Application of Independent Component Analysis With Adaptive Density Model to Complex-Valued fMRI Data

Abstract

Independent component analysis (ICA) has proven quite useful for the analysis of functional resonance magnetic imaging (fMRI) data, especially when the underlying nature of the data is hard to model. It is especially attractive for the analysis of fMRI data in its native complex form since very little is known about the nature of phase, which is typically discarded in most analyses. In this paper, we show that a complex ICA approach using a flexible nonlinearity that adapts to the source density is the more desirable one for performing ICA of complex fMRI data compared to the those that use fixed nonlinearity. We show that by adaptively matching the underlying fMRI density model, the analysis performance can be improved in terms of both the estimation of the spatial maps and the task-related time courses. We also define a procedure for analysis and visualization of complex-valued fMRI results, which includes the construction of bivariate t-maps for multiple subjects and a complex-valued ICASSO [1] scheme for evaluating the consistency of ICA algorithms.

Independent Component Analysis for Brain fMRI Does Indeed Select for Maximal Independence

“…This trend has continued and in recent years even more flexible algorithms such as those based on entropy bound minimization (EBM) or full blind source separation (FBSS) have been used increasingly to analyze fMRI data, outperforming both Infomax and FastICA [14], [17], [18]. In general, we would recommend that these and other more recent algorithms preferentially be applied to fMRI, as they are generally more robust to non-super-Gaussian and/or multimodal distributed sources which can occur in real fMRI data, observed in the context of certain artifacts.…”

Exploring Frequency-dependent Brain Networks from ongoing EEG using Spatial ICA during music listening

“…A common approach of data dimension reduction is principal component analysis (PCA) which is linear. Here we extended PCA to the complex domain by considering complex-valued eigenvalue decomposition (Li, Correa, Rodriguez, Calhoun, & Adali, 2011). The choice of model order was based on previous studies (Abou-Elseoud et al, 2010;Smith et al, 2009), which suggested the number of a dimension slightly larger than the expected number of underlying sources.…”

“…The correlation matrix was used as the similarity measure for clustering in real-valued ICASSO. For the complex case, since the ICs were complex-valued, we just considered the correlation matrix among the magnitude ICs to perform the clustering (Li et al, 2011). Then, we took the Iq as the criterion to examine stability of the ICA estimate.…”

The role of diversity in complex ICA algorithms for fMRI analysis

“…We can also see the clear improvement in the performance for each of the algorithms when Z c -maps are used rather than the Z -maps. This demonstrates the importance of accounting for the phase information and performing an ICA analysis on fMRI data in its native, complex, domain (Li et al, 2011, Rodriguez et al, 2011, 2012). …”

“…A second assumption involves analyzing the fMRI data in the real domain. Since fMRI data is naturally complex, performing an analysis in the real domain will lead to a loss of information (Hoogenraad et al, 1998, Menon, 2002, Rauscher et al, 2005, Tomasi and Caparelli, 2007, Arja et al, 2010, Yu et al., 2015) stemming from the transformation of the complex signal to the real domain and ignoring the potentially useful property of noncircularity, which fMRI data has been shown to exhibit (Li et al, 2011, Rodriguez et al, 2012, Loesch and Yang, 2013). A final implicit assumption made by the majority of ICA algorithms for fMRI analysis is that there exists no sample-to-sample dependence between adjacent voxels.…”