LearnMet: Learning domain-specific distance metrics for plots of scientific functions

Scientific experimental results are often depicted as plots of functions to aid their visual analysis and comparison. In computationally comparing these plots using techniques such as similarity search and clustering, the notion of similarity is typically distance. However, it is seldom known which distance metric(s) best preserve(s) semantics in the respective domain. It is thus desirable to learn such domain-specific distance metrics for the comparison of plots. This paper describes a technique called LearnMet proposed to learn such metrics. The input to LearnMet is a training set with actual clusters of plots. These are iteratively compared with clusters over the same plots predicted using an arbitrary but fixed clustering algorithm. Using a guessed initial metric for clustering, adjustments are made to the metric in each epoch based on the error between the predicted and actual clusters until the error is minimal or below a given threshold. The metric giving the lowest error is output as the learned metric. The proposed LearnMet technique and its enhancements are discussed in detail in this paper. The primary application of LearnMet is clustering plots in the Heat Treating domain. Hence it is rigorously evaluated using Heat Treating data. Given distinct test sets for evaluation, clusters of plots predicted using the learned metrics are compared with given actual clusters over the same plots. The extent to which the predicted and actual clusters match each other denotes the accuracy of the learned metrics.