Deep Learning methods, specifically convolutional neural networks (CNNs), have seen a lot of success in the domain of image-based data, where the data offers a clearly structured topology in the regular lattice of pixels. This 4-neighbourhood topological simplicity makes the application of convolutional masks straightforward for time series data, such as video applications, but many high-dimensional time series data are not organised in regular lattices, and instead values may have adjacency relationships with non-trivial topologies, such as small-world networks or trees. In our application case, human kinematics, it is currently unclear how to generalise convolutional kernels in a principled manner. Therefore we define and implement here a framework for general graph-structured CNNs for time series analysis. Our algorithm automatically builds convolutional layers using the specified adjacency matrix of the data dimensions and convolutional masks that scale with the hop distance. In the limit of a lattice-topology our method produces the well-known image convolutional masks. We test our method first on synthetic data of arbitrarily-connected graphs and human hand motion capture data, where the hand is represented by a tree capturing the mechanical dependencies of the joints. We are able to demonstrate, amongst other things, that inclusion of the graph structure of the data dimensions improves model prediction significantly, when compared against a benchmark CNN model with only time convolution layers
