Online logistic regression on manifolds

This paper describes a new method for online logistic regression when the feature vectors lie close to a low-dimensional manifold and when observations of the feature vectors may be noisy or have missing elements. The new method exploits the low-dimensional structure of the feature vector, finds a multi-scale union of linear subsets that approximates the manifold, and performs online logistic regression separately on each subset. The union of subsets enables better performance in the face of noisy and missing data, and offsets challenges associated with the curse of dimensionality. The effectiveness of the proposed method in predicting correct labels of the data and in adapting to slowly time-varying manifolds are demonstrated using numerical examples and real data.