LMNN

LMNN stands for Local Metric Learning for Nearest Neighbors. It is a distance metric learning algorithm that aims to learn a similarity metric from labeled data. The goal of LMNN is to find a metric that correctly classifies new data points by ensuring that points belonging to the same class are close together, while points from different classes are far apart. This is achieved by minimizing a cost function that penalizes misclassifications based on a learned distance.

The algorithm works by identifying "impostors" - data points from different classes that are closer to a given point than its "nearest neighbors" from the same class. LMNN then adjusts the learned metric to pull these impostors further away and push the same-class neighbors closer. This iterative process refines the distance metric to better reflect the underlying class structure of the data.

LMNN is a supervised learning technique, meaning it requires labeled training data to learn the optimal metric. It has been applied to various tasks, including classification, retrieval, and dimensionality reduction. Its effectiveness often depends on the quality and representativeness of the training data. Compared to some other metric learning methods, LMNN can be more robust to noisy data and can learn more discriminative metrics.