15 accepted papers
Graph neural networks (GNNs) face dual challenges of limited structural expressiveness and opaque decision-making processes. Recent research on Subgraph Neural Networks (SGNNs) enhance model expressiveness through subgraph ensembles. However, their reliance on predefined sampling strategies leads to
Multidimensional Scaling (MDS) is an essential technique in multivariate analysis, with Weighted MDS (WMDS) commonly employed for tasks such as dimensionality reduction and graph drawing. However, the optimization of WMDS poses significant challenges due to the highly non-convex nature of its object…
The Weisfeiler-Lehman (WL) test is a widely used algorithm in graph machine learning, including graph kernels, graph metrics, and graph neural networks. However, it focuses only on the consistency of the graph, which means that it is unable to detect slight structural differences. Consequently, this…
The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application to large-scale problems. To address this issue, loosening suc…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems, the graph class depends on not only the topological similarit…
Analysis of multi-view data has recently garnered growing attention because multi-view data frequently appear in real-world applications, which are collected or taken from many sources or captured using various sensors. A simple and popular promising approach is to learn a latent subspace shared by…
Efficient analysis of multiple sequential data is becoming necessary for identifying sequential patterns of multiple objects of interest. This analysis has major practical and technical importance because finding such patterns necessitates extraction and discovery of latent but meaningful groups of…
Network embedding is intended to produce low-dimensional vector representations of nodes in a network to preserve and extract the latent network structure, which has higher robustness to noise, outliers, and redundant data. Although a recently proposed multi-level nonnegative matrix factorization (N…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the intrinsic non-linear structure of the underlying manifold and the ab…
We consider an inexact variant of the popular Riemannian trust-region algorithm for structured big-data minimization problems. The proposed algorithm approximates the gradient and the Hessian in addition to the solution of a trust-region sub-problem. Addressing large-scale finite-sum problems, we sp…
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions on a Riemannian manifold. The present paper proposes a Riemannian stochastic recursive gradient algorithm (R-SRG), which does not require the inverse of re…
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and…
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Considering the stochastic learning in NMF, we specifically address the multiplicative update (MU) rule, which is the most…
We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint. A novel Riemannian metric or inner product is proposed that exploits the least-squares structure of the cost function and takes into account the structured symmetry that exists in…
We propose an online tensor subspace tracking algorithm based on the CP decomposition exploiting the recursive least squares (RLS), dubbed OnLine Low-rank Subspace tracking by TEnsor CP Decomposition (OLSTEC). Numerical evaluations show that the proposed OLSTEC algorithm gives faster convergence per…