Optimizing optimization: accurate detection of hidden interactions in active body systems from noisy data

Given deficient and noisy movement data from a pedestrian crowd—a class of active body systems, is it possible to uncover the hidden group interaction patterns or connections? Yes, it is possible. Here, we develop a general framework based on an optimal combination of the conventional compressive sensing (\(L_1\) minimization) and \(L_2\) optimization procedure to achieve optimal detection of the contact network embedded in pedestrian crowd under the data shortage conditions. Different from previous publications, in our framework, the optimal weights of the \(L_1\) and \(L_2\) components in the combination can be determined specifically from the noisy data, which can obtain more accurate detection for the corresponding system. To detect hidden interaction patterns from spatiotemporal data has broader applications, and our optimized compressive sensing-based framework provides a practically viable solution. In addition, we provide a relative entropy perspective to facilitate more general theoretical and technological extensions of the framework.