no code implementations • 30 Oct 2017 • 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.
no code implementations • 1 May 2017 • Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria, Atul Saroop
Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others.
no code implementations • 15 Mar 2017 • Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra
The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR).
no code implementations • 24 Aug 2016 • Hiromi Narimatsu, Hiroyuki Kasai
Therefore, we particularly examine the structure of sequential data, and extract the necessity of `state duration' and `state interval' of events for efficient and rich representation of sequential data.
no code implementations • 19 Aug 2016 • Hiroyuki Kasai, Wolfgang Kellerer, Martin Kleinsteuber
This problem is cast as a low-rank subspace tracking problem for normal flows under incomplete observations, and an outlier detection problem for abnormal flows.
no code implementations • 6 Jun 2015 • Hiroyuki Kasai, Bamdev Mishra
We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint.
no code implementations • 26 May 2016 • Hiroyuki Kasai, Bamdev Mishra
We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint.
no code implementations • 23 May 2016 • Bamdev Mishra, Hiroyuki Kasai, Atul Saroop
In this paper, we propose novel gossip algorithms for the low-rank decentralized matrix completion problem.
no code implementations • 20 Aug 2015 • Hiromi Narimatsu, Hiroyuki Kasai
Analysis of sequential event data has been recognized as one of the essential tools in data modeling and analysis field.
no code implementations • 11 Feb 2019 • Hiroyuki Kasai, Bamdev Mishra
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals.
no code implementations • 25 Jun 2019 • Bamdev Mishra, Hiroyuki Kasai, Pratik Jawanpuria
In this work, we generalize the probability simplex constraint to matrices, i. e., $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_K = \mathbf{I}$, where $\mathbf{X}_i \succeq 0$ is a symmetric positive semidefinite matrix of size $n\times n$ for all $i = \{1,\ldots, K \}$.
no code implementations • 28 Oct 2020 • Jianming Huang, Hiroyuki Kasai
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs.
no code implementations • 10 Mar 2021 • Takumi Fukunaga, Hiroyuki Kasai
To this end, addressing a convex semi-relaxed OT, we propose a fast block-coordinate Frank-Wolfe (BCFW) algorithm, which gives sparse solutions.
no code implementations • 29 Sep 2021 • Zhongxi Fang, Jianming Huang, Hiroyuki Kasai
Therefore, instead of using such categorical labels, we define a node distance between WL subtrees with tree edit distance and propose an efficient calculation algorithm.
no code implementations • 27 May 2022 • 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 of the standard OT problem.
no code implementations • 27 May 2022 • Takumi Fukunaga, Hiroyuki Kasai
As a superior alternative, we propose a fast block-coordinate Frank-Wolfe (BCFW) algorithm for a convex semi-relaxed OT.
no code implementations • 1 Jul 2023 • Xun Su, Zhongxi Fang, Hiroyuki Kasai
We demonstrate the feasibility of applying Safe Screening to the UOT problem with $\ell_2$-penalty and KL-penalty by conducting an analysis of the solution's bounds and considering the local strong convexity of the dual problem.
no code implementations • 24 Oct 2023 • Jianming Huang, Xun Su, Zhongxi Fang, Hiroyuki Kasai
Therefore, we propose a translated OT problem designated as the anchor space optimal transport (ASOT) problem, which is specially designed for batch processing of multiple OT problem solutions.
1 code implementation • 7 Dec 2020 • Jianming Huang, Zhongxi Fang, Hiroyuki Kasai
Therefore, we propose a novel metric space by exploiting the proposed LCS-based similarity, and compute a new Wasserstein-based graph distance in this metric space, which emphasizes more the comparison between similar paths.
1 code implementation • 14 Jun 2018 • Mukul Bhutani, Pratik Jawanpuria, Hiroyuki Kasai, Bamdev Mishra
We propose a low-rank approach to learning a Mahalanobis metric from data.
1 code implementation • 1 Mar 2021 • Bamdev Mishra, N T V Satyadev, Hiroyuki Kasai, Pratik Jawanpuria
In this work, we discuss how to computationally approach general non-linear OT problems within the framework of Riemannian manifold optimization.
1 code implementation • NeurIPS 2018 • Hiroyuki Kasai, Bamdev Mishra
We consider an inexact variant of the popular Riemannian trust-region algorithm for structured big-data minimization problems.
2 code implementations • 25 Nov 2020 • Mitsuhiko Horie, Hiroyuki Kasai
Among existing approaches, graph-based multi-view clustering (GMVC) achieves state-of-the-art performance by leveraging a shared graph matrix called the unified matrix.
1 code implementation • 9 Jul 2022 • Zhongxi Fang, Jianming Huang, Xun Su, Hiroyuki Kasai
In this paper, we propose a novel graph metric called the Wasserstein WL Subtree (WWLS) distance to address this problem.
1 code implementation • 25 Nov 2020 • Takumi Fukunaga, Hiroyuki Kasai
This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data by reducing Wasserstein distance computations and exploiting sparse simplex projection.
1 code implementation • 29 Sep 2017 • 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 linear subspace.
1 code implementation • 23 Feb 2016 • Hiroyuki Kasai
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 Analysis
1 code implementation • 18 Feb 2017 • 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.
1 code implementation • 24 May 2016 • Hiroyuki Kasai, Hiroyuki Sato, Bamdev Mishra
In this paper, we propose a novel Riemannian extension of the Euclidean stochastic variance reduced gradient algorithm (R-SVRG) to a compact manifold search space.
1 code implementation • ICML 2018 • 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 on a Riemannian manifold.
1 code implementation • 4 Feb 2019 • Hiroyuki Kasai, Pratik Jawanpuria, Bamdev Mishra
We propose novel stochastic gradient algorithms for problems on Riemannian matrix manifolds by adapting the row and column subspaces of gradients.
1 code implementation • 27 Oct 2017 • Hiroyuki Kasai
The purpose of the library is to provide researchers and implementers a comprehensive evaluation environment for the use of these algorithms on various ML problems.
1 code implementation • 3 Oct 2018 • Mayank Meghwanshi, Pratik Jawanpuria, Anoop Kunchukuttan, Hiroyuki Kasai, Bamdev Mishra
In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch.