Reconstruction of network structures from marked point processes using multi-dimensional scaling

We propose a method of estimating network structures only from observed marked point processes using the multi-dimensional scaling. In this method, first, we calculate a spike time metric which quantifies a metric distance between the observed marked point processes. Next, to represent a relationship among point processes in the Euclidean space, we apply the multi-dimensional scaling to the metric distance between point processes. Then we apply the partialization analysis to the obtained coordinate vectors by the multi-dimensional scaling. As a result, we can estimate the network structures from multiple point processes even though the elements have many common spurious inputs from the other elements.