# Welcome to fdasrsf’s documentation!¶

A python 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.

- User Guide
- Functional Alignment
- Functional Principal Component Analysis
- Elastic Functional Boxplots
- Functional Principal Least Squares
- Elastic Regression
- Elastic Principal Component Regression
- Elastic GLM Regression
- Elastic Functional Tolerance Bounds
- Elastic Functional Clustering
- Elastic Image Warping
- Curve Registration
- SRVF Geodesic Computation
- Utility Functions
- Curve Functions
- UMAP EFDA Metrics

# References¶

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.

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.

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.

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).

Cheng, W., Dryden, I. L., and Huang, X. (2016). Bayesian registration of functions and curves. Bayesian Analysis, 11(2), 447-475.

W. Xie, S. Kurtek, K. Bharath, and Y. Sun, A geometric approach to visualization of variability in functional data, Journal of American Statistical Association 112 (2017), pp. 979-993.

Lu, Y., R. Herbei, and S. Kurtek, 2017: Bayesian registration of functions with a Gaussian process prior. Journal of Computational and Graphical Statistics, 26, no. 4, 894–904.

Lee, S. and S. Jung, 2017: Combined analysis of amplitude and phase variations in functional data. arXiv:1603.01775 [stat.ME], 1–21.

J. D. Tucker, J. R. Lewis, and A. Srivastava, “Elastic Functional Principal Component Regression,” Statistical Analysis and Data Mining, vol. 12, no. 2, pp. 101-115, 2019.

J. D. Tucker, J. R. Lewis, C. King, and S. Kurtek, “A Geometric Approach for Computing Tolerance Bounds for Elastic Functional Data,” Journal of Applied Statistics, 10.1080/02664763.2019.1645818, 2019.

T. Harris, J. D. Tucker, B. Li, and L. Shand, “Elastic depths for detecting shape anomalies in functional data,” Technometrics, 10.1080/00401706.2020.1811156, 2020.

M. K. Ahn, J. D. Tucker, W. Wu, and A. Srivastava. “Regression Models Using Shapes of Functions as Predictors” Computational Statistics and Data Analysis, 10.1016/j.csda.2020.107017, 2020.

J. D. Tucker, L. Shand, and K. Chowdhary. “Multimodal Bayesian Registration of Noisy Functions using Hamiltonian Monte Carlo”, Computational Statistics and Data Analysis, accepted, 2021.

X. Zhang, S. Kurtek, O. Chkrebtii, and J. D. Tucker, “Elastic k-means clustering of functional data for posterior exploration, with an application to inference on acute respiratory infection dynamics”, arXiv:2011.12397 [stat.ME], 2020.

- 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