A method implements a virtual machine for interactive visual analysis. The method receives a data visualization data flow graph, which is a directed graph including data nodes and transform nodes. Each transform node specifies a set of inputs for retrieval, where each input corresponds to a data node. Each transform node also specifies a transform operator that identifies an operation to be performed on the inputs. Some transform nodes specify (a) a set of outputs corresponding to respective data nodes and (b) a function for use in performing the operation of the transform node. The method traverses the data flow graph according to directions of arcs between nodes in the data flow graph, thereby retrieving data corresponding to each data node and executing the respective transformation operator specified for each of the transform nodes. This generates a data visualization according to transform nodes that specify graphical rendering.