Search Results for author:
Found 33 papers, 15 papers with code
Riemannian preconditioning for tensor completion
We propose a novel Riemannian preconditioning approach for the tensor completion problem with rank constraint.
Duration and Interval Hidden Markov Model for Sequential Data Analysis
Analysis of sequential event data has been recognized as one of the essential tools in data modeling and analysis field.
Online Low-Rank Tensor Subspace Tracking from Incomplete Data by CP Decomposition using Recursive Least Squares
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
A Riemannian gossip approach to decentralized matrix completion
In this paper, we propose novel gossip algorithms for the low-rank decentralized matrix completion problem.
Riemannian stochastic variance reduced gradient on Grassmann manifold
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.
Low-rank tensor completion: a Riemannian manifold preconditioning approach
We propose a novel Riemannian manifold preconditioning approach for the tensor completion problem with rank constraint.
Network Volume Anomaly Detection and Identification in Large-scale Networks based on Online Time-structured Traffic Tensor Tracking
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.
State Duration and Interval Modeling in Hidden Semi-Markov Model for Sequential Data Analysis
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.
Riemannian stochastic variance reduced gradient algorithm with retraction and vector transport
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions.
Riemannian stochastic quasi-Newton algorithm with variance reduction and its convergence analysis
The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR).
A Riemannian gossip approach to subspace learning on Grassmann manifold
Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others.
Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations
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.
SGDLibrary: A MATLAB library for stochastic gradient descent algorithms
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.
Stochastic variance reduced multiplicative update for nonnegative matrix factorization
Nonnegative matrix factorization (NMF), a dimensionality reduction and factor analysis method, is a special case in which factor matrices have low-rank nonnegative constraints.
Low-rank geometric mean metric learning
We propose a low-rank approach to learning a Mahalanobis metric from data.
Riemannian Stochastic Recursive Gradient Algorithm with Retraction and Vector Transport and Its Convergence Analysis
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.
McTorch, a manifold optimization library for deep learning
In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch.
Inexact trust-region algorithms on Riemannian manifolds
We consider an inexact variant of the popular Riemannian trust-region algorithm for structured big-data minimization problems.
Riemannian adaptive stochastic gradient algorithms on matrix manifolds
We propose novel stochastic gradient algorithms for problems on Riemannian matrix manifolds by adapting the row and column subspaces of gradients.
Riemannian joint dimensionality reduction and dictionary learning on symmetric positive definite manifold
Dictionary leaning (DL) and dimensionality reduction (DR) are powerful tools to analyze high-dimensional noisy signals.
Riemannian optimization on the simplex of positive definite matrices
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 $i = \{1,\ldots, K \}$.
Graph embedding using multi-layer adjacent point merging model
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs.
Wasserstein k-means with sparse simplex projection
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.
Consistency-aware and Inconsistency-aware Graph-based Multi-view Clustering
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.
LCS Graph Kernel Based on Wasserstein Distance in Longest Common Subsequence Metric Space
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.
Manifold optimization for non-linear optimal transport problems
In this work, we discuss how to computationally approach general non-linear OT problems within the framework of Riemannian manifold optimization.
Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transport
To this end, addressing a convex semi-relaxed OT, we propose a fast block-coordinate Frank-Wolfe (BCFW) algorithm, which gives sparse solutions.
Wasserstein Weisfeiler-Lehman Subtree Distance for Graph-Structured Data
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.
On the Convergence of Semi-Relaxed Sinkhorn with Marginal Constraint and OT Distance Gaps
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.
Block-coordinate Frank-Wolfe algorithm and convergence analysis for semi-relaxed optimal transport problem
As a superior alternative, we propose a fast block-coordinate Frank-Wolfe (BCFW) algorithm for a convex semi-relaxed OT.
Wasserstein Graph Distance Based on $L_1$-Approximated Tree Edit Distance between Weisfeiler-Lehman Subtrees
In this paper, we propose a novel graph metric called the Wasserstein WL Subtree (WWLS) distance to address this problem.
Safe Screening for Unbalanced Optimal Transport
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.
Anchor Space Optimal Transport: Accelerating Batch Processing of Multiple OT Problems
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.
