Adaptive Neighborhood MinMax Projections

Dimensionality reduction as one of most attractive topics in machine learning research area has aroused extensive attentions in recent years. In order to preserve the local structure of data, most of dimensionality reduction methods consider constructing the relationships among each sample and its k nearest neighbors, and they find the neighbors in original space by using Euclidean distance. Since the data in original space contain some noises and redundant features, finding the neighbors in original space is incorrect and may degrade the subsequent performance. Therefore, how to find the optimal k nearest neighbors for each sample is the key point to improve the robustness of model. In this paper, we propose a novel dimensionality reduction method, named Adaptive Neighborhood MinMax Projections (ANMMP) which finds the neighbors in the optimal subspace by solving Trace Ratio problem in which the noises and redundant features have been removed already. Meanwhile, the samples within same class are pulled together while the samples between different classes are pushed far away in such learned subspace. Besides, proposed model is a general approach which can be implemented easily and applied on other methods to improve the robustness. Extensive experiments conducted on several synthetic data and real-world data sets and achieve some encouraging performance with comparison to metric learning and feature extraction methods, which demonstrates the efficiency of our method.