Dynamic Functional Magnetic Resonance Imaging Connectivity Tensor Decomposition: A New Approach to Analyze and Interpret Dynamic Brain Connectivity.

There is a growing interest in using so-called dynamic functional connectivity, as the conventional static brain connectivity models are being questioned. Brain network analyses yield complex network data that are difficult to analyze and interpret. To deal with the complex structures, decomposition/factorization techniques that simplify the data are often used. For dynamic network analyses, data simplification is of even greater importance, as dynamic connectivity analyses result in a time series of complex networks. A new challenge that must be faced when using these decomposition/factorization techniques is how to interpret the resulting connectivity patterns. Connectivity patterns resulting from decomposition analyses are often visualized as networks in brain space, in the same way that pairwise correlation networks are visualized. This elevates the risk of conflating connections between nodes that represent correlations between nodes' time series with connections between nodes that result from decomposition analyses. Moreover, dynamic connectivity data may be represented with three-dimensional or four-dimensional (4D) tensors and decomposition results require unique interpretations. Thus, the primary goal of this article is to (1) address the issues that must be considered when interpreting the connectivity patterns from decomposition techniques and (2) show how the data structure and decomposition method interact to affect this interpretation. The outcome of our analyses is summarized as follows. (1) The edge strength in decomposition connectivity patterns represents complex relationships not pairwise interactions between the nodes. (2) The structure of the data significantly alters the connectivity patterns, for example, 4D data result in connectivity patterns with higher regional connections. (3) Orthogonal decomposition methods outperform in feature reduction applications, whereas nonorthogonal decomposition methods are better for mechanistic interpretation.