The Application Of Regression Model Based On Nonnegative Matrix Factorization

Nonnegative matrix factorization( NMF) is applied to image processing and data compressions where it is used in learning a parts-representation of the overall data. Due to the non-negativity, the features extracted by NMF from an object have physical significance. A new way was provided to deal with large-scale data by NMF. With its simplicity and interpretability, NMF has been developed rapidly and is applied in almost every field of science and social arts.The basic theory of NMF and the multi-linear regression model by principal component analysis are introduced in this paper. The relationship between climatic factors and the yield of Biluochun tea is simulated and analyzed based on the observational data and multi-linear regression theory. The result shows that the impact of temperature to yield is the highest among all the factors, and the precipitation to the yield is almost the same with that of the sunshine duration.The climatic data and the yield of Dongting Biluochun tea are collected from the year 1995 to 2013 at Dong-Shan Mountain near Taihu Lake, Suzhou. The data is partitioned into the training part and the test part. The training data is used to build model and the test data is used to test the validity of model. Two regression models respectively based on the method of Principal Component Analysis(PCA) and NMF are built to simulate the relationship between the climatic factors and the yield of Biluochun tea. These two models were compared based on the simulation.Our simulation shows that the result based on NMF is better than that of PCA. The relationship between the original variables and the dependent variable can be explained easily by the factor matrices obtained from NMF. Besides, NMF has a relatively simple computing process while PCA is relatively slow in the computation.