82 citations · 324 across the 26 of their papers we have counts for
26 papers
Safe Screening for Unbalanced Optimal Transport
Xun Su, Zhongxi Fang, Hiroyuki Kasai
This paper introduces a framework that utilizes the Safe Screening technique to accelerate the optimization process of the Unbalanced Optimal Transport (UOT) problem by proactively…
Wasserstein Graph Distance Based on -Approximated Tree Edit Distance between Weisfeiler-Lehman Subtrees
Zhongxi Fang, Jianming Huang, Xun Su +1
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…
On the Convergence of Semi-Relaxed Sinkhorn with Marginal Constraint and OT Distance Gaps
Takumi Fukunaga, Hiroyuki Kasai
This paper presents consideration of the Semi-Relaxed Sinkhorn (SR-Sinkhorn) algorithm for the semi-relaxed optimal transport (SROT) problem, which relaxes one marginal constraint…
Block-coordinate Frank-Wolfe algorithm and convergence analysis for semi-relaxed optimal transport problem
Takumi Fukunaga, Hiroyuki Kasai
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-conservat…
Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transport
Takumi Fukunaga, Hiroyuki Kasai
Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Com…
Manifold optimization for non-linear optimal transport problems
Bamdev Mishra, N T V Satyadev, Hiroyuki Kasai +1
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in sev…
LCS Graph Kernel Based on Wasserstein Distance in Longest Common Subsequence Metric Space
Jianming Huang, Zhongxi Fang, Hiroyuki Kasai
For graph learning tasks, many existing methods utilize a message-passing mechanism where vertex features are updated iteratively by aggregation of neighbor information. This strat…
Wasserstein k-means with sparse simplex projection
Takumi Fukunaga, Hiroyuki Kasai
This paper presents a proposal of a faster Wasserstein -means algorithm for histogram data by reducing Wasserstein distance computations and exploiting sparse simplex projection…
Consistency-aware and Inconsistency-aware Graph-based Multi-view Clustering
Mitsuhiko Horie, Hiroyuki Kasai
Multi-view data analysis has gained increasing popularity because multi-view data are frequently encountered in machine learning applications. A simple but promising approach for c…
Graph embedding using multi-layer adjacent point merging model
Jianming Huang, Hiroyuki Kasai
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomo…
Riemannian optimization on the simplex of positive definite matrices
Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria
In this work, we generalize the probability simplex constraint to matrices, i.e., , where …
Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold
Hiroyuki Kasai, Bamdev Mishra
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals. This paper presents a proposal of a novel Riemannian joint d…
Riemannian adaptive stochastic gradient algorithms on matrix manifolds
Hiroyuki Kasai, Pratik Jawanpuria, Bamdev Mishra
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively ne…
McTorch, a manifold optimization library for deep learning
Mayank Meghwanshi, Pratik Jawanpuria, Anoop Kunchukuttan +2
In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch. It aims to lower the barrier for users wishing to use manifold constrai…
Low-rank geometric mean metric learning
Mukul Bhutani, Pratik Jawanpuria, Hiroyuki Kasai +1
We propose a low-rank approach to learning a Mahalanobis metric from data. Inspired by the recent geometric mean metric learning (GMML) algorithm, we propose a low-rank variant of…
SGDLibrary: A MATLAB library for stochastic gradient descent algorithms
Hiroyuki Kasai
We consider the problem of finding the minimizer of a function of the finite-sum form . This problem has…
Stochastic variance reduced multiplicative update for nonnegative matrix factorization
Hiroyuki Kasai
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints. Con…
Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations
Hiroyuki Kasai
We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional…
A Riemannian gossip approach to subspace learning on Grassmann manifold
Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria +1
In this paper, we focus on subspace learning problems on the Grassmann manifold. Interesting applications in this setting include low-rank matrix completion and low-dimensional mul…
Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis
Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra
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 Riema…
Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport
Hiroyuki Sato, Hiroyuki Kasai, Bamdev Mishra
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This pape…
Low-rank tensor completion: a Riemannian manifold preconditioning approach
Hiroyuki Kasai, Bamdev Mishra
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…
A Riemannian gossip approach to decentralized matrix completion
Bamdev Mishra, Hiroyuki Kasai, Atul Saroop
In this paper, we propose novel gossip algorithms for the low-rank decentralized matrix completion problem. The proposed approach is on the Riemannian Grassmann manifold that allow…
Riemannian stochastic variance reduced gradient on Grassmann manifold
Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite, number of loss functions. In this paper, we propose a novel…