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

Learning Hypergraph-regularized Attribute Predictors

We present a novel attribute learning framework named Hypergraph-based Attribute Predictor (HAP). In HAP, a hypergraph is leveraged to depict the attribute relations in the data. Then the attribute prediction problem is casted as a regularized hypergraph cut problem in which HAP jointly learns a collection of attribute projections from the feature space to a hypergraph embedding space aligned with the attribute space. The learned projections directly act as attribute classifiers (linear and kernelized). This formulation leads to a very efficient approach. By considering our model as a multi-graph cut task, our framework can flexibly incorporate other available information, in particular class label. We apply our approach to attribute prediction, Zero-shot and $N$-shot learning tasks. The results on AWA, USAA and CUB databases demonstrate the value of our methods in comparison with the state-of-the-art approaches.Comment: This is an attribute learning paper accepted by CVPR 201

Recent Advances of Manifold Regularization

Semi-supervised learning (SSL) that can make use of a small number of labeled data with a large number of unlabeled data to produce significant improvement in learning performance has been received considerable attention. Manifold regularization is one of the most popular works that exploits the geometry of the probability distribution that generates the data and incorporates them as regularization terms. There are many representative works of manifold regularization including Laplacian regularization (LapR), Hessian regularization (HesR) and p-Laplacian regularization (pLapR). Based on the manifold regularization framework, many extensions and applications have been reported. In the chapter, we review the LapR and HesR, and we introduce an approximation algorithm of graph p-Laplacian. We study several extensions of this framework for pairwise constraint, p-Laplacian learning, hypergraph learning, etc

New Approaches in Multi-View Clustering

Many real-world datasets can be naturally described by multiple views. Due to this, multi-view learning has drawn much attention from both academia and industry. Compared to single-view learning, multi-view learning has demonstrated plenty of advantages. Clustering has long been serving as a critical technique in data mining and machine learning. Recently, multi-view clustering has achieved great success in various applications. To provide a comprehensive review of the typical multi-view clustering methods and their corresponding recent developments, this chapter summarizes five kinds of popular clustering methods and their multi-view learning versions, which include k-means, spectral clustering, matrix factorization, tensor decomposition, and deep learning. These clustering methods are the most widely employed algorithms for single-view data, and lots of efforts have been devoted to extending them for multi-view clustering. Besides, many other multi-view clustering methods can be unified into the frameworks of these five methods. To promote further research and development of multi-view clustering, some popular and open datasets are summarized in two categories. Furthermore, several open issues that deserve more exploration are pointed out in the end