Producing Monomial Sets with Lower Calculation Complexity for Polynomial Fitting

In the physic world, exploring and discovering the mechanism behind the various phenomenon is crucial for us to know the world better. However, it is hard to discover the principle in case of enormous data and the mechanism may be too hard for a human to figure out. Data science gives us a way of knowing the world and finding the mechanism hidden in the data. Automatic tool like polynomial fitting is a useful method to fit the data well. When the variable number and degree are relatively low, the computation amount of polynomial is small. However, the number of monomials grows exponentially with the increasing variable number and degree. Problems in the real world are always in a high-dimension, and the problem may be complex that needs to use a high degree to fit data well. Plus, with the huge data, the computation complexity is high. Therefore, we think it is necessary to find a way to reduce the computation amount of fitted polynomial. In this paper, we propose to use the PSO algorithm to find the monomial sets that have lower computation amounts. Experiments show the effectiveness of our method.