Geometric Classification of Brain Network Dynamics via Conic Derivative Discriminants

Abstract

Over the past decade, pattern decoding techniques have granted neuroscientists improved anatomical specificity in mapping neural representations associated with function and cognition. Dynamical patterns are of particular interest, as evidenced by the proliferation and success of frequency domain methods that reveal structured spatiotemporal rhythmic brain activity. One drawback of such approaches, however, is the need to estimate spectral power, which limits the temporal resolution of classification. We propose an alternative method that enables classification of dynamical patterns with high temporal fidelity. The key feature of the method is a conversion of time-series into their temporal derivatives. By doing so, dynamically-coded information may be revealed in terms of geometric patterns in the phase space of the derivative signal. We derive a geometric classifier for this problem which simplifies into a straightforward calculation in terms of covariances. We demonstrate the relative advantages and disadvantages of the technique with simulated data and benchmark its performance with an EEG dataset of covert spatial attention. By mapping the weights anatomically we reveal a retinotopic organization of covert spatial attention. We especially highlight the ability of the method to provide strong group-level classification performance compared to existing benchmarks, while providing information that is synergistic to classical spectral-based techniques. The robustness and sensitivity of the method to noise is also examined relative to spectral-based techniques. The proposed classification technique enables decoding of dynamic patterns with high temporal resolution, performs favorably to benchmark methods, and facilitates anatomical inference.