Due to the improvement of network infrastructure and the application of Internet of Things equipment, a large number of sensors are deployed in the industrial pipeline production, and the large size of data is generated. The most typical case in the production line is product inspection, that is, defect inspection. To implement an efficient and robust detection system, in this study, we propose a classification computing model based on Lie Group Machine Learning, which can find the possible defective products in production. Usually, a workshop has a lot of assembly lines. How to process large data on so many production lines in real-time and accurately is a difficult problem. To solve this problem, we use the concept of fog computing to design the system. By offloading the computation burden from the cloud server center to the fog nodes, the system obtains the ability to deal with extremely data. Our system has two obvious advantages. The first one is to apply Lie Group Machine Learning to fog computing environment to improve the computational efficiency and robustness of the system. The other is that without increasing any production costs, it can quickly detect products, reduce network latency, and reduce the load on bandwidth. The simulations prove that, compared with the existing methods, the proposed method has an average running efficiency increase of 52.57%, an average delay reduction of 42.13%, and an average accuracy increase of 27.86%.

Intelligent manufacturing Lie Group Machine Learning: real-time and efficient inspection system based on fog computing

profound inherent theory. [5] It just can meet the needs of machine learning and describe the procedure of machine learning clearly. So Lie group machine learning is formed. This paper is based on the basic conceptions of machine learning and gives the generalization hypothesis axiom; the partition independence hypothesis axiom; the duality hypothesis axiom and the learning compatibility hypothesis axiom of Lie group machine learning. Index terms—Lie group; machine learning; Lie group machine leaning; hypothesis axiom

Lie group machine learning's axiom hypothesizes

This paper gives the method to design classifiers of Lie group Machine Learning (LML) based on the basic conceptions and the theory framework of it, which contains the following steps: (1) Map the observed data set in the learning system to the nonempty set G. (2) Construct the corresponding Lie group structure according to G. (3) Apply the obtained Lie group to build the LML model. (4) Form the corresponding classifier. (5) Test classification abilities and so on. At last, the design of SO(3) classifier and an example are given to test its classification ability.

SO（3） classifier of Lie group machine learning

The method of nondestructive testing for aircraft skin composite defects using infrared thermography is very effective. But, against the problem of how to rapidly and accurately identify for the defects of specific types needs to be further study. Based on the analysis of the existed classifier for skin damages, a complex group classifier based on lie group machine learning algorithm is introduced in this paper. According to the damage infrared thermal images obtained by the infrared thermal imager, the feature of internal defects of the skin specific defects is extracted and a discriminant function is established, and then a direct classification for the input image is realized. A simulation result proves that the algorithm given in this paper can satisfy the identification accuracy, and shows the effective of the algorithm.

Infrared image registration of damage in the aircraft skin based on lie group machine learning

In this paper, we propose a description of Machine Learning System (MLS) which is based on the category theory in order to study mapping mechanism of the learning expression. And a detailed instance is provided. This is that Decision Tree Learning (DTL) can be denoted based on category theory. In addition, we prove that the machine learning system is indeed a category, and propose the learning expression and the mapping mechanism of the learning expression based on category theory. Also we describe the proof and verify the mechanism.

Research on mapping mechanism of learning expression

Machine learning is a eternal problem in the researches of artificial intelligence. However, machine learning methods are short of systemic theoretic foundation at present and some preferable ones such as statistic learning theory are exploring ones. Therefore, this paper researches machine learning by Lie group which has good mathematics configuration advances some basic conceptions of machine learning (ML) based on Lie group and conceptions of learning based on dual space, and formed the basic learning theory frame based on Lie group. The theory frame can describe machine learning system by algebra and geometry methods. So that it makes a fine configuration for describing the procession of machine learning and makes up for the lack of other theories of machine learning. It can be believed that researches of machine learning could be profoundly influenced by these works.

Kang Yu

Papers

The study of machine learning theory frame based on Lie group

The initial-boundary value problem for a strictly hyperbolic equations