RETRACTED CHAPTER: Frame Networks

As an emerging branch of statistical and deep learning, frame networks can automatically acquire novel knowledge from observation data through a statistical learning process and then makes reliable predictions and downscaling. A frame network consists of three layers: the input layer, the hidden layer, and the output layer, where various frames are embedded into each node of the hidden layer and frame coefficients are used as the weight of the directed edges from one node to another node. Frame networks provide a unique nonlinear tool for simulation, downscaling, and prediction in the mining of big data. Different from frame networks, frames on networks deal with dynamical system living on complex networks and provide novel insights into topological and dynamical features of complex nonlinear systems over a wide range of spatial/temporal scales.