Adaptive reverse graph learning for robust subspace learning

Subspace learning decreases the dimensions for high-dimensional data by projecting the original data into a low-dimensional subspace, as well as preserving the similarity among data points. Besides, this way has been becoming one of the popular techniques of dimensionality reduction. However, many previous methods either conduct the transformation process or preserve the similarity structure on the original space, which usually contains redundancy and noise. As a result, the effectiveness of subspace learning is affected. Therefore, we design two strategies to minimize the impact of both redundancy and noisy data from the original space, i.e., reverse graph embedding and robust estimators. Specifically, we use the reverse graph embedding in the original space to learn the transformation projection, considering local relation among data from the low-dimensional subspace. We also automatically distribute large weights and small values, respectively, to important samples and unimportant samples by robust estimators for decreasing the effect of redundancy and noise. Moreover, we combine these two strategies to construct subspace learning in one architecture. Experiments on 12 practical and 2 location-based social network datasets show that the proposed method is superior to other subspace learning methods of state-of-the-art selection, regarding different evaluation metrics.