Tree-based cluster modeling: simulation of a violin

Tree-based Cluster Weighted Modeling: Towards A Massively Parallel Real-Time Digital Stradivarius (1997)

Ed Boyden's class project for Neural Networks (9.641), Fall 1997. Based on work by Bernd Schoner, Chris Douglas, Chuck Cooper, and Neil Gershenfeld.

Abstract

Cluster-weighted modeling (CWM) is a versatile inference algorithm for deriving a functional relationship between input data and output data by using a mixture of expert clusters. Each cluster is localized to a Gaussian input region and possesses its own trainable local model. The CWM algorithm uses expectation-maximization (EM) to find the optimal locations of clusters in the input space and to solve for the parameters of the local model. However, the CWM algorithm requires interactions between all the data and all the clusters. For a violin, whose training might easily require over a billion data points and a hundred thousand clusters, such an implementation is clearly undesirable. We use a variant of CWM that makes splits in the data to model the time-series relationship between time-lagged values of human input data and digital audio output data. We describe how this tree implementation would lend itself to a multiprocessor parallelization of the CWM algorithm and examine the expected reduction in time and space requirements. We also consider how this method could be used to perform intelligent training of the violin.