Unmixing fMRI with Independent Component Analysis Using ICA to Characterize High-Dimensional fMRI Data in a Concise Manner. BY VINCE D. CALHOUN AND TÜLAY ADALI

Independent component analysis (ICA) is a statistical method used to discover hidden factors (sources or features) from a set of measurements or observed data such that the sources are maximally independent. Typically, it assumes a generative model where observations are assumed to be linear mixtures of independent sources, and unlike principal component analysis (PCA), which uncorrelates the data, ICA works with higher-order statistics to achieve independence. An intuitive example of ICA can be given by a scatter-plot of two independent signals s1 and s2. Figure 1(a) shows a plot of the two independent signals (s1, s2) in a scatter plot. Figure 1(b) and (c) shows the projections for PCA and ICA, respectively, for a linear mixture of s1 and s2. PCA finds the orthogonal vectors u1, u2 but does not find independent vectors. In contrast, ICA is able to find the independent vectors a1, a2 of the linear mixed signals (s1, s2) and is thus able to restore the original sources. A typical ICA model assumes that the source signals are not observable, are statistically independent, and are nonGaussian, with an unknown but linear mixing process. Consider an observed M-dimensional random vector denoted by x = (x1, . . . xM) , which is generated by the ICA model: x = As, (1)