ISSN 1000-1239 CN 11-1777/TP

• 人工智能 •

### 线性正则化函数Logistic模型

1. 1(山西大学数学科学学院 太原 030006);2(计算智能与中文信息处理教育部重点实验室(山西大学) 太原 030006) (mengyf@sxu.edu.cn)
• 出版日期: 2020-08-01
• 基金资助:
国家自然科学基金项目(61807022, 61876103, 61976184)；山西省重点研发计划项目(201903D121162)；山西省自然科学基金项目(201801D221168)

### Linear Regularized Functional Logistic Model

Meng Yinfeng1, Liang Jiye2

1. 1(School of Mathematical Sciences, Shanxi University, Taiyuan 030006);2(Key Laboratory of Computational Intelligence and Chinese Information Processing (Shanxi University), Ministry of Education, Taiyuan 030006)
• Online: 2020-08-01
• Supported by:
This work was supported by the National Natural Science Foundation of China (61807022, 61876103, 61976184), the Projects of Key Research and Development Plan of Shanxi Province (201903D121162), and the Natural Science Foundation of Shanxi Province of China (201801D221168).

Abstract: The pattern recognition problems of functional data widely exist in various fields such as medicine, economy, finance, biology and meteorology, therefore, to explore classifiers with more better generalized performance is critical to accurately mining the hidden knowledge in functional data. Aiming at the low generalization performance of the classical functional logistic model, a linear regularized functional logistic model based on functional principal component representation is proposed and the model is acquired by means of solving an optimization problem. In the optimization problem, the former term is constructed based on the likelihood function of training functional samples to control the classification performance of functional samples. The latter term is the regularization term, which is used to control the complexity of the model. At the same time, the two terms are combined by linear weighted combination, which limits the value range of the regularizer and makes it convenient to give an empirical optimal parameter. Then, under the guidance of this empirical optimal parameter, a logistic model with the appropriate number of principal components can be selected for the classification of functional data. The experimental results show that the generalization performance of the selected linear regularized functional logistic model is better than that of the classical logistic model.