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

这个项目的目的是通过统计和机器学习以及偏微分方程方法的统一方式来攻击各种图像识别问题，并作为反馈发展理论本身。第一年我们主要通过机器学习方法进行探索，并提出了基于交叉熵的核LVQ来解决旧语言Estrangelo的识别，并提出了迭代核PCA来去除眼镜。这一结果在Cypros的计算统计数据分析会议上报告（介绍[19]，[20]，[21]）。在第二年，我们探讨了修复问题的手写旧文件ofEstrangelo的偏微分方程的方法。这一点在论文[9]中有所报道。同时，我们探索了将图像数据作为张量数据来处理。对于这个问题的基础，我们遇到了一组张量的最大秩问题。对于小规模的情形，我们提出了用Groebne的消元定理来解决问题 关于我们 R基理论（论文[8]），并在几次研讨会上发言（演讲[15]，[16]，[17]），并在书中发表[17]。在第三年，我们用偏方程方法解决了彩色修复问题，通过求解泊松方程来恢复日本旧雕像的旧照片的颜色（论文[1]，[2]）。结果仍然不令人满意，但获得了一些有益的启示，为今后的工作。一个想法是，颜色轴可以根据情况自适应地选择。另外，在这一年中，针对张量排序问题，我提出了“迫零法”，并进行了相关课题的研究（论文[4]，[5]）。有关NTF的研究结果也在文献中报道[3]。一个应用程序来恢复雕像的照片的颜色是非常有吸引力的主题，因为彩色图像修复也与稀疏编码和伊卡有关，这条线将在未来我们的工作中继续。基于张量的统计理论将在今后的研究中得到更全面的发展。Nishii教授致力于利用机器学习方法识别遥感图像数据，并在国际期刊上发表了多篇论文[6，[10]，[16]，并在许多国际会议上发表演讲。[7][11][13][14][15][16][17][18]他还在许多国际会议上发表演讲。这是非常有趣的，他的研究可能有一个连接到张量数据分析通过塞格雷地图。他们的基础研究也可能与未来的图像数据存储方法有关。我们将统一为这项研究建立的手工程序。少

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