Multiscale Graph Construction Using Non-local Cluster Features

This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain the hierarchical clusters, existing methods often use graph clustering; however, they may ignore signal variations. As a result, these methods could fail to detect the clusters having similar features on nodes. In this paper, we consider graph and node-wise features simultaneously for multiscale clustering of a graph. With given clusters of the graph, the clusters are merged hierarchically in three steps: 1) Feature vectors in the clusters are extracted. 2) Similarities among cluster features are calculated using optimal transport. 3) A variable $k$-nearest neighbor graph (V$k$NNG) is constructed and graph spectral clustering is applied to the V$k$NNG to obtain clusters at a coarser scale. Additionally, the multiscale graph in this paper has \textit{non-local} characteristics: Nodes with similar features are merged even if they are spatially separated. In experiments on multiscale image and point cloud segmentation, we demonstrate the effectiveness of the proposed method.

Time-Varying Graph Signal Estimation among Multiple Sub-Networks

This paper presents an estimation method for time-varying graph signals among multiple sub-networks. In many sensor networks, signals observed are associated with nodes (i.e., sensors), and edges of the network represent the inter-node connectivity. For a large sensor network, measuring signal values at all nodes over time requires huge resources, particularly in terms of energy consumption. To alleviate the issue, we consider a scenario that a sub-network, i.e., cluster, from the whole network is extracted and an intra-cluster analysis is performed based on the statistics in the cluster. The statistics are then utilized to estimate signal values in another cluster. This leads to the requirement for transferring a set of parameters of the sub-network to the others, while the numbers of nodes in the clusters are typically different. In this paper, we propose a cooperative Kalman filter between two sub-networks. The proposed method alternately estimates signals in time between two sub-networks. We formulate a state-space model in the source cluster and transfer it to the target cluster on the basis of optimal transport. In the signal estimation experiments of synthetic and real-world signals, we validate the effectiveness of the proposed method.

Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node $i$, to determine its polarity $\beta_i \in \{-1,1\}$ and edge weights $\{w_{i,j}\}_{j=1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce ``consistent" signs of edge weights $\{w_{i,j}\}_{j=1}^N$ with the polarities of connected nodes -- i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adapt projections on convex set (POCS) to determine a suitable CLIME parameter $\rho > 0$ that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver in $\mathcal{O}(N^{2.055})$. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph convolutional networks (GCNs) designed for positive graphs on signed graphs.

Single-channel electroencephalography decomposition by detector-atom network and its pre-trained model

This paper presents a novel single-channel decomposition approach to facilitate the decomposition of electroencephalography (EEG) signals recorded with limited channels. Our model posits that an EEG signal comprises short, shift-invariant waves, referred to as atoms. We design a decomposer as an artificial neural network aimed at estimating these atoms and detecting their time shifts and amplitude modulations within the input signal. The efficacy of our method was validated across various scenarios in brain--computer interfaces and neuroscience, demonstrating enhanced performance. Additionally, cross-dataset validation indicates the feasibility of a pre-trained model, enabling a plug-and-play signal decomposition module.

Physics-Inspired Synthesized Underwater Image Dataset

This paper introduces the physics-inspired synthesized underwater image dataset (PHISWID), a dataset tailored for enhancing underwater image processing through physics-inspired image synthesis. Deep learning approaches to underwater image enhancement typically demand extensive datasets, yet acquiring paired clean and degraded underwater ones poses significant challenges. While several underwater image datasets have been proposed using physics-based synthesis, a publicly accessible collection has been lacking. Additionally, most underwater image synthesis approaches do not intend to reproduce atmospheric scenes, resulting in incomplete enhancement. PHISWID addresses this gap by offering a set of paired ground-truth (atmospheric) and synthetically degraded underwater images, showcasing not only color degradation but also the often-neglected effects of marine snow, a composite of organic matter and sand particles that considerably impairs underwater image clarity. The dataset applies these degradations to atmospheric RGB-D images, enhancing the dataset's realism and applicability. PHISWID is particularly valuable for training deep neural networks in a supervised learning setting and for objectively assessing image quality in benchmark analyses. Our results reveal that even a basic U-Net architecture, when trained with PHISWID, substantially outperforms existing methods in underwater image enhancement. We intend to release PHISWID publicly, contributing a significant resource to the advancement of underwater imaging technology.

Lossy Compression of Adjacency Matrices by Graph Filter Banks

This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal processing, machine learning, and data mining. In many problems of interest, these adjacency matrices can be large, so efficient compression methods are crucial. In this paper, we propose a lossy compression of weighted adjacency matrices, where the binary adjacency information is encoded losslessly (so the topological information of the graph is preserved) while the edge weights are compressed lossily. For the edge weight compression, the target graph is converted into a line graph, whose nodes correspond to the edges of the original graph, and where the original edge weights are regarded as a graph signal on the line graph. We then transform the edge weights on the line graph with a graph filter bank for sparse representation. Experiments on synthetic data validate the effectiveness of the proposed method by comparing it with existing lossy matrix compression methods.

Optimizing $k$ in $k$NN Graphs with Graph Learning Perspective

In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal processing. The parameter $k$ represents the number of neighbors that are connected to the target node; however, its appropriate selection is still a challenging problem. Therefore, most $k$NNGs use ad hoc selection methods for $k$. In the proposed method, we assume that a different $k$ can be chosen for each node. We formulate a discrete optimization problem to seek the best $k$ with a constraint on the sum of distances of the connected nodes. The optimal $k$ values are efficiently obtained without solving a complex optimization. Furthermore, we reveal that the proposed method is closely related to existing graph learning methods. In experiments on real datasets, we demonstrate that the $k$NNGs obtained with our method are sparse and can determine an appropriate variable number of edges per node. We validate the effectiveness of the proposed method for point cloud denoising, comparing our denoising performance with achievable graph construction methods that can be scaled to typical point cloud sizes (e.g., thousands of nodes).