I had my kick-off meeting with Professor Verma on May 10 to discuss the scope of my research project, which involves an exploration of a metric learning algorithm that separates data in pre-defined clusters, but retains the structural integrity (to be defined) of each cluster. Since I have little knowledge in metric learning, Professor Verma suggested that I read the Mahalanobic Metric for Clustering (Xing et al., 2002) and Large Margin Nearest Neighbor (Weinberger and Saul, 2009) papers to get a sense for some of the existing methodologies.

MMC is one of the early papers in metric learning that presents it as a convex optimization problem, but makes an implicit assumption on the underlying distribution of the data, which ends up increasing the kNN error rate. LMNN learns the Mahalanobic distance for kNN classification using semidefinite programming, which is also a convex optimization; but in contrast, LMNN only penalizes large distances between target neighbors (as opposed to all examples in the same class), which appears to show better results.

The learning curve is steep as there is a fair amount of background knowledge I needed to acquire (via Wikipedia and Google search!) before I could understand the technical details of the papers, but I very much enjoyed the process!