Julia library for elastic functional data analysis
A Julia package for functional data analysis using the square root slope framework and curves using the square root velocity framework which performs pair-wise and group-wise alignment as well as modeling using functional component analysis and regression.
This package can be installed using and is only currently supported on linux
(v1.0) add ElasticFDA
This package relies on two c/cpp optimization routines which will either compile with icc or g++. One of the libraries relies LAPACK and BLAS. The makefile will detect if icc is installed and use it, otherwise it will default to g++. If icc is detected it will use MKL as the BLAS and LAPACK implementation. Otherwise OpenBLAS is used/required.
Tucker, J. D. 2014, Functional Component Analysis and Regression using Elastic Methods. Ph.D. Thesis, Florida State University.
Robinson, D. T. 2012, Function Data Analysis and Partial Shape Matching in the Square Root Velocity Framework. Ph.D. Thesis, Florida State University.
Huang, W. 2014, Optimization Algorithms on Riemannian Manifolds with Applications. Ph.D. Thesis, Florida State University.
Srivastava, A., Wu, W., Kurtek, S., Klassen, E. and Marron, J. S. (2011). Registration of Functional Data Using Fisher-Rao Metric. arXiv:1103.3817v2 [math.ST].
Tucker, J. D., Wu, W. and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics and Data Analysis 61, 50-66.
J. D. Tucker, W. Wu, and A. Srivastava, ``Phase-Amplitude Separation of Proteomics Data Using Extended Fisher-Rao Metric," Electronic Journal of Statistics, Vol 8, no. 2. pp 1724-1733, 2014.
J. D. Tucker, W. Wu, and A. Srivastava, "Analysis of signals under compositional noise With applications to SONAR data," IEEE Journal of Oceanic Engineering, Vol 29, no. 2. pp 318-330, Apr 2014.
S. Kurtek, A. Srivastava, and W. Wu. Signal estimation under random time-warpings and nonlinear signal alignment. In Proceedings of Neural Information Processing Systems (NIPS), 2011.
Joshi, S.H., Srivastava, A., Klassen, E. and Jermyn, I. (2007). A Novel Representation for Computing Geodesics Between n-Dimensional Elastic Curves. IEEE Conference on computer Vision and Pattern Recognition (CVPR), Minneapolis, MN.
Srivastava, A., Klassen, E., Joshi, S., Jermyn, I., (2011). Shape analysis of elastic curves in euclidean spaces. Pattern Analysis and Machine Intelligence, IEEE Transactions on 33 (7), 1415-1428.
Wen Huang, Kyle A. Gallivan, Anuj Srivastava, Pierre-Antoine Absil. "Riemannian Optimization for Elastic Shape Analysis", Short version, The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014).
Q. Xie, S. Kurtek, E. Klassen, G. E. Christensen and A. Srivastava. Metric-based pairwise and multiple image registration. IEEE European Conference on Computer Vision (ECCV), September, 2014
Cheng, W., Dryden, I. L., & Huang, X. (2016). Bayesian registration of functions and curves. Bayesian Analysis, 11(2), 447–475.
Y. Lu, R. Herbei and S. Kurtek (2017). "Bayesian Registration of Functions with a Gaussian Process Prior." Journal of Computational and Graphical Statistics: in press: 1-34