Developing data-structure-mining methods in deep learning

• Project/Area Number: 18K11459
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61040:Soft computing-related
• Research Institution: Yamagata University
• Principal Investigator: Yasuda Muneki 山形大学, 大学院理工学研究科, 教授 (20532774)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 深層学習 / 人工知能 / データマイニング / ベイズ統計 / 逆問題 / 情報統計力学 / アルゴリズム / 統計力学

Outline of Final Research Achievements

The aim of this research is to develop data-structure mining techniques in deep learning models to resolve the black box problem of deep learning. We have obtained the following results during this research period: (1) an estimaiton algorithm for the mutual information between the input and output layers in deep learning models and (2) an algorithm that can solve the inverse problem in deep learning models (i.e., the inverse inference from outputs to inputs).

Academic Significance and Societal Importance of the Research Achievements

深層学習のブラックボックス問題の解決に対する要請は、学術界はもちろんであるが、それよりむしろモノづくりの現場である民間のエンジニアリング界からの方が強い。本研究の成果はその要請に対して学術界からの具体的な実践的回答を与えるきっかけとなるものであり、深層学習の分野で未だ存在する学術界とモノづくり界の障壁を打ち崩す可能性を秘めている。つまり、本研究の成果は、将来の人工知能産業への多くの民間企業のスムーズな参入を助けるものになると期待される。

Research Products

• [Journal Article] A Generalization of Spatial Monte Carlo Integration (2021)
  • Author(s): Muneki Yasuda and Kei Uchizawa
  • Journal Title: Neural Computation Volume: 33 Issue: 4 Pages: 1037-1062
  • DOI: 10.1162/neco_a_01365
  • Peer Reviewed / Open Access
• [Journal Article] Multi-layered Discriminative Restricted Boltzmann Machine with Untrained Probabilistic Layer (2021)
  • Author(s): Yuri Kanno and Muneki Yasuda
  • Journal Title: Proceedings of the 25th International Conference on Pattern Recognition Volume: - Pages: 7655-7660
  • Peer Reviewed
• [Journal Article] Adaptive Thouless-Anderson-Palmer equation for higher-order Markov random fields (2020)
  • Author(s): Chako Takahashi, Muneki Yasuda, and Kazuyuki Tanaka
  • Journal Title: Journal of the Physical Society of Japan Volume: 89 Issue: 6 Pages: 064007-064007
  • DOI: 10.7566/jpsj.89.064007
  • NAID: 40022254148
  • Peer Reviewed / Open Access
• [Journal Article] Changing Tendency Analysis of Sleep Quality Based on Temperature and Respiratory Frequency Using Neural Network Model (2020)
  • Author(s): Minami Tsuchiya, Seung-Il Cho, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Journal Title: International Journal of Fuzzy Logic and Intelligent Systems Volume: 20 Issue: 2 Pages: 87-95
  • DOI: 10.5391/ijfis.2020.20.2.87
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Consistent batch normalization for weighted loss in imbalanced-data environment (2020)
  • Author(s): Muneki Yasuda, Yeo Xian En, and Seishirou Ueno
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: 11 Issue: 4 Pages: 454-465
  • DOI: 10.1587/nolta.11.454
  • NAID: 130007921451
  • ISSN: 2185-4106
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Visualization and evaluation of the relation between the estimated sleep satisfaction levels using nonlinear multiple regression analysis and autonomic nervous system (2020)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: 11 Issue: 4 Pages: 517-526
  • DOI: 10.1587/nolta.11.517
  • NAID: 130007921443
  • ISSN: 2185-4106
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Effective Fine-Tuning Algorithm for Deep Boltzmann Machine (2020)
  • Author(s): Tomu Katsumata and Muneki Yasuda
  • Journal Title: Proceedings of the 2020 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 29-32
  • Peer Reviewed
• [Journal Article] A Study on the Correlation Between the Subjective Satisfaction of Sleep and Phase of a 90-Minute Periodic Signal (2020)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Journal Title: Proceedings of the 2020 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 37-39
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] An efficient test method for noise robustness of deep neural networks (2019)
  • Author(s): Muneki Yasuda, Hironori Sakata, Seung-Il Cho, Tomochika Harada, Atushi Tanaka, and Michio Yokoyama
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: 10 Issue: 2 Pages: 221-235
  • DOI: 10.1587/nolta.10.221
  • NAID: 130007622356
  • ISSN: 2185-4106
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Bayesian Image Denoising with Multiple Noisy Images (2019)
  • Author(s): Shun Kataoka and Muneki Yasuda
  • Journal Title: The Review of Socionetwork Strategies Volume: 13 Issue: 2 Pages: 267-280
  • DOI: 10.1007/s12626-019-00043-3
  • NAID: 120006767844
  • Peer Reviewed / Open Access
• [Journal Article] Restricted Boltzmann Machine with Multivalued Hidden Variables: a model suppressing over-fitting (2019)
  • Author(s): Yuuki Yokoyama, Tomu Katsumata, and Muneki Yasuda
  • Journal Title: The Review of Socionetwork Strategies Volume: 12 Issue: 2 Pages: 253-266
  • DOI: 10.1007/s12626-019-00042-4
  • Peer Reviewed / Open Access
• [Journal Article] Detection of human-interaction network using Markov random field (2019)
  • Author(s): Muneki Yasuda, Kouta Katou, Yoshitaka Mikuni, Yuuki Yokoyama, Tomochika Harada, Atsushi Tanaka, and Michio Yokoyama
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: 10 Issue: 4 Pages: 485-495
  • DOI: 10.1587/nolta.10.485
  • NAID: 130007722625
  • ISSN: 2185-4106
  • Peer Reviewed / Open Access
• [Journal Article] Estimation of sleep onset and awaking time using a deep neural network with physiological data during sleep (2019)
  • Author(s): Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, Seung-Il Cho, and Michio Yokoyama
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: 10 Issue: 4 Pages: 366-372
  • DOI: 10.1587/nolta.10.366
  • NAID: 130007722645
  • ISSN: 2185-4106
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Sublinear Computational Time Modeling by Momentum-Space Renormalization Group Theory in Statistical Machine Learning Procedures (2019)
  • Author(s): Kazuyuki Tanaka, Masayuki Ohzeki, and Muneki Yasuda
  • Journal Title: The Review of Socionetwork Strategies Volume: 13 Issue: 2 Pages: 281-306
  • DOI: 10.1007/s12626-019-00053-1
  • Peer Reviewed / Open Access
• [Journal Article] Empirical Bayes method for Boltzmann machines (2019)
  • Author(s): Muneki Yasuda and Tomoyuki Obuchi
  • Journal Title: Journal of Physics A: Mathematical and Theoretical Volume: 53 Issue: 1 Pages: 014004-014004
  • DOI: 10.1088/1751-8121/ab57a7
  • Peer Reviewed / Open Access
• [Journal Article] Improvement of Batch Normalization in Imbalanced Data (2019)
  • Author(s): Muneki Yasuda and Seishirou Ueno
  • Journal Title: Proceedings of the 2019 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 146-149
  • Peer Reviewed
• [Journal Article] A Study on the Relation Between the Estimated Sleep Satisfaction Levels Using Multiple Regression Analysis and Autonomic Nervous System (2019)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Journal Title: Proceedings of the 2019 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 153-156
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Overcoming Chasm Phenomena in Diffusion on Cookpad Community (2019)
  • Author(s): Atsushi Tanaka, Shin Nagasawa, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Journal Title: Proceedings of the 2019 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 150-152
  • Peer Reviewed
• [Journal Article] An efficient test method for noise robustness of deep neural networks (2019)
  • Author(s): Muneki Yasuda, Hironori Sakata, Seung-Il Cho, Tomochika Harada, Atushi Tanaka, and Michio Yokoyama
  • Journal Title: Nonlinear Theory and its Applications Volume: -
  • NAID: 130007622356
  • Peer Reviewed
• [Journal Article] Linear-Time Algorithm in Bayesian Image Denoising based on Gaussian Markov Random Field (2018)
  • Author(s): Muneki Yasuda, Jyunpei Watanabe, Shun Kataoka, and Kazuyuki Tanaka
  • Journal Title: IEICE Transactions on Information and Systems Volume: E101.D Issue: 6 Pages: 1629-1639
  • DOI: 10.1587/transinf.2017EDP7346
  • NAID: 130007382462
  • ISSN: 0916-8532, 1745-1361
  • Year and Date: 2018-06-01
  • Peer Reviewed / Open Access
• [Journal Article] Momentum-Space Renormalization Group Transformation in Bayesian Image Modeling by Gaussian Graphical Model (2018)
  • Author(s): Kazuyuki Tanaka, Masamichi Nakamura, Shun Kataoka, Masayuki Ohzeki, and Muneki Yasuda
  • Journal Title: Journal of the Physical Society of Japan Volume: 87 Issue: 8 Pages: 1-2
  • DOI: 10.7566/jpsj.87.085001
  • NAID: 210000134931
  • Peer Reviewed / Open Access
• [Journal Article] Estimation System of Blood Pressure Variation with Photoplethysmography Signals Using Multiple Regression Analysis and Neural Network (2018)
  • Author(s): Cho Seung-Il、Negishi Takumi、Tsuchiya Minami、Yasuda Muneki、Yokoyama Michio
  • Journal Title: INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS Volume: 18 Issue: 4 Pages: 229-236
  • DOI: 10.5391/ijfis.2018.18.4.229
  • Peer Reviewed / Open Access
• [Journal Article] Estimation System of Blood Pressure Variation Using Multiple Regression Analysis and Neural Network (2018)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Muneki Yasuda and Michio Yokoyama
  • Journal Title: Proceedings of the International Conference on Advances in Next Generation Computer and Information Technology V (NGCIT2018), Advanced Science and Technology Letters Volume: 152 Pages: 61-64
  • DOI: 10.14257/astl
  • Peer Reviewed
• [Journal Article] Estimation of Awaking Time Using a Deep Neural Network with Physiological Data During Sleep (2018)
  • Author(s): Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, Seung-Il Cho, and Michio Yokoyama
  • Journal Title: Proceedings of the 2018 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 27-30
  • Peer Reviewed
• [Journal Article] The Multiple Beacon System for Detection of the Gathering Degree of People in a Certain Place (2018)
  • Author(s): Tomochika Harada, Michio Yokoyama, Muneki Yasuda, and Atsushi Tanaka
  • Journal Title: Proceedings of the 2018 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 31-33
  • Peer Reviewed
• [Journal Article] Detecting Human-Interaction Networks Based on Statistical Machine Learning and Sparse Modeling (2018)
  • Author(s): Muneki Yasuda, Yoshitaka Mikuni, Yuuki Yokoyama, Tomochika Harada, Atsushi Tanaka, and Michio Yokoyama
  • Journal Title: Proceedings of the 2018 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 34-37
  • Peer Reviewed
• [Journal Article] Community Analysis of Social Networks Based on Network Indexes (2018)
  • Author(s): Atsushi Tanaka, Seung-Il Cho, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Journal Title: Proceedings of the 2018 International Symposium on Nonlinear Theory and its Applications Volume: - Pages: 38-41
  • Peer Reviewed
• [Journal Article] Estimation of Correlation between Multiple Parameters and Sleep Satisfaction Using Deep Neural Network for Pleasant Sleeping Support System (2018)
  • Author(s): Seung-Il Cho, Muneki Yasuda, Minami Tsuchiya, Tomochika Harada, Atsushi Tanaka, and Michio Yokoyama
  • Journal Title: Proceedings of the 31th International Conference on Computer Applications in Industry and Engineering Volume: - Pages: 26-30
  • Peer Reviewed
• [Presentation] Multi-layered Discriminative Restricted Boltzmann Machine with Untrained Probabilistic Layer (2021)
  • Author(s): Yuri Kanno and Muneki Yasuda
  • Organizer: The 25th International Conference on Pattern Recognition
  • Int'l Joint Research
• [Presentation] ノイズの相関構造を考慮した確率的画像処理 (2021)
  • Author(s): 矯徳慧，安田宗樹
  • Organizer: 情報処理学会東北支部研究会
• [Presentation] 深層ボルツマンマシンに対する統計力学的解析 (2021)
  • Author(s): 前野陵介，安田宗樹
  • Organizer: 日本物理学会 第76回年次大会
• [Presentation] 空間モンテカルロ積分法と焼なまし重点サンプリングを組み合わせた高性能サンプリング近似法 (2021)
  • Author(s): 関本快士，安田宗樹
  • Organizer: 情報処理学会 第83回全国大会
• [Presentation] 不均衡回帰問題に対する重み付きバッチ正規化法の検証 (2021)
  • Author(s): 楊顕恩，安田宗樹
  • Organizer: 情報処理学会 第83回全国大会
• [Presentation] 非学習型確率層により多層化された制限ボルツマンマシン分類器の性能の検討 (2021)
  • Author(s): 菅野友理，安田宗樹
  • Organizer: 情報処理学会 第83回全国大会
• [Presentation] 深層ボルツマンマシンにおける学習アルゴリズムの改良 (2021)
  • Author(s): 勝亦利宗，安田宗樹
  • Organizer: 情報処理学会 第83回全国大会
• [Presentation] マルコフ確率場と非局所パッチ法を組み合わせた画像補修アルゴリズム (2021)
  • Author(s): 門馬維紀，安田宗樹
  • Organizer: 情報処理学会 第83回全国大会
• [Presentation] 眠りSCANを用いた寝姿勢推定システムの構築 (2021)
  • Author(s): 葛原優樹，近藤栄太郎，豊田彩織，椎野俊秀，木暮貴政，安田宗樹
  • Organizer: 情報処理学会 第83回全国大会
• [Presentation] Effective Fine-Tuning Algorithm for Deep Boltzmann Machine (2020)
  • Author(s): Tomu Katsumata and Muneki Yasuda
  • Organizer: The 2020 International Symposium on Nonlinear Theory and its Applications
  • Int'l Joint Research
• [Presentation] Study on the Correlation Between the Subjective Satisfaction of Sleep and Phase of a 90-Minute Periodic Signal (2020)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Organizer: The 2020 International Symposium on Nonlinear Theory and its Applications
  • Int'l Joint Research
• [Presentation] ボルツマンマシンのグラフマイニングへの応用 (2020)
  • Author(s): 安田宗樹
  • Organizer: 電子情報通信学会総合大会
  • Invited
• [Presentation] スパース中間層を持つ制限ボルツマンマシン分類器 (2020)
  • Author(s): 勝亦利宗，安田宗樹
  • Organizer: 情報処理学会第８２回全国大会
• [Presentation] 経験ベイズ法を用いた連続値ボルツマンマシンのハイパーパラメータ推定 (2020)
  • Author(s): 加藤航太，安田宗樹
  • Organizer: 情報処理学会第８２回全国大会
• [Presentation] ニューラルネットワーク上の入出力逆問題と相互情報量の解析 (2020)
  • Author(s): 千田翼，安田宗樹
  • Organizer: 情報処理学会第８２回全国大会
• [Presentation] 確率的極端学習機械による制限ボルツマンマシン分類器の多層化 (2020)
  • Author(s): 菅野友理，安田宗樹
  • Organizer: 情報処理学会第８２回全国大会
• [Presentation] Linear-Time Algorithm in Bayesian Image Denoising based on Gaussian Markov Random Field (2019)
  • Author(s): Muneki Yasuda
  • Organizer: International Workshop on Innovative Algorithms for Big Data
  • Int'l Joint Research
• [Presentation] Improvement of Batch Normalization in Imbalanced Data (2019)
  • Author(s): Muneki Yasuda and Seishirou Ueno
  • Organizer: 2019 International Symposium on Nonlinear Theory and its Applications
  • Int'l Joint Research
• [Presentation] A Study on the Relation Between the Estimated Sleep Satisfaction Levels Using Multiple Regression Analysis and Autonomic Nervous System (2019)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Organizer: 2019 International Symposium on Nonlinear Theory and its Applications
  • Int'l Joint Research
• [Presentation] Overcoming Chasm Phenomena in Diffusion on Cookpad Community (2019)
  • Author(s): Atsushi Tanaka, Shin Nagasawa, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Organizer: 2019 International Symposium on Nonlinear Theory and its Applications
  • Int'l Joint Research
• [Presentation] Empirical Bayes method for Boltzmann machines (2019)
  • Author(s): Muneki Yasuda
  • Organizer: Workshop on Statistical Physics of Disordered Systems and Its Applications
  • Int'l Joint Research / Invited
• [Presentation] ディープラーニングの基礎の考え方と実践のコツ～最新の人工知能技術の本質と実践法を理解する～ (2019)
  • Author(s): 安田宗樹
  • Organizer: 株式会社R&D支援センターセミナー
  • Invited
• [Presentation] 確率的グラフィカルモデルの基礎とその応用 ～データ生成モデル、データマイニング、そして、人工知能への応用～ (2019)
  • Author(s): 安田宗樹
  • Organizer: 株式会社トリケップスセミナー
  • Invited
• [Presentation] レプリカ法を用いたボルツマンマシンに対する経験ベイズ推定 (2019)
  • Author(s): 安田宗樹，小渕智之
  • Organizer: 日本物理学会 第74回年次大会
• [Presentation] Estimation System of Blood Pressure Variation Using Multiple Regression Analysis and Neural Network (2018)
  • Author(s): Seung-Il Cho, Minami Tsuchiya, Muneki Yasuda and Michio Yokoyama
  • Organizer: The International Conference on Advances in Next Generation Computer and Information Technology V (NGCIT2018)
  • Int'l Joint Research
• [Presentation] Estimation of Awaking Time Using a Deep Neural Network with Physiological Data During Sleep (2018)
  • Author(s): Minami Tsuchiya, Atsushi Tanaka, Muneki Yasuda, Tomochika Harada, Seung-Il Cho, and Michio Yokoyama
  • Organizer: The 2018 International Symposium on Nonlinear Theory and its Applications (NOLTA2018)
  • Int'l Joint Research
• [Presentation] The Multiple Beacon System for Detection of the Gathering Degree of People in a Certain Place (2018)
  • Author(s): Tomochika Harada, Michio Yokoyama, Muneki Yasuda, and Atsushi Tanaka
  • Organizer: The 2018 International Symposium on Nonlinear Theory and its Applications (NOLTA2018)
  • Int'l Joint Research
• [Presentation] Detecting Human-Interaction Networks Based on Statistical Machine Learning and Sparse Modeling (2018)
  • Author(s): Muneki Yasuda, Yoshitaka Mikuni, Yuuki Yokoyama, Tomochika Harada, Atsushi Tanaka, and Michio Yokoyama
  • Organizer: The 2018 International Symposium on Nonlinear Theory and its Applications (NOLTA2018)
  • Int'l Joint Research
• [Presentation] Community Analysis of Social Networks Based on Network Indexes (2018)
  • Author(s): Atsushi Tanaka, Seung-Il Cho, Muneki Yasuda, Tomochika Harada, and Michio Yokoyama
  • Organizer: The 2018 International Symposium on Nonlinear Theory and its Applications (NOLTA2018)
  • Int'l Joint Research
• [Presentation] Estimation of Correlation between Multiple Parameters and Sleep Satisfaction Using Deep Neural Network for Pleasant Sleeping Support System (2018)
  • Author(s): Seung-Il Cho, Muneki Yasuda, Minami Tsuchiya, Tomochika Harada, Atsushi Tanaka, and Michio Yokoyama
  • Organizer: The 31th International Conference on Computer Applications in Industry and Engineering (CAINE2018)
  • Int'l Joint Research
• [Presentation] ディープラーニングとパターン認識、最先端の人工知能へ (2018)
  • Author(s): 安田宗樹
  • Organizer: 株式会社トリケップスセミナー
  • Invited
• [Presentation] 確率的グラフィカルモデルの基礎とその応用 (2018)
  • Author(s): 安田宗樹
  • Organizer: 株式会社日本テクノセンターセミナー
  • Invited
• [Presentation] 統計的機械学習 (2018)
  • Author(s): 安田宗樹
  • Organizer: 第37回日本医用画像工学会大会
  • Invited
• [Presentation] 人と機械のデータサイエンス (2018)
  • Author(s): 安田宗樹
  • Organizer: 第54回日本眼光学学会総会
  • Invited
• [Presentation] 確率的グラフィカルモデルの基礎と人工知能への応用 (2018)
  • Author(s): 安田宗樹
  • Organizer: 株式会社日本テクノセンターセミナー
  • Invited
• [Presentation] 適応 Thouless-Anderson-Palmer 近似による勾配法を用いた制限ボルツマンマシンの学習 (2018)
  • Author(s): 高橋茶子，安田宗樹，田中和之
  • Organizer: 第21回情報論的学習理論ワークショップ (IBIS2018)
• [Book] スパースモデリング 理論、アルゴリズム、応用 (2019)
  • Author(s): Irina Rish、Genady Ya. Grabarnik、竹澤邦夫、大関真之、高橋茶子、竹田晃人、徳田悟、藤本晃司、安田宗樹
  • Total Pages: 248
  • Publisher: ジャムハウス
  • ISBN: 9784906768738
• [Book] 画像処理の統計モデリング ―確率的グラフィカルモデルとスパースモデリングからのアプローチ― (2018)
  • Author(s): 片岡駿，大関真之，安田宗樹，田中和之
  • Total Pages: 262
  • Publisher: 共立出版
  • ISBN: 9784320111233
• [Remarks] 成果に関する web ページ
  • URL: http://www.adv-pip.yz.yamagata-u.ac.jp/~muneki/index.html