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Kohonen's Self-Organizing Maps (SOMs) have proven to be a successful data-reduction method to identify the intrinsic lower-dimensional sub-manifold of a data set that is scattered in the higher-dimensional feature space. Motivated by the possibly non-Euclidian nature of the feature space and of the intrinsic geometry of the data set, we extend the definition of classic SOMs to obtain the General Riemannian SOM (GRiSOM). We additionally provide an implementation as a proof-of-concept forarXiv:1505.03917v1 fatcat:tyhrmjkuf5dx3gmjsfc6gamuem