Multi-view local linear KNN classification: theoretical and experimental studies on image classification

When handling special multi-view scenarios where data from each view keep the same features, we may perhaps encounter two serious challenges: (1) samples from different views of the same class are less similar than those from the same view but different class, which sometimes happen in local way in both training and/or testing phases; (2) training an explicit prediction model becomes unreliable and even infeasible for test samples in multi-view scenarios. In this study, we prefer the philosophy of the k nearest neighbor method (KNN) to circumvent the second challenge. Without an explicit prediction model trained directly from the above multi-view data, a new multi-view local linear k nearest neighbor method (MV-LLKNN) is then developed to circumvent the two challenges so as to predict the label of each test sample. MV-LLKNN has its two reliable assumptions. One is the theoretically and experimentally provable assumption that any test sample can be well approximated by a linear combination of its neighbors in the multi-view training dataset. The other assumes that these neighbors should demonstrate their clustering property according to certain commonality-based similarity measure between the multi-view test sample and these multi-view neighbors so as to avoid the first challenge. MV-LLKNN can realize its effective prediction for a test multi-view sample by cheaply using both on-hand fast iterative shrinkage thresholding algorithm (FISTA) and KNN. Our theoretical analysis and experimental results about real multi-view face datasets indicate the effectiveness of MV-LLKNN.