We present an approach for learning a reaction coordinate that can be used to enhance sampling directly between two biomolecular structures. The current method is based on our previous molecular simulation clustering algorithm entitled Size-and-Shape Space Gaussian Mixture Models (shapeGMM). By overcoming rotational invariance using robust alignment protocols, shapeGMM clusters molecular structures using particle positions. The result of shapeGMM is a set of cluster means and covariances that, unlike many internal coordinate methods, do not overdetermine the structures. shapeGMM was found to produce physically meaningful clusters on a 300-microsecond trajectory of a fast-folding HP35 Nle/Nle mutant; the trajectory was obtained from D. E. Shaw Research Institute. To further study the folding and unfolding pathways of this system, we compute a reaction coordinate between corresponding cluster means using Linear Discriminate Analysis (LDA); LDA is a supervised classification technique that identifies the linear coordinate which simultaneously maximizes the between cluster variance and minimizes the within cluster variance. Barriers in the free energy surface (FES) along the first linear discriminant (LD1) corresponded to the point where the committor is 0.5, suggesting this is a good reaction coordinate. Metadynamics simulations biased along LD1, a method we have implemented in PLUMED, achieved a FES in reasonable agreement with that generated from the long MD simulation, suggesting that LD1 is also a good sampling coordinate. FESs produced along coordinates obtained from subsets of the data close to the centers of the cluster means also agree well with the committor, suggesting this approach may be appropriate for situations where both states of a molecule are known, but extensive unbiased data is not available.