| Summary: | Many brain imaging modalities reveal interpretable patterns after the data dimensionality is reduced and summarized via data-driven approaches. In functional magnetic resonance imaging (fMRI) studies, such summarization is often achieved through independent component analysis (ICA). ICA transforms the original data into a relatively small number of interpretable bases in voxel space (referred to as ICA spatial components, or spatial maps) and corresponding bases in the time domain (referred to as time-courses of corresponding spatial maps) In this work, we use the word “basis” to broadly refer to either of the two factors resulting from the transformation. A precise summarization for fMRI requires accurately detecting co-activation of voxels by measuring temporal dependence. Accurate measurement of dependence requires a proper understanding of the underlying temporal characteristics of the data. One way to understand such characteristics is to study the frequency spectrum of fMRI data. Researchers have argued that information regarding the underlying neuronal activity might be spread over a range of frequencies as a result of the heterogeneous temporal nature of the neuronal activity, which is reflected in its frequency spectrum. Many studies have accounted for heterogeneous characteristics of the frequency of the signal by either directly inspecting the contents of frequency domain-transformed data or augmenting their analyses with such information. For example, studies on fMRI data have investigated brain functional connectivity by leveraging frequency-adjusted measures of dependence (e.g., when a correlation is measured as a function of frequency, as with “coherence”). Although these studies measure dependence as a function of frequency, the formulation does not capture all characteristics of the frequency-based dependence. Incorporating frequency information into a summarization approach would enable the retention of important frequency-related information that exists in the original space but might be lost after performing a frequency-independent summarization. We propose a novel data-driven approach built upon ICA, which is based on measuring dependence as a generalized function of frequency. Applying this approach to fMRI data provides evidence of existing cross-frequency functional connectivity between different areas of the brain.
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