Nearest subspace classification with missing data

We consider the problem of multi-class classification when there are missing entries in both the training samples and the test samples. A modified version of the nearest subspace classifier is proposed and analyzed to handle missing data. We show the performance of the nearest subspace classifier is close to its counterpart when no missing data are present as long as the probability of observing each entry in the training set is δ ≳ O((log M/n_i)¹/²), where M is the sample dimension and ni ≳ O(log M) is the training size of the ith class. Finally, numerical results are provided for digit recognition when only a subset of the pixels are observed.