arXiv 2001.003452020-01-02cs.LGcond-mat.softstat.ML

视觉机器学习：通过2D颗粒结构中的特征向量、Chladni模式和社区发现进行洞察

Visual Machine Learning: Insight through Eigenvectors, Chladni patterns and community detection in 2D particulate structures

School of Minerals, Metallurgical and Materials Engineering, Indian Institute of Technology（印度理工学院布巴内斯瓦尔分校矿物、冶金与材料工程学院）；Virtual and Augmented Reality Centre of Excellence, Indian Institute of Technology（印度理工学院布巴内斯瓦尔分校虚拟与增强虚拟现实卓越中心）；NetTantra Technologies (India) Pvt. Ltd.（NetTantra技术（印度）私人有限公司）；Washington University in Saint Louis（圣路易斯华盛顿大学）；St. Louis University（圣路易斯大学）

Raj Kishore, S. Swayamjyoti, Shreeja Das, Ajay K. Gogineni, Zohar Nussinov, D. Solenov, Kisor K. Sahu

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摘要：

机器学习（ML）正在迅速成为一种强大的工具，在极其广泛的学科和商业活动中具有多种应用。通常，ML被用作一个黑盒子，几乎没有提供其输出的启发性合理化。在目前的工作中，我们的目标是更好地理解无监督ML背后的一般直觉，重点是物理系统。在这里作为测试案例研究的系统包括六个不同的2维（2-D）不同复杂性的颗粒系统。值得注意的是，这项研究的结果对于任何无监督的ML问题都是通用的，并且不仅限于材料系统。三个基本的无监督ML技术采用的邻接（连通性）矩阵的六个研究系统：（i）使用主特征值和特征向量的邻接矩阵，（ii）谱分解，和（iii）基于波茨模型的社区发现技术，其中模块化函数被最大化。我们证明，在解决一个完全经典的问题，ML技术产生的功能，是明显连接到量子力学的解决方案。剖析这些特征有助于我们通过ML技术的万花筒来理解经典非线性世界和量子力学线性世界之间的深刻联系，这可能在物理科学和ML领域产生深远的影响。

英文摘要：

Machine learning (ML) is quickly emerging as a powerful tool with diverse applications across an extremely broad spectrum of disciplines and commercial endeavors. Typically, ML is used as a black box that provides little illuminating rationalization of its output. In the current work, we aim to better understand the generic intuition underlying unsupervised ML with a focus on physical systems. The systems that are studied here as test cases comprise of six different 2-dimensional (2-D) particulate systems of different complexities. It is noted that the findings of this study are generic to any unsupervised ML problem and are not restricted to materials systems alone. Three rudimentary unsupervised ML techniques are employed on the adjacency (connectivity) matrix of the six studied systems: (i) using principal eigenvalue and eigenvectors of the adjacency matrix, (ii) spectral decomposition, and (iii) a Potts model based community detection technique in which a modularity function is maximized. We demonstrate that, while solving a completely classical problem, ML technique produces features that are distinctly connected to quantum mechanical solutions. Dissecting these features help us to understand the deep connection between the classical non-linear world and the quantum mechanical linear world through the kaleidoscope of ML technique, which might have far reaching consequences both in the arena of physical sciences and ML.

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