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 \(\ell 1\)-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 \(\ell 1\)-norm by assuming a version of the compatibility condition.
high-dimensional lasso sparse recovery multiclass consistency