Junya Hara

Reina Kaneko, Hayate Kojima, Kenta Yanagiya et al.

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.

Asuka Tamaru, Junya Hara, Hiroshi Higashi et al.

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).