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… Click to show full abstract
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.
               
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