Robust Tensor Clustering with Non-Greedy Maximization

Abstract

Tensors are increasingly common in several areas such as data mining, computer graphics, and computer vision. Tensor clustering is a fundamental tool for data analysis and pattern discovery. However, there usually exist outlying data points in real world datasets, which will reduce the performance of clustering. This motivates us to develop a tensor clustering algorithm that is robust to the outliers. In this paper, we propose an algorithm of Robust Tensor Clustering (RTC). The RTC firstly finds a lower rank approximation of the original tensor data using a L1 norm optimization function. Because the L1 norm doesn't exaggerate the effect of outliers compared with L2 norm, the minimization of the L1 norm approximation function makes RTC robust to outliers. Then we compute the HOSVD decomposition of this approximate tensor to obtain the final clustering results. Different from the traditional algorithm solving the approximation function with a greedy strategy, we utilize a non-greedy strategy to obtain a better solution. Experiments demonstrate that RTC has better performance than the state-of-the-art algorithms and is more robust to outliers.