Say you want to do K-Nearest Neighbour classification. Besides selecting K, you also have to chose a distance function, in order to define "nearest". I'll talk about a novel method for *learning* -- from the data itself -- a distance measure to be used in KNN classification. The learning algorithm, Neighbourhood Components Analysis (NCA) directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and very fast classification in high dimensions. Of course, the resulting classification model is non-parametric, making no assumptions about the shape of the class distributions or the boundaries between them. If time permits, I'll also talk about newer work on learning the same kind of distance metric for use inside a Gaussian Kernel SVM classifier.