Single Port Laparoscopic Surgery for Right Colon Cancer Cause Analysis for Conversion to Laparotomy

Pham, Trung Vy; Pham, Nhu Hiep; Le, Loc; Lê, Minh Tâm; Bui, Duc Phu; Ho, Huu Thien; Phạm, Anh Vũ; Phan, Hai Thanh; Nguyễn, Thanh Xuân; Tran, Nghiem Trung; Van, Tien Nhan; Tran, Sy Doan Diem; Pham, Xuan Dong; Hieu, Trung

doi:10.34071/jmp.2014.4_5.14

Cited by 5 publications

(11 citation statements)

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“…The π-subproblem is equivalent to the entropic regularized unbalanced optimal transport problem. Thus, we adopt the Sinkhorn algorithm for unbalanced optimal transport to solve the subproblem for π [11,26].…”

Section: Bregman Proximal Alternating Linearized Methods (Bpalm)mentioning

confidence: 99%

Outlier-Robust Gromov Wasserstein for Graph Data

Kong¹,

Li²,

So³

2023

Preprint

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Gromov Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. It has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is known to be highly sensitive to outliers, which can result in large inaccuracies if the outliers are given the same weight as other samples in the objective function. To mitigate this issue, we introduce a new and robust version of the GW distance called RGW. RGW features optimistically perturbed marginal constraints within a ϕ-divergence based ambiguity set. To make the benefits of RGW more accessible in practice, we develop a computationally efficient algorithm, Bregman proximal alternating linearization minimization, with a theoretical convergence guarantee. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of RGW on real-world graph learning tasks, such as subgraph matching and partial shape correspondence.

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Section: Bregman Proximal Alternating Linearized Methods (Bpalm)mentioning

confidence: 99%

Outlier-Robust Gromov Wasserstein for Graph Data

Kong¹,

Li²,

So³

2023

Preprint

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“…For example, (Altschuler, Niles-Weed, and Rigollet 2017), (Lin, Ho, and Jordan 2019b), and (Alaya et al 2019) proposed using greedy, randomized, and safe-screening strategies, respectively, to efficiently update the dual variables. Primal-dual algorithms have received much attention (Dvurechensky, Gasnikov, and Kroshnin 2018;Lin, Ho, and Jordan 2019a;Guo, Ho, and Jordan 2020) because they report faster computation than the Sinkhorn algorithm and its variants but are rarely used in practice due to the difficulty of implementation (Pham et al 2020). This paper focuses on the network simplex algorithm and Sinkhorn algorithm because they are widely used.…”

Section: Related Workmentioning

confidence: 99%

Optimal Transport with Cyclic Symmetry

Takeda,

Akagi,

Marumo

et al. 2024

AAAI

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We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph processing. Our main idea is to reduce OT to a small optimization problem that has significantly fewer variables by utilizing cyclic symmetry and various optimization techniques. On the basis of this reduction, our algorithms solve the small optimization problem instead of the original OT. As a result, our algorithms obtain the optimal solution and the objective function value of the original OT faster than solving the original OT directly. In this paper, our focus is on two crucial OT formulations: the linear programming OT (LOT) and the strongly convex-regularized OT, which includes the well-known entropy-regularized OT (EROT). Experiments show the effectiveness of our algorithms for LOT and EROT in synthetic/real-world data that has a strict/approximate cyclic symmetry structure. Through theoretical and experimental results, this paper successfully introduces the concept of symmetry into the OT research field for the first time.

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“…These systems are related to the unbalanced optimal transport in machine learning [60][61][62][63][64].…”

Section: Envara For Chemical Reactionsmentioning

confidence: 99%