Sparse distance metric learning

Nearest neighbour classification requires a good distance metric. Previous approaches try to learn a quadratic distance metric learning so that observations of different classes are well separated. For high-dimensional problems, where many uninformative 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. We investigate the -regularized metric learning problem, making a connection with the Lasso algorithm in the linear least squared settings. We show that the fitted transformation matrix is close to the desired transformation matrix in -norm by assuming a version of the compatibility condition.