
• Bonhomme, V., Picq, S., Gaucherel, C., and Claude, J. (2014), “Momocs: Outline Analysis using R,” Journal of Statistical Software, 56, 1–24.
   Web of Science ®Google Scholar
• Brockhaus, S., Melcher, M., Leisch, F., and Greven, S. (2017), “Boosting Flexible Functional Regression Models with a High Number of Functional Historical Effects,” Statistics and Computing, 27, 913–926.
   Web of Science ®Google Scholar
• Brockhaus, S., Rügamer, D., and Greven, S. (2020), “Boosting Functional Regression Models with FDboost,” Journal of Statistical Software, 94, 1–50.
   Web of Science ®Google Scholar
• Brockhaus, S., Scheipl, F., and Greven, S. (2015), “The Functional Linear Array Model,” Statistical Modelling, 15, 279–300.
   Web of Science ®Google Scholar
• Bühlmann, P., and Yu, B. (2003), “Boosting with the L2 Loss: Regression and Classification,” Journal of the American Statistical Association, 98, 324–339.
   Web of Science ®Google Scholar
• Clutton-Brock, J., Dennis-Bryan, K., Armitage, P. L., and Jewell, P. A. (1990), “Osteology of the Soay Sheep,” Bulletin of the British Museum (Natural History), 56, 1–56.
   Google Scholar
• Cornea, E., Zhu, H., Kim, P., Ibrahim, J. G., and the Alzheimer’s Disease Neuroimaging Initiative. (2017), “Regression Models on Riemannian Symmetric Spaces,” Journal of the Royal Statistical Society, Series B, 79, 463–482.
   Google Scholar
• Davis, B. C., Fletcher, P. T., Bullitt, E., and Joshi, S. (2010), “Population Shape Regression from Random Design Data,” International Journal of Computer Vision, 90, 255–266.
   Web of Science ®Google Scholar
• Dryden, I. L., and Mardia, K. V. (2016), Statistical Shape Analysis: With Applications in R, Chichjester: Wiley.
   Google Scholar
• Ferraty, F., Goia, A., Salinelli, E., and Vieu, P. (2011), “Recent Advances on Functional Additive Regression,” in Recent Advances in Functional Data Analysis and Related Topics, ed. F. Ferraty, pp. 97–102, Heidelberg: Springer.
   Google Scholar
• Fletcher, P. T. (2013), “Geodesic Regression and the Theory of Least Squares on Riemannian Manifolds,” International Journal of Computer Vision, 105, 171–185.
   Web of Science ®Google Scholar
• Greven, S., and Scheipl, F. (2017), “A General Framework for Functional Regression Modelling,” (with discussion and rejoinder), Statistical Modelling, 17(1–2), 1–35 and 100–115.
   Web of Science ®Google Scholar
• Happ, C., and Greven, S. (2018), “Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains,” Journal of the American Statistical Association, 113, 649–659.
   Web of Science ®Google Scholar
• Hinkle, J., Fletcher, P. T., and Joshi, S. (2014), “Intrinsic Polynomials for Regression on Riemannian Manifolds,” Journal of Mathematical Imaging and Vision, 50, 32–52.
   Web of Science ®Google Scholar
• Hofner, B., Hothorn, T., Kneib, T., and Schmid, M. (2011), “A Framework for Unbiased Model Selection Based on Boosting,” Journal of Computational and Graphical Statistics, 20, 956–971.
   Web of Science ®Google Scholar
• Hofner, B., Kneib, T., and Hothorn, T. (2016), “A Unified Framework of Constrained Regression,” Statistics and Computing, 26, 1–14.
   Web of Science ®Google Scholar
• Hong, Y., Singh, N., Kwitt, R., and Niethammer, M. (2014), “Time-Warped Geodesic Regression,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 105–112, Springer.
   Google Scholar
• Hothorn, T., Bühlmann, P., Kneib, T., Schmid, M., and Hofner, B. (2010), “Model-based Boosting 2.0,” Journal of Machine Learning Research, 11, 2109–2113.
   Web of Science ®Google Scholar
• Huckemann, S., Hotz, T., and Munk, A. (2010), “Intrinsic MANOVA for Riemannian Manifolds with an Application to Kendall’s Space of Planar Shapes,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 32, 593–603.
   PubMed Web of Science ®Google Scholar
• Jeon, J. M., and Park, B. U. (2020), “Additive Regression with Hilbertian Responses,” The Annals of Statistics, 48, 2671–2697.
   Web of Science ®Google Scholar
• Jeon, J. M., Lee, Y. K., Mammen, E., and Park, B. U. (2022), “Locally Polynomial Hilbertian Additive Regression,” Bernoulli, 28, 2034–2066.
   Web of Science ®Google Scholar
• Jeon, J. M., Park, B. U., and Van Keilegom, I. (2021), “Additive Regression for Non-Euclidean Responses and Predictors,” The Annals of Statistics, 49, 2611–2641.
   Web of Science ®Google Scholar
• Jupp, P. E., and Kent, J. T. (1987), “Fitting Smooth Paths to Spherical Data,” Journal of the Royal Statistical Society, Series C, 36, 34–46.
   Web of Science ®Google Scholar
• Karcher, H. (1977), “Riemannian Center of Mass and Mollifier Smoothing,” Communications on Pure and Applied Mathematics, 30, 509–541.
   Web of Science ®Google Scholar
• Kendall, D. G., Barden, D., Carne, T. K., and Le, H. (1999), Shape and Shape Theory (Vol. 500), Chichester: Wiley.
   Google Scholar
• Kent, J. T., Mardia, K. V., Morris, R. J., and Aykroyd, R. G. (2001), “Functional Models of Growth for Landmark Data,” in Proceedings in Functional and Spatial Data Analysis, 109115.
   Google Scholar
• Kim, H. J., Adluru, N., Collins, M. D., Chung, M. K., Bendlin, B. B., Johnson, S. C., Davidson, R. J., and Singh, V. (2014), “Multivariate General Linear Models (mglm) on Riemannian Manifolds with Applications to Statistical Analysis of Diffusion Weighted Images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2705–2712.
   Google Scholar
• Kim, H. J., Adluru, N., Suri, H., Vemuri, B. C., Johnson, S. C., and Singh, V. (2017), “Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 5777–5786.
   Google Scholar
• Klingenberg, W. (1995), Riemannian Geometry, Berlin: de Gruyter.
   Google Scholar
• Kneib, T., Hothorn, T., and Tutz, G. (2009), “Variable Selection and Model Choice in Geoadditive Regression Models,” Biometrics, 65, 626–634. DOI: 10.1111/j.1541-0420.2008.01112.x.
   PubMed Web of Science ®Google Scholar
• Kume, A., Dryden, I. L., and Le, H. (2007), “Shape-Space Smoothing Splines for Planar Landmark Data,” Biometrika, 94, 513–528.
   Web of Science ®Google Scholar
• Lay, D. M. (1967), “A Study of the Mammals of Iran: Resulting from the Street Expedition of 1962-63,” in Fieldiana: Zoology 54. Field Museum of Natural History.
   Google Scholar
• Li, Y., and Ruppert, D. (2008), “On the Asymptotics of Penalized Splines,” Biometrika, 95, 415–436.
   Web of Science ®Google Scholar
• Lin, L., St. Thomas, B., Zhu, H., and Dunson, D. B. (2017), “Extrinsic Local Regression on Manifold-Valued Data,” Journal of the American Statistical Association, 112, 1261–1273. DOI: 10.1080/01621459.2016.1208615.
   PubMed Web of Science ®Google Scholar
• Lin, Z., Müller, H.-G., and Park, B. U. (2020), “Additive Models for Symmetric Positive-Definite Matrices, Riemannian Manifolds and Lie Groups,” arXiv preprint arXiv:2009.08789.
   Google Scholar
• Lutz, R. W., and Bühlmann, P. (2006), “Boosting for High-Multivariate Responses in High-Dimensional Linear Regression,” Statistica Sinica, 16, 471–494.
   Web of Science ®Google Scholar
• Mallasto, A., and Feragen, A. (2018), “Wrapped Gaussian Process Regression on Riemannian Manifolds,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5580–5588.
   Google Scholar
• Mayr, A., Binder, H., Gefeller, O., and Schmid, M. (2014), “The Evolution of Boosting Algorithms,” Methods of Information in Medicine, 53, 419–427. DOI: 10.3414/ME13-01-0122.
   PubMed Web of Science ®Google Scholar
• Meyer, M. J., Coull, B. A., Versace, F., Cinciripini, P., and Morris, J. S. (2015), “Bayesian Function-on-Function Regression for Multilevel Functional Data,” Biometrics, 71, 563–574. DOI: 10.1111/biom.12299.
   PubMed Web of Science ®Google Scholar
• Morris, J. S. (2015), “Functional Regression,” Annual Review of Statistics and its Applications, 2, 321–359.
   Web of Science ®Google Scholar
• Morris, J. S., and Carroll, R. J. (2006), “Wavelet-based Functional Mixed Models,” Journal of the Royal Statistical Society, Series B, 68, 179–199. DOI: 10.1111/j.1467-9868.2006.00539.x.
   Google Scholar
• Müller, H.-G., and Yao, F. (2008), “Functional Additive Models,” Journal of the American Statistical Association, 103, 1534–1544.
   Google Scholar
• Muralidharan, P., and Fletcher, P. T. (2012), “Sasaki Metrics for Analysis of Longitudinal Data on Manifolds,” in 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp. 1027–1034, IEEE.
   Google Scholar
• Olsen, N. L., Markussen, B., and Raket, L. L. (2018), “Simultaneous Inference for Misaligned Multivariate Functional Data,” Journal of the Royal Statistical Society, Series C, 67, 1147–1176.
   Google Scholar
• Pennec, X. (2006), “Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements,” Journal of Mathematical Imaging and Vision, 25, 127–154.
   Web of Science ®Google Scholar
• Petersen, A., and Müller, H.-G. (2019), “Fréchet Regression for Random Objects with Euclidean Predictors,” The Annals of Statistics, 47, 691–719.
   Web of Science ®Google Scholar
• Pigoli, D., Menafoglio, A., and Secchi, P. (2016), “Kriging Prediction for Manifold-Valued Random Fields,” Journal of Multivariate Analysis, 145, 117–131.
   Web of Science ®Google Scholar
• Pöllath, N., Schafberg, R., and Peters, J. (2019), “Astragalar Morphology: Approaching the Cultural Trajectories of Wild and Domestic Sheep Applying Geometric Morphometrics,” Journal of Archaeological Science: Reports, 23, 810–821.
   Google Scholar
• R Core Team (2018), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, New York: Springer.
   Google Scholar
• Rosen, O., and Thompson, W. K. (2009), “A Bayesian Regression Model for Multivariate Functional Data,” Computational Statistics & Data Analysis, 53, 3773–3786. DOI: 10.1016/j.csda.2009.03.026.
   PubMed Web of Science ®Google Scholar
• Schafberg, R., and Wussow, J. (2010), “Julius Kühn. Das Lebenswerk eines agrarwissenschaftlichen Visionärs,” Züchtungskunde, 82, 468–484.
   Google Scholar
• Schaffer, S. A. (2021), “Cytoskeletal Dynamics in Confined Cell Migration: Experiment and Modelling,” PhD thesis, LMU Munich. DOI: 10.5282/edoc.28480.
   Google Scholar
• Scheipl, F., Staicu, A.-M., and Greven, S. (2015), “Functional Additive Mixed Models,” Journal of Computational and Graphical Statistics, 24, 477–501. DOI: 10.1080/10618600.2014.901914.
   PubMed Web of Science ®Google Scholar
• Schiratti, J.-B., Allassonnière, S., Colliot, O., and Durrleman, S. (2017), “A Bayesian Mixed-Effects Model to Learn Trajectories of Changes from Repeated Manifold-Valued Observations,” The Journal of Machine Learning Research, 18, 4840–4872.
   Web of Science ®Google Scholar
• Shi, X., Styner, M., Lieberman, J., Ibrahim, J. G., Lin, W., and Zhu, H. (2009), “Intrinsic Regression Models for Manifold-Valued Data,” in International Conference on Medical Image Computing and Computer-Assisted Intervention, pp. 192–199, Springer.
   Google Scholar
• Srivastava, A., and Klassen, E. P. (2016), Functional and Shape Data Analysis, New York: Springer-Verlag.
   Google Scholar
• Stöcker, A., Brockhaus, S., Schaffer, S. A., Bronk, B. v., Opitz, M., and Greven, S. (2021), “Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition,” Statistical Modelling, 21, 385–404.
   Web of Science ®Google Scholar
• Stöcker, A., Pfeuffer, M., Steyer, L., and Greven, S. (2022), “Elastic Full Procrustes Analysis of Plane Curves via Hermitian Covariance Smoothing.” DOI: 10.48550/arXiv.2203.10522.
   Google Scholar
• Thüroff, F., Goychuk, A., Reiter, M., and Frey, E. (2019), “Bridging the Gap between Single-Cell Migration and Collective Dynamics,” eLife, 8, e46842.
   PubMed Web of Science ®Google Scholar
• Volkmann, A., Stöcker, A., Scheipl, F., and Greven, S. (2021), “Multivariate Functional Additive Mixed Models,” Statistical Modelling. DOI: 10.1177/1471082X211056158.
   Web of Science ®Google Scholar
• Wood, S. N., Pya, N., and Säfken, B. (2016), “Smoothing Parameter and Model Selection for General Smooth Models,” Journal of the American Statistical Association, 111, 1548–1563.
   Web of Science ®Google Scholar
• Yao, F., Müller, H., and Wang, J. (2005), “Functional Data Analysis for Sparse Longitudinal Data,” Journal of the American Statistical Association, 100, 577–590.
   Web of Science ®Google Scholar
• Zeder, M. A. (2006), “Reconciling Rates of Long Bone Fusion and Tooth Eruption and Wear in Sheep (Ovis) and Goat (Capra),” Recent Advances in Ageing and Sexing Animal Bones, 9, 87–118.
   Google Scholar
• Zhu, H., Chen, Y., Ibrahim, J. G., Li, Y., Hall, C., and Lin, W. (2009), “Intrinsic Regression Models for Positive-Definite Matrices with Applications to Diffusion Tensor Imaging,” Journal of the American Statistical Association, 104, 1203–1212.
   PubMed Web of Science ®Google Scholar
• Zhu, H., Li, R., and Kong, L. (2012), “Multivariate Varying Coefficient Model for Functional Responses,” Annals of Statistics, 40, 2634–2666.
   PubMed Web of Science ®Google Scholar
• Zhu, H., Morris, J. S., Wei, F., and Cox, D. D. (2017), “Multivariate Functional Response Regression, with Application to Fluorescence Spectroscopy in a Cervical Pre-cancer Study,” Computational Statistics and Data Analysis, 111, 88–101.
   PubMed Web of Science ®Google Scholar