Graph Regularized Non-negative Matrix Factorization By Maximizing Correntropy

Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are $l_2$ distance or Kullback-Leibler (KL) divergence. However, nonlinear cases are not properly handled when we use these error measures. As a consequence, alternative measures based on nonlinear kernels, such as correntropy, are proposed. However, the current correntropy-based NMF only targets on the low-level features without considering the intrinsic geometrical distribution of data. In this paper, we propose a new NMF algorithm that preserves local invariance by adding graph regularization into the process of max-correntropy-based matrix factorization. Meanwhile, each feature can learn corresponding kernel from the data. The experiment results of Caltech101 and Caltech256 show the benefits of such combination against other NMF algorithms for the unsupervised image clustering

Deep Metric Learning Assisted by Intra-variance in A Semi-supervised View of Learning

Deep metric learning aims to construct an embedding space where samples of the same class are close to each other, while samples of different classes are far away from each other. Most existing deep metric learning methods attempt to maximize the difference of inter-class features. And semantic related information is obtained by increasing the distance between samples of different classes in the embedding space. However, compressing all positive samples together while creating large margins between different classes unconsciously destroys the local structure between similar samples. Ignoring the intra-class variance contained in the local structure between similar samples, the embedding space obtained from training receives lower generalizability over unseen classes, which would lead to the network overfitting the training set and crashing on the test set. To address these considerations, this paper designs a self-supervised generative assisted ranking framework that provides a semi-supervised view of intra-class variance learning scheme for typical supervised deep metric learning. Specifically, this paper performs sample synthesis with different intensities and diversity for samples satisfying certain conditions to simulate the complex transformation of intra-class samples. And an intra-class ranking loss function is designed using the idea of self-supervised learning to constrain the network to maintain the intra-class distribution during the training process to capture the subtle intra-class variance. With this approach, a more realistic embedding space can be obtained in which global and local structures of samples are well preserved, thus enhancing the effectiveness of downstream tasks. Extensive experiments on four benchmarks have shown that this approach surpasses state-of-the-art method