The covariance perceptron: A new paradigm for classification and processing of time series in recurrent neuronal networks
Fig 2
From mean-based to covariance-based time-series classification.
A: Network with n = 2 output nodes generates a time series (in dark brown on the right) from the noisy time series of m = 10 input nodes (in light brown on the left). The afferent (feed-forward) connections B (green links and green arrow) and, when existing, recurrent connections A (purple dashed links and arrow) determine the input-output mapping. We observe the time series over a window of duration d. B: Each set of time series in panel A corresponds to a covariance pattern, namely an m × m matrix for the inputs on the left-hand side and an n × n matrix for the output on the right-hand side, where darker pixels indicate higher values. See Eq (7) for the formal definition of the averaging over the observation window of length d in panel A. As an example, we define two categories (or classes) that are represented by larger variance of either of the two nodes, node 1 for the red category and node 2 for the blue category. The classification scheme is implemented by tuning the connectivity weights A and B such that several input covariance patterns are mapped to the single output covariance pattern of the corresponding category. C: As a comparison, considering the mean activities instead of the within-trial covariances, corresponds to the mapping between input and output vectors in Eq (6), which can be formalized in the context of the classical perceptron (linear or non-linear). There, the categories for the input pattern (m-dimensional vectors on the left-hand side) are defined by the output pattern (n-dimensional vector on the right-hand side), the red category with neuron 1 highly active and the blue category with neuron 2 highly active.