Data science analysis of Vassiliev invariants and knot similarity based on distributed machine learning

Abstract

INTRODUCTION: Knot theory has a long history, and as a branch of topology, it has received extensive attention. At present, the scientific analysis of data based on the similarity of Vassiliev invariants and knots under machine learning technology is the focus of the mathematical community. However, at present, there are some difficulties in the research work on the similarity of Vassiliev invariants and knots. These difficulties not only delay the progress of Vassiliev invariants research, but also slow down the speed of knot similarity research.OBJECTIVES: However, with the acceleration of the intelligent process, various intelligent technologies have been applied in the research of mathematics, biology and physics, providing excellent help for the research of many disciplines. Therefore, machine learning technology could be used to carry out new research on Vassiliev invariants and knot similarity.METHODS: Traditional knot analysis technology was combined with machine learning technology to find a more efficient and stable way of exploring Vassiliev invariants and knot similarity. his paper proposed a research method of data scientific analysis based on Vassiliev invariants and knot similarity under machine learning technology. Its purpose was to combine traditional knot research methods with machine learning technology to improve the efficiency of knot research. The algorithm proposed in this paper was the knot Vassiliev invariant analysis algorithm based on machine learning, which could use the intelligent and efficient analysis algorithm of machine learning technology to process the data of complex knots. This algorithm has improved the accuracy of the analysis of knot characteristics, and reduced the analysis time and the memory consumption at runtime.RESULTS: By testing the similarity between the Vassiliev invariant based on machine learning and the knot, the results showed that the analysis accuracy of the traditional Vassiliev invariant computing technology for the chiral characteristics, the number of intersections and the number of knots in the knot image was 84.25%, 83.27% and 85.56% respectively. The accuracy of knot Vassiliev invariant analysis algorithm based on machine learning for these indicators was 91.87%, 92.66% and 92.12% respectively. Obviously, the knot Vassiliev invariant analysis algorithm based on machine learning was superior to the traditional knot computing technology, and its analysis results were more excellent.CONCLUSION: In general, the research topic proposed in this paper has been proved to be of practical value. This research result proved that machine learning technology could play an excellent role in the current knot research, which correspondingly expanded the research direction of Vassiliev invariants and knot similarity.