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

Document Clustering Based On Max-Correntropy Non-Negative Matrix Factorization

Nonnegative matrix factorization (NMF) has been successfully applied to many areas for classification and clustering. Commonly-used NMF algorithms mainly target on minimizing the $l_2$ distance or Kullback-Leibler (KL) divergence, which may not be suitable for nonlinear case. In this paper, we propose a new decomposition method by maximizing the correntropy between the original and the product of two low-rank matrices for document clustering. This method also allows us to learn the new basis vectors of the semantic feature space from the data. To our knowledge, we haven't seen any work has been done by maximizing correntropy in NMF to cluster high dimensional document data. Our experiment results show the supremacy of our proposed method over other variants of NMF algorithm on Reuters21578 and TDT2 databasets.Comment: International Conference of Machine Learning and Cybernetics (ICMLC) 201

Partial Maximum Correntropy Regression for Robust Trajectory Decoding from Noisy Epidural Electrocorticographic Signals

The Partial Least Square Regression (PLSR) exhibits admirable competence for predicting continuous variables from inter-correlated brain recordings in the brain-computer interface. However, PLSR is in essence formulated based on the least square criterion, thus, being non-robust with respect to noises. The aim of this study is to propose a new robust implementation for PLSR. To this end, the maximum correntropy criterion (MCC) is used to propose a new robust variant of PLSR, called as Partial Maximum Correntropy Regression (PMCR). The half-quadratic optimization is utilized to calculate the robust projectors for the dimensionality reduction, and the regression coefficients are optimized by a fixed-point approach. We evaluate the proposed PMCR with a synthetic example and the public Neurotycho electrocorticography (ECoG) datasets. The extensive experimental results demonstrate that, the proposed PMCR can achieve better prediction performance than the conventional PLSR and existing variants with three different performance indicators in high-dimensional and noisy regression tasks. PMCR can suppress the performance degradation caused by the adverse noise, ameliorating the decoding robustness of the brain-computer interface