We should implement and test Modified Akaike Information Criterion (mAIC) [1] for estimating the optimal roughness penalty in the Smoothing_F class.

References

[1] Fujikoshi, Y. 1997. “Modified AIC and Cp in Multivariate Linear Regression.” Biometrika 84 (3). Oxford University Press: 707–16. doi:10.1093/biomet/84.3.707.

We need to implement and test Generalized Cross Validation (GCV) [1, 2] for estimating the optimal roughness penalty in the Smoothing_F class.

References

• [1] Ramsay, J. O., and B. W. Silverman. 2005. Functional Data Analysis. 2nd ed. Springer Series in Statistics. New York: Springer-Verlag. doi:10.1007/b98888.
• [2] Golub, Gene H, Michael Heath, and Grace Wahba. 1979. “Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter.” Technometrics 21 (2): 215. doi:10.2307/1268518.

We need to implement the k-means++ method [1] for choosing the initial centroids in k-means.

References

[1] David Arthur and Sergei Vassilvitskii. 2007. k-means++: the advantages of careful seeding. In Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms (SODA '07). Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1027-1035.

We need to implement and test the Gap statistic [1] for choosing the optimal k value (number of clusters) in K-Means.

References

[1] Tibshirani, Robert, Guenther Walther, and Trevor Hastie. 2001. “Estimating the Number of Clusters in a Data Set via the Gap Statistic.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (2). Blackwell Publishers Ltd.: 411–23. doi:10.1111/1467-9868.00293.

After almost 30 minutes of waiting for the compilation process to finish, I got the following error:

qjava.lang.OutOfMemoryError: GC overhead limit exceeded
at scala.tools.nsc.backend.jvm.analysis.AliasingFrame.(AliasingFrame.scala:43)

We need to implement and test Tight Clustering [1].

References

[1] Tseng, George C., and Wing H. Wong. 2005. “Tight Clustering: A Resampling-Based Approach for Identifying Stable and Tight Patterns in Data.” Biometrics 61 (1). Blackwell Publishing: 10–16. doi:10.1111/j.0006-341X.2005.031032.x.

This issue is for discussion surround the fitting of differential equations to functional data, commonly referred to as Principal Differential Analysis (PDA) [1].

References

[1] Ramsay, J. O., and B. W. Silverman. 2005. Chapter 19. Functional Data Analysis. 2nd ed. Springer Series in Statistics. New York: Springer-Verlag. doi:10.1007/b98888.

Need to be able to load the gene iso form expression time course dataset provided by Xiaoxiao. This should be loaded and made available in a MatrixD.

We should implement and test Generalized Bayesian Information Criterion (GBIC) [1] for estimating the optimal roughness penalty in the Smoothing_F class.

References

[1] Konishi, Sadanori, Tomohiro Ando, and Seiya Imoto. 2004. “Bayesian Information Criteria and Smoothing Parameter Selection in Radial Basis Function Networks.” Biometrika 91 (1). Oxford University Press: 27–43. http://www.jstor.org/stable/20441077

We should implement and test Generalized Information Criterion (GIC) [1] for estimating the optimal roughness penalty in the Smoothing_F class.

References

[1] Konoshi, Sadanori, and Genshiro Kitagawa. 1996. “Generalised Information Criteria in Model Selection.” Biometrika 83 (4). Oxford University Press: 875–90. https://www.jstor.org/stable/2337290

The GeneIsoform sample application is setup so that we can explore #4 on a gene isoform expression time course dataset.

Need to write instructions/documentation for the software (I've included information in a related email to help get you started) and include these instructions in the README.md file for the package.

To make things easier, we'll use the https://github.com/scalation/fda/tree/ftclust branch for code/instructions/etc related to the paper.

We should implement and test Lasso regression [1] that performs both variable selection and regularization in order to enhance the prediction accuracy and interpretability of the statistical model it produces.

References

[1] Tibshirani, Robert. 1996. “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society. Series B (Methodological) 58 (1). [Royal Statistical Society, Wiley]: 267–88. http://www.jstor.org/stable/2346178

We need to test the Smoothing_F class against a real dataset. Perhaps a comparison with R (or similar) would be good too.

Need to run the software on the simulated data (attached in a related) provided by Xiaoxiao and email the results to Xiaoxiao and myself. This dataset needs to be converted to CSV and included with the package. You may want to explore running this on sapelo if it takes too long to run.