JOTA paper is added

Author: ikeda46

content/posts/2025.08.JOTA.ja.md

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+---
+date: 2025-08-25
+publishDate: 2025-08-25
+title: Majorization-minimization Bregman proximal gradient algorithms for NMF with the Kullback--Leibler divergence
+tags: ["Journal Paper"]
+math: true
+draft: false
+---
+
+Accepted for publication in JOTA.
+
+### Authors:
+- Shota Takahashi
+- Mirai Tanaka
+- Shiro Ikeda
+
+### keywords:
+- Nonnegative Matrix Factorization
+- Bregman divergence
+- proximal gradient algorithm
+
+### URL:
+- <a href="https://arxiv.org/abs/2405.11185" target="_blank" rel="noopener">arXiv Link</a>
+
+---
+
+### Abstract:
+
+Nonnegative matrix factorization (NMF) is a popular method in machine learning and signal processing to decompose a given nonnegative matrix into two nonnegative matrices. In this paper, we propose new algorithms, called majorization-minimization Bregman proximal gradient algorithm (MMBPG) and MMBPG with extrapolation (MMBPGe) to solve NMF. These iterative algorithms minimize the objective function and its potential function monotonically. Assuming the Kurdyka--Łojasiewicz property, we establish that a sequence generated by MMBPG(e) globally converges to a stationary point. We apply MMBPG and MMBPGe to the Kullback--Leibler (KL) divergence-based NMF. While most existing KL-based NMF methods update two blocks or each variable alternately, our algorithms update all variables simultaneously. MMBPG and MMBPGe for KL-based NMF are equipped with a separable Bregman distance that satisfies the smooth adaptable property and that makes its subproblem solvable in closed form. Using this fact, we guarantee that a sequence generated by MMBPG(e) globally converges to a Karush--Kuhn--Tucker (KKT) point of KL-based NMF. In numerical experiments, we compare proposed algorithms with existing algorithms on synthetic data and real-world data.

content/posts/2025.08.JOTA.md

@@ -0,0 +1,29 @@
+---
+date: 2025-08-25
+publishDate: 2025-08-25
+title: Majorization-minimization Bregman proximal gradient algorithms for NMF with the Kullback--Leibler divergence
+tags: ["Journal Paper"]
+math: true
+draft: false
+---
+
+Accepted for publication in JOTA.
+
+### Authors:
+- Shota Takahashi
+- Mirai Tanaka
+- Shiro Ikeda
+
+### keywords:
+- Nonnegative Matrix Factorization
+- Bregman divergence
+- proximal gradient algorithm
+
+### URL:
+- <a href="https://arxiv.org/abs/2405.11185" target="_blank" rel="noopener">arXiv Link</a>
+
+---
+
+### Abstract:
+
+Nonnegative matrix factorization (NMF) is a popular method in machine learning and signal processing to decompose a given nonnegative matrix into two nonnegative matrices. In this paper, we propose new algorithms, called majorization-minimization Bregman proximal gradient algorithm (MMBPG) and MMBPG with extrapolation (MMBPGe) to solve NMF. These iterative algorithms minimize the objective function and its potential function monotonically. Assuming the Kurdyka--Łojasiewicz property, we establish that a sequence generated by MMBPG(e) globally converges to a stationary point. We apply MMBPG and MMBPGe to the Kullback--Leibler (KL) divergence-based NMF. While most existing KL-based NMF methods update two blocks or each variable alternately, our algorithms update all variables simultaneously. MMBPG and MMBPGe for KL-based NMF are equipped with a separable Bregman distance that satisfies the smooth adaptable property and that makes its subproblem solvable in closed form. Using this fact, we guarantee that a sequence generated by MMBPG(e) globally converges to a Karush--Kuhn--Tucker (KKT) point of KL-based NMF. In numerical experiments, we compare proposed algorithms with existing algorithms on synthetic data and real-world data.