Extreme Learning Machines for Datasets with Missing Values Using the Unscented Transform

Abstract

The existence of missing data is a common fact in real applications which can significantly affect the data analysis process. In order to overcome this problem, many methods have been proposed in the literature. Extreme Learning Machine (ELM) has become a very popular research topic in machine learning and artificial intelligence areas due to its characteristics such as fast training procedure, good generalization and universal approximation capability. Although ELM has been successfully applied in different domains, its basic formulation cannot handle datasets with missing values properly. This paper presents a variant of the Extreme Learning Machine (ELM) for datasets with missing values. In the proposed method, probability distributions for the missing values are estimated using the expectation maximization (EM) algorithm, assuming that data is normally distributed. The Unscented Transform (UT) is used to estimate the values of the hidden layer outputs, and the weights of the output layer are assigned using the Moore-Penrose Pseudoinverse. Numerical experiments are carried out in order to evaluate the performance of the proposed method in four real world and two synthetic regression datasets. The results show that the proposed method presented a good performance in terms of Average RootMean-Squared Error (ARMSE).