We present a novel approach to shared control of human-machine systems. Our method assumes no a priori knowledge of the system dynamics. Instead, we learn both the dynamics and information about the user's interaction from observation through the use of the Koopman operator. Using the learned model, we define an optimization problem to compute the optimal policy for a given task, and compare the user input to the optimal input. We demonstrate the efficacy of our approach with a user study. We also analyze the individual nature of the learned models by comparing the effectiveness of our approach when the demonstration data comes from a user's own interactions, from the interactions of a group of users and from a domain expert. Positive results include statistically significant improvements on task metrics when comparing a user-only control paradigm with our shared control paradigm. Surprising results include findings that suggest that individualizing the model based on a user's own data does not effect the ability to learn a useful dynamic system. We explore this tension as it relates to developing human-in-the-loop systems further in the discussion.
Abstract Background There is a broad need in neuroscience to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes recording dynamic brain activity over minutes to hours. Such datasets are characterized by coherent patterns across both space and time, yet existing computational methods are typically restricted to analysis either in space or in time separately. New method Here we report the adaptation of dynamic mode decomposition (DMD), an algorithm originally developed for studying fluid physics, to large-scale neural recordings. DMD is a modal decomposition algorithm that describes high-dimensional dynamic data using coupled spatial–temporal modes. The algorithm is robust to variations in noise and subsampling rate; it scales easily to very large numbers of simultaneously acquired measurements. Results We first validate the DMD approach on sub-dural electrode array recordings from human subjects performing a known motor task. Next, we combine DMD with unsupervised clustering, developing a novel method to extract spindle networks during sleep. We uncovered several distinct sleep spindle networks identifiable by their stereotypical cortical distribution patterns, frequency, and duration. Comparison with existing methods DMD is closely related to principal components analysis (PCA) and discrete Fourier transform (DFT). We may think of DMD as a rotation of the low-dimensional PCA space such that each basis vector has coherent dynamics. Conclusions The resulting analysis combines key features of performing PCA in space and power spectral analysis in time, making it particularly suitable for analyzing large-scale neural recordings. The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders. The presence of cyclic expansions and contractions in the economy has been known for over a century. The work reported here searches for similar cyclic behavior in stock valuations. The variations are subtle and can only be extracted through analysis of price variations of a large number of stocks. Koopman mode analysis is a natural approach to establish such collective oscillatory behavior. The difficulty is that even non-cyclic and stochastic constituents of a finite data set may be interpreted as a sum of periodic motions. However, deconvolution of these irregular dynamical facets may be expected to be non-robust, i.e., to depend on specific data set. We propose an approach to differentiate robust and non-robust features in a time series; it is based on identifying robust features with reproducible Koopman modes, i.e., those that persist between distinct sub-groupings of the data. Our analysis of stock data discovered four reproducible modes, one of which has period close to the number of trading days year. To the best of our knowledge these cycles were not reported previously. It is particularly interesting that the cyclic behaviors persisted through the great recession even though phase relationships between stocks within the modes evolved in the intervening period.