  Knowledge of functional groupings of neurons can shed light on structures of
neural circuits and is valuable in many types of neuroimaging studies. However,
accurately determining which neurons carry out similar neurological tasks via
controlled experiments is both labor-intensive and prohibitively expensive on a
large scale. Thus, it is of great interest to cluster neurons that have similar
connectivity profiles into functionally coherent groups in a data-driven
manner. In this work, we propose the clustered Gaussian graphical model (GGM)
and a novel symmetric convex clustering penalty in an unified convex
optimization framework for inferring functional clusters among neurons from
neural activity data. A parallelizable multi-block Alternating Direction Method
of Multipliers (ADMM) algorithm is used to solve the corresponding convex
optimization problem. In addition, we establish convergence guarantees for the
proposed ADMM algorithm. Experimental results on both synthetic data and
real-world neuroscientific data demonstrate the effectiveness of our approach.
