Non-commutativity arises in many places in statistical signal processing including information fusion, graphical models and distributed estimation. Any problem where the model or the processing lacks symmetry, permutation invariance or revocable actions will have non-commutativity. This talk will discuss several signal processing areas where non-commutativity is manifested and some challenges and opportunities.

Non‐commutativity is intrinsic to emerging complex sensing and processing systems. This symposium aims to bring multidisciplinary researchers whose work addresses development or application of new non‐commutative information measures. These measures and their application domain target data collection for non-commutative information structures intrinsic to hierarchical representations, distributed sensing, and adaptive online processing. Such non-commutative measures and approaches include but are not limited to combination of theory of random matrices, free probability, and statistical machine learning. Application domains of interest include: 1) community detection in dynamic social networks; 2) recognizing and describing complex human activities from video; 3) fusion of directed information flows; 4) interactive machine learning with humans and crowdsourcing; and 5) networks of brain‐computer interfaces.