MIMO Multiway Relaying with Clustered Full Data Exchange: Signal Space Alignment and Degrees of Freedom

We investigate achievable degrees of freedom (DoF) for a multiple-input multiple-output (MIMO) multiway relay channel (mRC) with $L$ clusters and $K$ users per cluster. Each user is equipped with $M$ antennas and the relay with $N$ antennas. We assume a new data exchange model, termed \emph{clustered full data exchange}, i.e., each user in a cluster wants to learn the messages of all the other users in the same cluster. Novel signal alignment techniques are developed to systematically construct the beamforming matrices at the users and the relay for efficient physical-layer network coding. Based on that, we derive an achievable DoF of the MIMO mRC with an arbitrary network configuration of $L$ and $K$, as well as with an arbitrary antenna configuration of $M$ and $N$. We show that our proposed scheme achieves the DoF capacity when $\frac{M}{N} \leq \frac{1}{LK-1}$ and $\frac{M}{N} \geq \frac{(K-1)L+1}{KL}$.Comment: 13 pages, 4 figure

Twin Learning for Similarity and Clustering: A Unified Kernel Approach

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.Comment: Published in AAAI 201