Machine Learning Algorithm Research And Application Based On Functional Data Analysis

Functional data is an important data type in machine learning. In this paper, we study the machine learning algorithms based on functional data: new methods of feature extraction and prediction are proposed for economic and medical data, a multi-task least squares regularized regression algorithm is proposed for multi-task learning problem. The proposed algorithms achieve good prediction performance on test data set, and we provide new ideas for the design of machine learning algorithm based on functional data."Total retail sales of social consumer goods" is an important economic indicator in the national economy. In this paper, based on the data of China during the period of 1984-2010, we design a method to extract features of the long-term trend and seasonal fluctuation. We use the principal differential analysis based regularized regression iterative algorithm to fit the data as the sum of a low and a high frequency function. The low frequency function reflects the long-term trend of the data, and the high frequency one shows the seasonal variation characteristics of the data. Further, based on feature extraction, we propose a method to predict the long-term trend and seasonal trend separately, and use the sum of them as the final prediction. In the long term trend prediction, the method for balancing long term linear trend and local derivative information is adopted. In the seasonal trend prediction, the weighted algorithm of the early seasonal pattern is designed. In this paper, the proposed method achieves good short-term prediction results in the real data.Glaucoma is a serious ophthalmic disease, and it is difficult to diagnose in early stage. In this paper, we propose a method of feature extraction and glaucoma prediction based on the fundus images. It transforms the boundaries of optic disc and optic cup to a continuous curve, which reflects the local cup-to-disc ratio. Furthermore, drawn lessons from doctor's priori knowledge, two evaluating indicators, the vertical cup-to-disc ratio and ISNT-score, are designed based on this curve. With these two indicators, support vector machine algorithm is used for the binary classification of the fundus images. On the test data set, our method obtains 93% prediction accuracy.The goal of multi-task learning is to improve the prediction accuracy of the target task, with the help of the related tasks information. In this paper, a multi-task least square regularized regression algorithm is designed. The algorithm uses samples of related tasks to select the most appropriate model parameter for target task, and then use samples of the target to predict the regression function for the target task. In the simulation experiment, the proposed multi-task learning algorithm obtains better prediction results than single-task learning and selects more suitable model parameters.