Koki Yamada

Koki Yamada

The problem of recovering graph signals is one of the main topics in graph signal processing. A representative approach to this problem is the graph Wiener filter, which utilizes the statistical information of the target signal computed from historical data to construct an effective estimator. However, we often encounter situations where the current graph differs from that of historical data due to topology changes, leading to performance degradation of the estimator. This paper proposes a graph filter transfer method, which learns an effective estimator from historical data under topology changes. The proposed method leverages the probability density ratio of the current and historical observations and constructs an estimator that minimizes the reconstruction error in the current graph domain. The experiment on synthetic data demonstrates that the proposed method outperforms other methods.

Katsuki Fukumoto, Koki Yamada, Yuichi Tanaka et al.

We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal processing, machine learning, and data mining. Although most existing studies focus on the clustering of nodes in static graphs, we often encounter time-varying graphs for time-series data, e.g., social networks, brain functional connectivity, and point clouds. In this paper, we formulate a node clustering of time-varying graphs as an optimization problem based on spectral clustering, with a smoothness constraint of the node labels. We solve the problem with a primal-dual splitting algorithm. Experiments on synthetic and real-world time-varying graphs are performed to validate the effectiveness of the proposed approach.

Masatoshi Nagahama, Koki Yamada, Yuichi Tanaka et al.

Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the sensing process, thus requiring restoration. In this paper, we propose two graph signal restoration methods based on deep algorithm unrolling (DAU). First, we present a graph signal denoiser by unrolling iterations of the alternating direction method of multiplier (ADMM). We then suggest a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second approach, the unrolled ADMM-based denoiser is incorporated as a submodule, leading to a nested DAU structure. The parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Our approach is interpretable and keeps the number of parameters small since we only tune graph-independent regularization parameters. We overcome two main challenges in existing graph signal restoration methods: 1) limited performance of convex optimization algorithms due to fixed parameters which are often determined manually. 2) large number of parameters of graph neural networks that result in difficulty of training. Several experiments for graph signal denoising and interpolation are performed on synthetic and real-world data. The proposed methods show performance improvements over several existing techniques in terms of root mean squared error in both tasks.

Kazuma Iwata, Koki Yamada, Yuichi Tanaka

We propose a blind deconvolution method for signals on graphs, with the exact sparseness constraint for the original signal. Graph blind deconvolution is an algorithm for estimating the original signal on a graph from a set of blurred and noisy measurements. Imposing a constraint on the number of nonzero elements is desirable for many different applications. This paper deals with the problem with constraints placed on the exact number of original sources, which is given by an optimization problem with an $\ell_0$ norm constraint. We solve this non-convex optimization problem using the ADMM iterative solver. Numerical experiments using synthetic signals demonstrate the effectiveness of the proposed method.

Haruki Yokota, Koki Yamada, Yuichi Tanaka et al.

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of available measurements. To achieve this, we introduce two regularization terms in convex optimization problems that constrain sparseness of temporal variations of the time-varying networks. Moreover, a computationally-scalable algorithm is introduced to efficiently solve the optimization problem. The experimental results with synthetic and real datasets (point cloud and temperature data) demonstrate our proposed method outperforms the existing state-of-the-art methods.