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Theory and Methods

Linear Non-Gaussian Component Analysis Via Maximum Likelihood

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Pages 332-343 | Received 01 Oct 2015, Published online: 09 Jul 2018

References

  • Allassonniere, S., and Younes, L. (2012), “A Stochastic Algorithm for Probabilistic Independent Component Analysis,” The Annals of Applied Statistics, 6, 125–160.
  • Amato, U., Antoniadis, A., Samarov, A., and Tsybakov, A. (2010), “Noisy Independent Factor Analysis Model for Density Estimation and Classification,” Electronic Journal of Statistics, 4, 707–736.
  • Attias, H. (1999), “Independent Factor Analysis,” Neural Computation, 11, 803–851.
  • Bach, F. R., and Jordan, M. I. (2003), “Kernel Independent Component Analysis,” The Journal of Machine Learning Research, 3, 1–48.
  • Bartlett, M. S., Movellan, J. R., and Sejnowski, T. J. (2002), “Face Recognition by Independent Component Analysis,” IEEE Transactions on Neural Networks, 13, 1450–1464.
  • Beckmann, C. F. (2012), “Modelling with Independent Components,” NeuroImage, 62, 891–901.
  • Beckmann, C. F., and Smith, S. M. (2004), “Probabilistic Independent Component Analysis for Functional Magnetic Resonance Imaging,” IEEE Transactions on Medical Imaging, 23, 137–152.
  • Bell, A. J., and Sejnowski, T. J. (1995), “An Information-Maximization Approach to Blind Separation and Blind Deconvolution,” Neural Computation, 7, 1129–1159.
  • Blanchard, G., Kawanabe, M., Sugiyama, M., Spokoiny, V., and Müller, K.-R. (2006), “In Search of Non-Gaussian Components of a High-Dimensional Distribution,” The Journal of Machine Learning Research, 7, 247–282.
  • Calhoun, V. D., and Adali, T. (2006), “Unmixing fMRI with Independent Component Analysis,” IEEE Engineering in Medicine and Biology Magazine, 25, 79–90.
  • Cardoso, J. F., and Souloumiac, A. (1993), “Blind Beamforming for Non-Gaussian Signals,” in IEEE Proceedings F –Radar and Signal Processing, Vol. 140, pp. 362–370.
  • Chen, A., and Bickel, P. J. (2006), “Efficient Independent Component Analysis,” The Annals of Statistics, 34, 2825–2855.
  • Correa, N., Adali, T., and Calhoun, V. D. (2007), “Performance of Blind Source Separation Algorithms for fMRI Analysis Using a Group ICA Method,” Magnetic Resonance Imaging, 25, 684–694.
  • Cover, T. M., and Thomas, J. A. (2006). Elements of Information Theory, New Jersey: Wiley.
  • Eloyan, A., and Ghosh, S. K. (2013), “A Semiparametric Approach to Source Separation Using Independent Component Analysis,” Computational Statistics and Data Analysis, 58, 383–396.
  • Friston, K. J., Williams, S., Howard, R., Frackowiak, R. S., and Turner, R. (1996), “Movement-Related Effects in fMRI Time-Series,” Magnetic Resonance in Medicine, 35, 346–355.
  • Glasser, M. F., Sotiropoulos, S. N., Wilson, J. A., Coalson, T. S., Fischl, B., Andersson, J. L., Xu, J., Jbabdi, S., Webster, M., Polimeni, J. R., Van Essen, D. C., and Jenkinson, M., for the WU-Minn HCP Consortium. (2013), “The Minimal Preprocessing Pipelines for the Human Connectome Project,” NeuroImage, 80, 105–124.
  • Green, C. G., Nandy, R. R., and Cordes, D. (2002), “PCA-Preprocessing of fMRI Data Adversely Affects the Results of ICA,” in Proceedings of International Society of Magnetic Resonance in Medicine, p. 10.
  • Griffanti, L., Salimi-Khorshidi, G., Beckmann, C. F., Auerbach, E. J., Douaud, G., Sexton, C. E., Zsoldos, E., Ebmeier, K. P., Filippini, N., Mackay, C. E., Moeller, S., Xu, J., Yacoub, E., Baselli, G., Ugurbil, K., Miller, K. L., and Smith, S. M. (2014). “ICA-Based Artefact Removal and Accelerated fMRI Acquisition for Improved Resting State Network Imaging,” NeuroImage, 95, 232–247.
  • Guo, Y., and Tang, L. (2013), “A Hierarchical Model for Probabilistic Independent Component Analysis of Multi-Subject fMRI Studies,” Biometrics, 69, 970–981.
  • Hastie, T. (2013), GAM: Generalized Additive Models, R package version 1.08.
  • Hastie, T., and Tibshirani, R. (2003), “Independent Components Analysis Through Product Density Estimation,” Advances in Neural Information Processing Systems, 15, 649–656.
  • Hastie, T., and Tibshirani, R. (2010), ProDenICA: Product Density Estimation for ICA using tilted Gaussian density estimates, R package version 1.0.
  • Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning, New York: Springer.
  • Huber, P. J. (1985), “Projection Pursuit,” The Annals of Statistics, 13, 435–475.
  • Hyvarinen, A. (1999), “Fast and Robust Fixed-Point Algorithms for Independent Component Analysis,” IEEE Transactions on Neural Networks, 10, 626–634.
  • Hyvärinen, A., Karhunen, J., and Oja, E. (2001), Independent Component Analysis, Wiley-Interscience.
  • Hyvärinen, A., and Oja, E. (1998), “Independent Component Analysis by General Nonlinear Hebbian-Like Learning Rules,” Signal Processing, 64, 301–313.
  • ——— (2000), “Independent Component Analysis: Algorithms and Applications,” Neural Networks, 13, 411–430.
  • Ilmonen, P., Nordhausen, K., Oja, H., and Ollila, E. (2010), “A New Performance Index for ICA: Properties, Computation and Asymptotic Analysis,” in Latent Variable Analysis and Signal Separation, eds. V. Vigneron, V. Zarzosa, E. Moreau, R. Brigonval, and E. Vincent, 229–236, Berlin: Springer, Lecture Notes in Computer Science 6365.
  • Kagan, A. M., Rao, C. R., and Linnik, Y. V. (1973), Characterization Problems in Mathematical Statistics, New York: Wiley.
  • Kawanabe, M., Sugiyama, M., Blanchard, G., and Müller, K. (2007), “A New Algorithm of Non-Gaussian Component Analysis with Radial Kernel Functions,” Annals of the Institute of Statistical Mathematics, 59, 57–75.
  • Lee, T. W., Girolami, M., and Sejnowski, T. J. (1999), “Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources,” Neural Computation, 11, 417–441.
  • Marchini, J. L., Heaton, C., and Ripley, B. D. (2010), FastICA: FastICA Algorithms to perform ICA and Projection Pursuit, R package version 1.1-13.
  • Matteson, D. S., and Tsay, R. S. (2016), “Independent Component Analysis via Distance Covariance,” Journal of the American Statistical Association, 112, 623–637.
  • Miettinen, J., Nordhausen, K., Oja, H., and Taskinen, S. (2014), “Deflation-Based FastICA with Adaptive Choices of Nonlinearities,” IEEE Transactions on Signal Processing, 62, 5716–5724.
  • Miettinen, J., Nordhausen, K., Oja, H., Taskinen, S., and Virta, J. (2017), “The Squared Symmetric Fastica Estimator,” Signal Processing, 131, 402–411.
  • Miettinen, J., Taskinen, S., Nordhausen, K., and Oja, H. (2015), “Fourth Moments and Independent Component Analysis,” Statistical Science, 30, 372–390.
  • Nordhausen, K., Ilmonen, P., Mandal, A., Oja, H., and Ollila, E. (2011), “Deflation-Based Fastica Reloaded,” in Proceedings of the 19th European Signal Processing Conference, pp. 1854–1858.
  • Nordhausen, K., Oja, H., and Tyler, D. E. (2016), “Asymptotic and Bootstrap Tests for Subspace Dimension,” arXiv:1611.04908.
  • Nordhausen, K., Oja, H., Tyler, D. E., and Virta, J. (2017), “Asymptotic and Bootstrap Tests for the Dimension of the Non-Gaussian Subspace,” IEEE Signal Processing Letters, 24, 887–891.
  • Pruim, R. H., Mennes, M., van Rooij, D., Llera, A., Buitelaar, J. K., and Beckmann, C. F. (2015), “ICA-AROMA: A Robust ICA-Based Strategy for Removing Motion Artifacts from fMRI Data,” NeuroImage, 112, 267–277.
  • Risk, B. B., Matteson, D. S., Ruppert, D., Eloyan, A., and Caffo, B. S. (2014), “An Evaluation of Independent Component Analyses with an Application to Resting-State fMRI,” Biometrics, 70, 224–236.
  • Salimi-Khorshidi, G., Douaud, G., Beckmann, C. F., Glasser, M. F., Griffanti, L., and Smith, S. M. (2014), “Automatic Denoising of Functional MRI Data: Combining Independent Component Analysis and Hierarchical Fusion of Classifiers,” Neuroimage, 90, 449–468.
  • Samworth, R. J., and Yuan, M. (2012), “Independent Component Analysis via Nonparametric Maximum Likelihood Estimation,” The Annals of Statistics, 40, 2973–3002.
  • Shi, R., and Guo, Y. (2016), “Investigating Differences in Brain Functional Networks Using Hierarchical Covariate-Adjusted Independent Component Analysis,” Annals of Applied Statistics, 10, 1930–1957.
  • Silva, P. F., Marcal, A. R., and da Silva, R. M. A. (2013), “Evaluation of Features for Leaf Discrimination,” Springer Lecture Notes in Computer Science, 7950.
  • Stögbauer, H., Kraskov, A., Astakhov, S. A., and Grassberger, P. (2004), “Least-Dependent-Component Analysis Based on Mutual Information,” Physical Review E, 70, 066123.
  • Tipping, M. E., and Bishop, C. M. (1999), “Probabilistic Principal Component Analysis,” Journal of the Royal Statistical Society, Series B, 61, 611–622.
  • Virta, J., Nordhausen, K., and Oja, H. (2015), “Joint Use of Third and Fourth Cumulants in Independent Component Analysis,” arXiv:1505.02613.
  • Virta, J., Nordhausen, K., and Oja, H. (2016), “Projection Pursuit for Non-Gaussian Independent Components,” arXiv:1612.05445.
  • Wei, T. (2015), “A Convergence and Asymptotic Analysis of the Generalized Symmetric FastICA Algorithm,” IEEE Transactions on Signal Processing, 63, 6445–6458.
  • Welvaert, M., Durnez, J., Moerkerke, B., Verdoolaege, G., and Rosseel, Y. (2011), “neuRosim: An R Package for Generating fMRI Data,” Journal of Statistical Software, 44, 1–18.

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