Sparse distance metric learning - Choy, T (2014)
A good distance metric can improve the accuracy of a nearest neighbour classifier. Xing et al. (2002) proposed distance metric learning to find a linear transformation of the data so that observations of different classes are better separated. For high-dimensional problems where many un-informative variables are present, it is attractive to select a sparse distance metric, both to increase predictive accuracy but also to aid interpretation of the result. In this thesis, we investigate three different types of sparsity assumption for distance metric learning and show that sparse recovery is possible under each type of sparsity assumption with an appropriate choice of L1-type penalty. We show that a lasso penalty promotes learning a transformation matrix having lots of zero entries, a group lasso penalty recovers a transformation matrix having zero rows/columns and a trace norm penalty allows us to learn a low rank transformation matrix. The regularization allows us to consider a large number of covariates and we apply the technique to an expanded set of basis called rule ensemble to allow for a more flexible fit. Finally, we illustrate an application of the metric learning problem via a document retrieval example and discuss how similarity-based information can be applied to learn a classifier.