Evaluating model misspecification in independent component analysis

<div><p>Independent component analysis (ICA) is a popular blind source separation technique used in many scientific disciplines. Current ICA approaches have focused on developing efficient algorithms under specific ICA models, such as instantaneous or convolutive mixing conditions, intrinsically assuming temporal independence or autocorrelation of the sources. In practice, the true model is not known and different ICA algorithms can produce very different results. Although it is critical to choose an ICA model, there has not been enough research done on evaluating mixing models and assumptions, and how the associated algorithms may perform under different scenarios. In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases. Our simulation studies show that the performance of ICA algorithms is highly dependent on mixing conditions and temporal independence of the sources. Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters.</p></div

Normalized brain structure volumes.

<p>Results with <i>p</i><0.01 are shown in bold face. <i>Abbreviations</i>. <i>HV</i>, healthy volunteers. <i>MS</i>, multiple sclerosis. <i>SD</i>, standard deviation.</p

Partial correlations of normalized brain structure with one another in MS cases.

<p>Results are adjusted for linear effects of age and sex. The <i>p</i>-values are shown in parentheses, and results with <i>p</i><0.01 are shown in boldface.</p

Partial correlations of impairment measures with normalized structure volumes.

<p>Results are adjusted for linear effects of age and sex. The <i>p</i>-values are shown in parentheses, and results with <i>p</i><0.01 are shown in boldface. <i>Abbreviations</i>. <i>EDSS</i>, Expanded Disability Status Scale. <i>MSSS</i>, MS Severity Score. <i>MSFC</i>, Multiple Sclerosis Functional Composite <i>z</i>-score. <i>PASAT-3</i>, Paced Auditory Serial Addition Test, 3-second version.</p

Partial correlations of impairment measures with normalized structure volumes computed by FSL FAST segmentation tool.

<p>Results are adjusted for linear effects of age and sex. The <i>p</i>-values are shown in parentheses, and results with <i>p</i><0.01 are shown in boldface. <i>Abbreviations</i>. <i>EDSS</i>, Expanded Disability Status Scale. <i>MSSS</i>, MS Severity Score. <i>MSFC</i>, Multiple Sclerosis Functional Composite. <i>PASAT-3</i>, Paced Auditory Serial Addition Test, 3-second version.</p

Cohort demographic data.

a<p> <i>median (range),</i></p>b<p> <i>mean z-score (standard deviation),</i></p>c<p> <i>median (interquartile range).</i></p>*<p>Vibration units are amplitudes, proportional to the square of the applied voltage.</p><p><i>Abbreviations</i>. <i>RRMS</i>, relapsing remitting multiple sclerosis. <i>SPMS</i>, secondary progressive multiple sclerosis. <i>PPMS</i>, primary progressive multiple sclerosis. <i>CIS</i>, clinically isolated syndrome. <i>EDSS</i>, Expanded Disability Status Scale. <i>MSSS</i>, Multiple Sclerosis Severity Score. <i>MSFC</i>, Multiple Sclerosis Functional Composite. <i>PASAT-3</i>, Paced Auditory Serial-Addition Task, 3 second version.</p

Lesion-TOADS segmentation results.

<p>Representative slices from the T1-weighted (A) and FLAIR (B) scans of one of the MS cases. Lesions are depicted in red (C). 3D rendering of ventricles (blue), putamen (green), caudate (orange), thalamus (pink), brainstem (yellow), and lesions (red), generated by Lesion-TOADS (D).</p

Figure 2

<p>Distributions of normalized cortical gray matter (A) and cerebral white matter (B) volumes in healthy volunteers vs. MS cases. White matter volume is not significantly atrophic in the MS group, whereas cortical GM volume is substantially lower in MS.</p