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Sparse Dictionary Learning and Deep Convolutional Auto-encoders as Alternative Methods to ICA for Resting-State Network Detection
Alice Shen1, Gregory Simchick2,3, Brandon Campbell1, and Qun Zhao2,3

1University of Georgia, Athens, GA, United States, 2Physics and Astronomy, University of Georgia, Athens, GA, United States, 3Bio-Imaging Research Center, University of Georgia, Athens, GA, United States

Synopsis

Though Independent Component Analysis (ICA) is a commonly-used method for resting state network (RSN) detection from resting-state fMRI (rsfMRI) data, it is limited by its assumption of spatial independence requiring that detected networks be non-overlapping. This study investigates the use of Sparse Dictionary Learning (SDL) and Deep Convolutional Auto-Encoders (DCAE) as alternative methods for RSN detection using Human Connectome Project rsfMRI data. Using the Smith10 RSN Atlas as a ground truth, Pearson spatial correlation and spatial overlap scores were used as metrics of performance, and it was found that SDL and DCAE outperform ICA in detecting RSNs in single session analyses.

Introduction

Independent component analysis (ICA) and its variants are the dominant methods used in detecting resting state networks (RSNs) in resting-state fMRI (rsfMRI) data.1,2 ICA-based methods treat RSN detection as a blind source separation (BSS) problem, where each RSN is modeled as an independent spatial component of the brain volume of rsfMRI signals.3

Despite the popularity of ICA, the method has limitations, particularly in detecting spatially overlapping components.4 One of the assumptions of spatial ICA is that the components forming the mixed signal must be spatially independent, or non-overlapping.4,5 For detecting functional networks, this assumption may not hold, as connectivity research has found that networks may have significant spatial overlap.6,7

Alternative methods have been proposed to supplement ICA methods, including Sparse Dictionary Learning (SDL), as well as deep learning methods like Deep Convolutional Auto-Encoders (DCAEs), both of which can solve BSS-like problems without the assumption of spatial independence required by ICA.8

Although ICA is typically performed group-wise on multiple sessions of data, this study is concerned with the performance of RSN detection during single-session analysis. Single-session analysis is relevant for studies where longitudinal assessment of an individual is desired, such as monitoring changes in an individual’s functional connectivity pre- and post- operation or treatment.

Methods

10 sessions (5 subjects, 2 sessions each) of rsfMRI data were taken from the Human Connectome Project dataset.9 RSN detection was performed individually on each session using three methods: spatial independent component analysis (ICA), temporal sparse dictionary learning (SDL), and temporal Deep Convolutional Auto-Encoding (DCAE).

SDL was performed using the SPArse Modeling Software (SPAMS) library.8 The autoencoder used in DCAE was written using Keras.10 FastICA was performed using the Group ICA of fMRI (GIFT) toolbox on each session of data individually, not group-wise.11

Each method yielded a set of candidate RSN maps for each of the 10 sessions. To assess the performance of each method, the candidate maps generated by each method were compared to a ground truth using the Smith10 RSN Atlas, a widely-accepted atlas of 10 brain maps commonly used as a reference for known RSNs.12 A pairwise Pearson spatial correlation was calculated between each of the Smith10 maps and candidate maps generated by each method.

For each method and session, the candidate map with the highest Pearson correlation for each of the Smith10 maps was identified and an overlap score was calculated. These maximal Pearson correlation scores and overlap scores per Smith10 map were averaged method-wise over 10 sessions for an average performance score. All Pearson correlation values and overlap metrics were calculated using the ICN Atlas package for SPM12.13,14

Results

The average of the maximal Pearson correlation scores and overlap scores over 10 sessions for each RSN and method are given in Figures 1 and 2, respectively. By Pearson correlation scores, the spatial ICA method significantly underperforms in detecting RSNs found in all but four (Maps 1, 4, 5 and 8) of the Smith10 atlas in comparison to SDL and DCAE methods. By overlap scores, the spatial ICA method significantly underperforms in detecting RSNs found in all but two (Maps 1 and 6) of the Smith10 atlas in comparison to SDL and DCAE methods.

Figures 3 and 4 depict the averaged map generated by each method over 10 sessions with the maximal Pearson correlation values for Smith10 maps 4 (Default Mode Network) and 7 (Auditory Network), respectively.

Discussion and Conclusions

The maximal Pearson correlations found range within [0.13 0.29], of which 66% exceed 0.20, a threshold used previously to indicate valid RSN detection.12 Preliminary results suggest that DCAE and SDL methods outperform spatial ICA in detecting a majority (>60%) of the RSNs from the Smith10 Atlas. However, spatial ICA may be more robust at detecting specific RSNs, namely Smith Map 1 (Visual network) and Map 8 (Executive Control network). From a visual inspection of the Smith10 maps, it is possible that ICA has improved performance in detecting these networks due to their lessened overlap with other RSNs, better fulfilling the spatial independence assumption required by the ICA model.8

The lower values of Pearson correlations and overlaps found in this study may be due to its single-session methodology, as opposed to group analysis.15 ICA has been found to have improved performance when run on multiple datasets group-wise.15 However, the superior performance of the DCAE and SDL methods in detecting RSNs from single-session data suggests that these techniques may be used to supplement ICA during single-session analyses of individualized differences in functional connectivity, such as studies comparing subjects pre- and post- therapeutic treatment.

Acknowledgements

This study was partially supported by NIH grant R01NS099596.

References

1. Calhoun V. D, Adali T. (2012). Multisubject independent component analysis of fMRI: a decade of intrinsic networks, default mode, and neurodiagnostic discovery. IEEE Reviews in Biomedical Engineering, 5, pp. 60-73.

2. Beckmann C. F, DeLuca M, Devlin JT, Smith SM. (2005). Investigations into resting-state connectivity using independent component analysis. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 360(1457), pp. 1001-1013.

3. Hu X, Huang H, Peng B, Han J, Liu N, Lv J, Guo L, Guo C, Liu T. (2018). Latent source mining in FMRI via restricted Boltzmann machine. Hum Brain Mapp., 39(6), pp. 2368-2380.

4. Beckmann C. F. (2012). Modelling with independent components. Neuroimage, 62(2), 891-901.

5. Bingham E, Hyvarinen A. (2000). A fast fixed-point algorithm for independent component analysis of complex valued signals. International Journal of Neural Systems, 10(1), pp. 1-8.

6. Harris K. D, Mrsic-Flogel TD. (2013). Cortical connectivity and sensory coding. Nature, 503(7474), pp. 51-58.

7. Perin R, Berger TK, Markram H. (2011). A synaptic organizing principle for cortical neuronal groups. Proceedings of the National Academy of Sciences, 108(13), pp. 5419-5424.

8. Mairal J, Bach F, Ponce J, Sapiro G. (2010). Online learning for matrix factorization and sparse coding. The Journal of Machine Learning Research, 11, pp. 19- 60.

9. Van Essen DC, Smith SM, Barch DM, Behrens TEJ, Yacoub E, Ugurbil K. (2013). The WU-Minn Human Connectome Project: An overview. NeuroImage, 80(2013):62-79.

10. Chollet, Francois, et al. (2015). Keras. Online at https://keras.io.

11. Calhoun V, Adali T. (2004). Group ICA of fMRI toolbox (GIFT). Online at http://icatb.sourceforge.net.

12. Smith SM, Fox PT, Miller KL, Glahn DC, MickleFox P, Mackay CE, Filippini N, Watkins KE, Toro R, Laird AR, Beckmann CF. (2009). Correspondence of the brain's functional architecture during activation and rest. Proceedings of the National Academy of Sciences, 106 (31), 13040-13045.

13. Kozák LR, van Graan LA, Chaudhary UJ, Szabó AG, Lemieux L. (2017). ICN_Atlas: Automated description and quantification of functional MRI activation patterns in the framework of intrinsic connectivity networks. NeuroImage, 163, pp. 319-341.

14. Penny, W.D., et al. (2011). Statistical parametric mapping: the analysis of functional brain images. Academic Press.

15. Calhoun, V. D., Liu, J., Adali, T. (2008). A review of group ICA for fMRI data and ICA for joint inference of imaging, genetic, and ERP data. NeuroImage, 45(1 Suppl), S163-72.

Figures

Figure 1. a.) The average (n=10) of the maximal Pearson correlation scores per each method and Smith10 map. Each method was run on individual sessions of data to generate a set of candidate RSN maps. Pearson spatial correlation scores were calculated pairwise between each candidate map and Smith10 maps. The maximum Pearson correlation score from each method per Smith map was averaged over 10 sessions. Standard deviation is represented as error bars. b.) Calculated (two-tailed t-test) p-values for Figure 1a. Non-black numbers indicate a significant difference (p < 0.05) in averages. The color of the p-value indicates the method with better performance.

Figure 2. a.) The average (n=10) overlap scores of generated maps with the highest Pearson correlation for each Smith10 map. Each method was run on each session of data to generate candidate RSN maps. Pearson spatial correlation scores were calculated pairwise between each candidate and the Smith10 maps. The candidate for each method with the highest Pearson correlation per Smith10 map was used to calculate an overlap score and averaged over 10 sessions. b.) Calculated p-values (two-tailed t-test) for Figure 2a. Non-black numbers indicate a significant difference (p < 0.05) in averages. The color of the p-value signifies the method with better performance.

Figure 3. Average thresholded maps (n=10) generated by each method with the highest Pearson correlation to Smith Map 4 (Default Mode Network). Each method was run on individual sessions of data to generate a set of candidate RSN maps. Pearson spatial correlation scores were calculated between each candidate map and Smith Map 4. The candidate maps with the highest Pearson correlation scores for each session were then averaged together to generate an average map per method. Averaged maps were thresholded for clarity and ease of visual analysis.

Figure 4. Average thresholded maps (n=10) generated by each method with the highest Pearson correlation to Smith Map 7 (Auditory Network). Each method was run on individual sessions of data to generate a set of candidate RSN maps. Pearson spatial correlation scores were calculated between each candidate map and Smith Map 7. The candidate maps with the highest Pearson correlation scores for each session were then averaged together to generate an average map per method. Averaged maps were thresholded for clarity and ease of visual analysis.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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