Individualized Multilayer Tensor Learning With an Application in Imaging Analysis

References

• Abbasi-Asl, R., and Yu, B. (2017a), “Interpreting Convolutional Neural Networks Through Compression,” arXiv no. 1711.02329.
   Google Scholar
• Abbasi-Asl, R., and Yu, B. (2017b), “Structural Compression of Convolutional Neural Networks Based on Greedy Filter Pruning,” arXiv no. 1705.07356.
   Google Scholar
• Beckmann, C. F., and Smith, S. M. (2005), “Tensorial Extensions of Independent Component Analysis for Multisubject FMRI Analysis,” NeuroImage, 25, 294–311. DOI: 10.1016/j.neuroimage.2004.10.043.
   PubMed Web of Science ®Google Scholar
• Bowman, F. D. (2007), “Spatiotemporal Models for Region of Interest Analyses of Functional Neuroimaging Data,” Journal of American Statistics Association, 102, 442–453. DOI: 10.1198/016214506000001347.
   Web of Science ®Google Scholar
• Bowman, F. D., Caffo, B., Bassett, S. S., and Kilts, C. (2008), “A Bayesian Hierarchical Framework for Spatial Modeling of FMRI Data,” NeuroImage, 39, 146–156. DOI: 10.1016/j.neuroimage.2007.08.012.
   PubMed Web of Science ®Google Scholar
• Caffo, B., Crainiceanu, C., Verduzco, G., Joel, S., Mostofsky, S. H., Bassett, S., and Pekar, J. (2010), “Two-Stage Decompositions for the Analysis of Functional Connectivity for FMRI With Application to Alzheimer’s Disease Risk,” NeuroImage, 51, 1140–1149. DOI: 10.1016/j.neuroimage.2010.02.081.
   PubMed Web of Science ®Google Scholar
• Carroll, J. D., and Chang, J. J. (1970), “Analysis of Individual Differences in Multidimensional Scaling via an N-Way Generalization of ‘Eckart-Young’ Decomposition,” Psychometrika, 35, 283–319. DOI: 10.1007/BF02310791.
   Web of Science ®Google Scholar
• Chen, B., He, S., Li, Z., and Zhang, S. (2012), “Maximum Block Improvement and Polynomial Optimization,” SIAM Journal on Optimization, 22, 87–107. DOI: 10.1137/110834524.
   Web of Science ®Google Scholar
• Chu, S., Tai, S., Ho, C., Lin, C., and Sun, C. (2005), “High-Resolution Simultaneous Three-Photon Fluorescence and Third-Harmonic-Generation Microscopy,” Microscopy Research and Techniques, 66, 193–197. DOI: 10.1002/jemt.20160.
   PubMed Web of Science ®Google Scholar
• Ciresan, D. C., Meier, U., Masci, J., Maria Gambardella, L., and Schmidhuber, J. (2011), “Flexible, High Performance Convolutional Neural Networks for Image Classification,” in IJCAI Proceedings-International Joint Conference on Artificial Intelligence, Barcelona, Spain (Vol. 22), p. 1237.
   Google Scholar
• Cong, F., Phan, A. H., Zhao, Q., Huttunen-Scott, T., Kaartinen, J., Ristaniemi, T., Lyytinen, H., and Cichocki, A. (2012), “Benefits of Multi-domain Feature of Mismatch Negativity Extracted by Non-negative Tensor Factorization From EEG Collected by Low-Density Array,” International Journal of Neural Systems, 22, 1250025. DOI: 10.1142/S0129065712500256.
   PubMed Web of Science ®Google Scholar
• Coppi, R., and Bolasco, S. (1988), “Rank Decomposition and Uniqueness for 3-Way and N-Way Arrays,” in Multiway Data Analysis, Amsterdam: North-Holland, pp. 7–18.
   Google Scholar
• De Leeuw, J. (1994), “Block-Relaxation Algorithms in Statistics,” in Information Systems and Data Analysis, Berlin: Springer.
   Google Scholar
• Derado, G., Bowman, F. D., and Kilts, C. D. (2010), “Modeling the Spatial and Temporal Dependence in FMRI Data,” Biometrics, 66, 949–957. DOI: 10.1111/j.1541-0420.2009.01355.x.
   PubMed Web of Science ®Google Scholar
• Fass, L. (2008), “Imaging and Cancer: A Review,” Molecular Oncology, 2, 115–152. DOI: 10.1016/j.molonc.2008.04.001.
   PubMed Web of Science ®Google Scholar
• Friedman, J., Hastie, T., and Tibshirani, R. (2010), “Regularization Paths for Generalized Linear Models via Coordinate Descent,” Journal of Statistical Software, 33, 1–22.
   PubMed Web of Science ®Google Scholar
• Friston, K. J. (2009), “Modalities, Modes, and Models in Functional Neuroimaging,” Science, 326, 399–403. DOI: 10.1126/science.1174521.
   PubMed Web of Science ®Google Scholar
• Hinrichs, C., Singh, V., Mukherjee, L., Xu, G., Chung, M. K., Johnson, S. C., and ADNI (2009), “Spatially Augmented LPboosting for AD Classification With Evaluations on the ADNI Dataset,” NeuroImage, 48, 138–149. DOI: 10.1016/j.neuroimage.2009.05.056.
   PubMed Web of Science ®Google Scholar
• Hinrichs, C., Singh, V., Xu, G., Johnson, S. C., and ADNI (2011), “Predictive Markers for AD in a Multimodality Framework: An Analysis of MCI Progression in the ADNI Population,” Neuroimage, 55, 574–589. DOI: 10.1016/j.neuroimage.2010.10.081.
   PubMed Web of Science ®Google Scholar
• Horton, N. G., Wang, K., Kobat, D., Clark, C. G., Wise, F. W., Schaffer, C. B., and Xu, C. (2013), “In Vivo Three-Photon Microscopy of Subcortical Structures Within an Intact Mouse Brain,” Nature Photonics, 7, 205–209. DOI: 10.1038/nphoton.2012.336.
   PubMed Web of Science ®Google Scholar
• Kang, H., Ombao, H., Linkletter, C., Long, N., and Badre, D. (2012), “Spatio-spectral Mixed Effects Model for Functional Magnetic Resonance Imaging Data,” Journal of American Statistical Association, 107, 568–577. DOI: 10.1080/01621459.2012.664503.
   PubMed Web of Science ®Google Scholar
• Karahan, E., Rojas-Lopez, P. A., Bringas-Vega, M. L., Valdes-Hernandez, P. A., and Valdes-Sosa, P. A. (2015), “Tensor Analysis and Fusion of Multimodal Brain Images,” Proceedings of the IEEE, 103, 1531–1559. DOI: 10.1109/JPROC.2015.2455028.
   Web of Science ®Google Scholar
• Keshari, R., Vatsa, M., Singh, R., and Noore, A. (2018), “Learning Structure and Strength of CNN Filters for Small Sample Size Training,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9349–9358.
   Google Scholar
• Kolda, T. G. (2006), Multilinear Operators for Higher-Order Decompositions (Vol. 2), United States: Department of Energy.
   Google Scholar
• Kolda, T. G., and Bader, B. W. (2009), “Tensor Decompositions and Applications,” SIAM Review, 51, 455–500. DOI: 10.1137/07070111X.
   Web of Science ®Google Scholar
• Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012), “Imagenet Classification With Deep Convolutional Neural Networks,” in Advances in Neural Information Processing Systems, pp. 1097–1105.
   Google Scholar
• Lange, K. (2010), Numerical Analysis for Statisticians, New York: Springer-Verlag.
   Google Scholar
• Lazar, N. (2008), The Statistical Analysis of Functional MRI Data, New York: Springer-Verlag.
   Google Scholar
• Lee, H., Kim, Y. D., Cichocki, A., and Choi, S. (2007), “Nonnegative Tensor Factorization for Continuous EEG Classification,” International Journal of Neural Systems, 17, 305–317. DOI: 10.1142/S0129065707001159.
   PubMed Web of Science ®Google Scholar
• Li, F., Zhang, T., Wang, Q., Gonzalez, M. Z., Maresh, E. L., and Coan, J. A. (2015), “Spatial Bayesian Variable Selection and Grouping for High-Dimensional Scalar-on-Image Regression,” Annals of Applied Statistics, 9, 687–713. DOI: 10.1214/15-AOAS818.
   Web of Science ®Google Scholar
• Li, L., and Zhang, X. (2017), “Parsimonious Tensor Response Regression,” Journal of the American Statistical Association, 112, 1131–1146. DOI: 10.1080/01621459.2016.1193022.
   Web of Science ®Google Scholar
• Li, X., Xu, D., Zhou, H., and Li, L. (2013), “Tucker Tensor Regression and Neuroimaging Analysis,” Statistics in Biosciences, 10, 520–545. DOI: 10.1007/s12561-018-9215-6.
   Google Scholar
• Lindquist, M. (2008), “The Statistical Analysis of FMRI Data,” Statistical Science, 23, 439–464. DOI: 10.1214/09-STS282.
   Web of Science ®Google Scholar
• Liu, F., Wee, C. Y., Chen, H., and Shen, D. (2014), “Inter-modality Relationship Constrained Multi-modality Multi-task Feature Selection for Alzheimer’s Disease and Mild Cognitive Impairment Identification,” NeuroImage, 84, 466–475. DOI: 10.1016/j.neuroimage.2013.09.015.
   PubMed Web of Science ®Google Scholar
• Luan, H., Qi, F., Xue, Z., Chen, L., and Shen, D. (2008), “Multimodality Image Registration by Maximization of Quantitative-Qualitative Measure of Mutual Information,” Pattern Recognition, 41, 285–98. DOI: 10.1016/j.patcog.2007.04.002.
   Web of Science ®Google Scholar
• Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., and Suetens, P. (1997), “Multimodality Image Registration by Maximization of Mutual Information,” IEEE Transactions on Medical Imaging, 16, 187–198. DOI: 10.1109/42.563664.
   PubMed Web of Science ®Google Scholar
• Martino, F. D., Valente, G., Staeren, N., Ashburner, J., Goebel, R., and Formisano, E. (2008), “Combining Multivariate Voxel Selection and Support Vector Machines for Mapping and Classification of FMRI Spatial Patterns,” NeuroImage, 43, 44–58. DOI: 10.1016/j.neuroimage.2008.06.037.
   PubMed Web of Science ®Google Scholar
• McCullagh, P., and Nelder, J. A. (2018), Generalized Linear Models, Boca Raton, FL: Routledge.
   Google Scholar
• Miranda, M. F., Zhu, H., and Ibrahim, J. G. (2018), “TPRM: Tensor Partition Regression Models With Applications in Imaging Biomarker Detection,” The Annals of Applied Statistics, 12, 1422–1450. DOI: 10.1214/17-AOAS1116.
   PubMed Web of Science ®Google Scholar
• Mørup, M., Hansen, L. K., Herrmann, C. S., Parnas, J., and Arnfred, S. M. (2006), “Parallel Factor Analysis as an Exploratory Tool for Wavelet Transformed Event-Related EEG,” NeuroImage, 29, 938–947. DOI: 10.1016/j.neuroimage.2005.08.005.
   PubMed Web of Science ®Google Scholar
• Nocedal, J., and Wright, S. J. (2006), Numerical Optimization, New York: Springer.
   Google Scholar
• Penny, W. D., Trujillo-Barreto, N. J., and Friston, K. J. (2005), “Bayesian FMRI Time Series Analysis With Spatial Priors,” NeuroImage, 24, 350–362. DOI: 10.1016/j.neuroimage.2004.08.034.
   PubMed Web of Science ®Google Scholar
• Rao, C. R., and Mitra, S. K. (1971), Generalized Inverse of Matrices and Its Applications, New York: Wiley. DOI: 10.2307/1266840.
   Google Scholar
• Reiss, P., and Ogden, R. (2010), “Functional Generalized Linear Models With Images as Predictors,” Biometrics, 66, 61–69. DOI: 10.1111/j.1541-0420.2009.01233.x.
   PubMed Web of Science ®Google Scholar
• Shen, X. (1998), “On the Method of Penalization,” Statistica Sinica, 8, 337–357.
   Web of Science ®Google Scholar
• Sidiropoulos, N. D., and Bro, R. (2000), “On the Uniqueness of Multilinear Decomposition of N-Way Arrays,” Journal of Chemometrics, 14, 229–239. DOI: 10.1002/1099-128X(200005/06)14:3<229::AID-CEM587>3.0.CO;2-N.
   Web of Science ®Google Scholar
• Tu, H., Liu, Y., Turchinovich, D., Marjanovic, M., Lyngsø, J. K., Laegsgaard, J., Chaney, E. J., Zhao, Y., You, S., Wilson, W., Xu, B., Dantus, M., and Boppart, S. A. (2016), “Stain-Free Histopathology by Programmable Supercontinuum Pulses,” Nature Photonics, 10, 534–540. DOI: 10.1038/nphoton.2016.94.
   PubMed Web of Science ®Google Scholar
• Tucker, L. R. (1966), “Some Mathematical Notes on Three-Mode Factor Analysis,” Psychometrika, 31, 279–311.
   PubMed Web of Science ®Google Scholar
• Vapnik, V., Guyon, I., and Hastie, T. (1995), “Support Vector Machines,” Machine Learning, 20, 273–297. DOI: 10.1007/BF00994018.
   Web of Science ®Google Scholar
• Vedaldi, A., and Lenc, K. (2015), “MatConvNet-Convolutional Neural Networks for MATLAB, in Proceeding of the ACM Int. Conf. on Multimedia.
   Google Scholar
• Wagner, R., Thom, M., Schweiger, R., Palm, G., and Rothermel, A. (2013), “Learning Convolutional Neural Networks From Few Samples,” in Proceedings of International Joint Conference on Neural Networks, Dallas, Texas, USA, August, 2013.
   Google Scholar
• Wang, A., Sun, H., and Guan, Y. (2006), “The Application of Wavelet Transform to Multi-modality Medical Image Fusion,” in Networking, Sensing and Control, 2006. ICNSC’06. Proceedings of the 2006 IEEE International Conference, pp. 270–274.
   Google Scholar
• Wang, L., Zhang, Z., and Dunson, D. (2017), “Common and Individual Structure of Brain Networks,” arXiv no. 1707.06360.
   Google Scholar
• Wang, X., Zhu, H., and ADNI. (2017), “Generalized Scalar-on-Image Regression Models via Total Variation,” Journal of the American Statistical Association, 112, 1156–1168. DOI: 10.1080/01621459.2016.1194846.
   PubMed Web of Science ®Google Scholar
• Yuan, L., Wang, Y., Thompson, P. M., Narayan, V. A., Ye, J., and ADNI (2012), “Multi-source Feature Learning for Joint Analysis of Incomplete Multiple Heterogeneous Neuroimaging Data,” NeuroImage, 61, 622–632. DOI: 10.1016/j.neuroimage.2012.03.059.
   PubMed Web of Science ®Google Scholar
• Zhang, D., and Shen, D. (2012), “Multi-modal Multi-task Learning for Joint Prediction of Multiple Regression and Classification Variables in Alzheimer’s Disease,” NeuroImage, 59, 895–907. DOI: 10.1016/j.neuroimage.2011.09.069.
   PubMed Web of Science ®Google Scholar
• Zhou, H. (2013), “Matlab TensorReg Toolbox Version 0.0.2,” available at https://hua-zhou.github.io/TensorReg/.
   Google Scholar
• Zhou, H., Li, L., and Zhu, H. (2013), “Tensor Regression With Applications in Neuroimaging Data Analysis,” Journal of American Statistics Association, 108, 229–239.
   Web of Science ®Google Scholar