A Study of Image Recognition by Statistics, Machine Learning, and Partial differential equations

通过统计学、机器学习和偏微分方程进行图像识别的研究

• 批准号: 17540122
• 负责人: SAKATA Toshio
• 金额: $ 1.61万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540122/
• 关键词: Statistical and machine learning Image recognition; Inpainting by partial equation methods; Tensor data; Maximal rank of a tensor; Application of Groebner Basis; Segre map; Color inpainting; Recovery of Old documents and old statue photos; テンソルデータ

The purpose of this project was to attack various image recognition problems through a unified way of statistical and machine learning and partial differential equation methods, and as a feedback develop the theory itself First year we explored mainly by machine learning method, and proposed cross entropy based kernel LVQ to solve the recognition of old language, Estrangelo, and proposed iterative kernel PCA for eye glass removing. The result of this were reported in the conference of Computational Statistical Data Analysis in Cypros (presentation[19],[20],[21]). In the second year we explored the inpainting problem of hand written old documents ofEstrangelo by a partial differential equation method. This was reported in the paper [9]. At the same time we explored to handle image data as the tensor data For a basics of this problem we encountered the maximal rank problem of a set of tensors. We proposed to solve the problem for small size cases by using the elimination idela of Groebne … More r basis theory (the paper [8]) and talked in several symposiums (presentions [15],[16],[17]), and published in the book [17]. In the third year we attacked the color inpainting problem by partial equation method, by solving a Poisson equation to recover the color of the old photos of old Japanese statues (the papers [1],[2]). The result is still unsatisfactory however some insights useful for the future work were obtained. An idea is that color axis may be chosen adaptively case by case. Also, in this year, for the tensor ranking problem I proposed “zero forcing method" and pursued the related topics ( the papers [4],[5]). The result about NTF was also reported in the papers [3]. An application to recover the color of photos of statues is very attractive topics, as color image inpainting is related also to Sparse coding and ICA, this line will be pursued in the future our work.. Statistical theory based on tensors will be developed more comprehensively in our future research. Prof. Nishii worked in the field of recognition of remote sensing image data by using machine learning method and published several papers for international journals [6,[10],[16] and gave talks at many international conferences. Prof. Sawae explored the filed of Quantum computing [7],[11][13],[14]. He also gave talks at many international conference. It is very interesting his research might have a connection to tensor data analysis through Segre map. Also their basic research might have a connection to image data storage method in the future. We will unify over handred programs build for the study. Less

该项目的目的是通过统一的统计和机器学习方式和部分微分方程方法来攻击各种图像识别问题，并且作为反馈，我们主要是通过机器学习方法探索的理论本身，并提出了基于交叉熵的内核LVQ来求解对旧语言的识别，estrangelo，Estrangelo，以及提议的Issusisation Isseperative interative interative interative insey keernelelele seyemeylelelemeymeyplepa。在塞浦路斯的计算统计数据分析会议上报告了这一点的结果（介绍[19]，[20]，[21]）。在第二年，我们通过部分微分方程方法探索了埃斯特朗格洛（Estrangelo）手写的旧文档的介绍问题。这是在论文[9]中报道的。同时，我们探索以将图像数据作为张量数据处理此问题的基础知识，我们遇到了一组张量的最大等级问题。我们建议通过使用Groebne的消除IDELA……更多的基础理论（论文[8]）解决问题，并在几个研讨会（介绍[15]，[16]，[17]）中进行了讨论，并在书[17]中发表。在第三年，我们通过解决泊松方程来恢复旧日本雕像的旧照片的颜色（The Papers [1]，[2]）来攻击颜色的涂层问题。结果仍然不令人满意，但是获得了一些对未来工作有用的见解。一个想法是，可以根据情况适当选择颜色轴。同样，在今年，对于张量排名问题，我提出了“零强迫方法”，并提出了相关主题（论文[4]，[5]）。论文中还报告了关于NTF的结果[3]。恢复雕像照片颜色的应用是非常有吸引力的主题，因为颜色图像介绍也与稀疏编码和ICA有关，将来将追求这一行。.我们的工作将在我们的工作中进行。统计理论将在我们未来的研究中更全面地开发。 Nishii教授通过使用机器学习方法在认可遥感图像数据的识别领域工作，并为国际期刊发表了几篇论文[6，[10]，[16]，并在许多国际会议上进行了演讲。 Sawae教授探索了量子计算的提交[7]，[11] [13]，[14]。他还在许多国际会议上发表了会谈。有趣的是，他的研究可能通过Segre Map与张量数据分析有联系。此外，他们的基础研究将来可能与图像数据存储方法有联系。我们将统一超级计划为研究构建。较少的

项目成果

A method of calculating the maximal rank of a set of tensors

计算一组张量的最大秩的方法

• 发表时间: 2007
• 期刊: The proc. of the International Associ ation of Statistical Computing-Asian Regional Section, Special Conference
• 作者: Toshio Sakata;Toshio Sumi;Ryuichi Sawae
• 通讯作者: Ryuichi Sawae

脳波解析とグレブナー基底

EEG 分析和 Gröbner 基础

• 发表时间: 2007
• 作者: 坂本博康;谷卓哉;坂田年男;坂田年男
• 通讯作者: 坂田年男

A simple error correction method for NMR quantum computer

核磁共振量子计算机的一种简单纠错方法

• 发表时间: 2006
• 作者: Minaru Kawamura;Takuji Mori moto;Yoshiyuki Mori;Ryuichi Sawae and;et al.
• 通讯作者: et al.

Hidimensional array data and Groebner Basis (In Japansese)

高维数组数据和 Groebner 基础（日语）

• 发表时间: 2006
• 期刊: The presestatus of Groebner Basis (Takayuki Hibi) (Sugaku syobo) 4
• 作者: Yasuhiro;Takei;Tbshio Sakata
• 通讯作者: Tbshio Sakata

正則化テストリスクを用いたBoostingによる高次元データ判別と変数選択

使用正则化测试风险通过 Boosting 进行高维数据判别和变量选择

• 发表时间: 2006
• 作者: 川口修治;西井龍映
• 通讯作者: 西井龍映