A New Approach for Functional Connectivity via Alignment of Blood Oxygen Level-Dependent Signals

Due to technological advances, spatially indexed objects, such as blood oxygen level-dependent time series or electroencephalography data, are commonly observed across different scientific disciplines. Such object data are typically high dimensional and therefore challenging to handle. We propose a new approach for spatially indexed object data by mapping their spatial locations to a targeted one-dimensional interval so objects that are similar are placed near each other on the new target space. The proposed alignment not only provides a visualization tool for such complex object data but also facilitates a new way to study brain functional connectivity. Specifically, we introduce a new concept of path length to quantify the functional connectivity and a new community detection method. The advantages of the proposed methods are illustrated by simulations and in a study of functional connectivity for Alzheimer's disease.