Adaptive Missing Data Imputation with Incremental Neuro-Fuzzy Gaussian Mixture Network (INFGMN)

Many real-world machine learning applications face a common problem: the occurrence of missing data due to losses or failures in the collection mechanisms. This article presents a new approach to deal with problems in which the data is missing completely at random (MCAR) or missing at random (MAR). This approach is based on an extension of the INFGMN (Incremental Neuro-Fuzzy Gaussian Mixture Network), using an approximated incremental version of the Expectation Maximization (EM) algorithm, to carry out the imputation process of the missing data during the execution of the recalling operation in the network layer of the INFGMN, making it capable of dealing with missing data. By adding the imputation mechanism to the INFGMN network, we obtained a neuro-fuzzy network that can produce reasonable estimates based on few training data, even in the occurrence of missing data. Unlike other neuro-fuzzy networks, the INFGMN neuro-fuzzy network does not require that the missing data be filled in prior to training and network use (this is done during its use and adaptively). The learning and modeling performance of the INFGMN in the presence of missing data are evaluated using several benchmark applications and we conclude that the proposed model can be used as a viable alternative to the existing ones for the data imputation.