High-Order Co-Clustering via Strictly Orthogonal and Symmetric L1-Norm Nonnegative Matrix Tri-Factorization

High-Order Co-Clustering via Strictly Orthogonal and Symmetric L1-Norm Nonnegative Matrix Tri-Factorization

Kai Liu, Hua Wang

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
Main track. Pages 2454-2460. https://doi.org/10.24963/ijcai.2018/340

Different to traditional clustering methods that deal with one single type of data, High-Order Co- Clustering (HOCC) aims to cluster multiple types of data simultaneously by utilizing the inter- or/and intra-type relationships across different data types. In existing HOCC methods, data points routinely enter the objective functions with squared residual errors. As a result, outlying data samples can dominate the objective functions, which may lead to incorrect clustering results. Moreover, existing methods usually suffer from soft clustering, where the probabilities to different groups can be very close. In this paper, we propose an L1 -norm symmetric nonnegative matrix tri-factorization method to solve the HOCC problem. Due to the orthogonal constraints and the symmetric L1 -norm formulation in our new objective, conventional auxiliary function approach no longer works. Thus we derive the solution algorithm using the alternating direction method of multipliers. Extensive experiments have been conducted on a real world data set, in which promising empirical results, including less time consumption, strictly orthogonal membership matrix, lower local minima etc., have demonstrated the effectiveness of our proposed method.
Keywords:
Machine Learning: Unsupervised Learning
Machine Learning Applications: Applications of Unsupervised Learning
Machine Learning: Clustering