Prof. Xinwang Liu
Title: SimpleMKKM: Simple Multiple Kernel k-means
Xinwang Liu received his PhD degree from National University of Defense Technology (NUDT), China, in 2013. He is now Professor at School of Computer, NUDT. His current research interests include kernel learning, multi-view clustering and unsupervised feature learning. Dr. Liu has published 100+ peer-reviewed papers, including those in highly regarded journals and conferences such as IEEE T-PAMI, IEEE T-KDE, IEEE T-IP, IEEE T-NNLS, IEEE T-MM, IEEE T-IFS, ICML, NeurIPS, CVPR, ICCV, AAAI, IJCAI, etc. He is an Associate Editor of IEEE T-NNLS and Information Fusion Journal. More information can be found at https://xinwangliu.github.io/.
We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given by an intractable minimization-maximization problem in the kernel coefficient and clustering partition matrix. To optimize it, we equivalently rewrite the minimization-maximization formulation as a minimization of an optimal value function, prove its differenentiablity, and design a reduced gradient descent algorithm to decrease it. Furthermore, we prove that the resultant solution of SimpleMKKM is the global optimum. We theoretically analyze the performance of SimpleMKKM in terms of its clustering generalization error. Finally, we briefly introduce two variants of SimpleMKKM.