Robust adaptive online sequential extreme learning machine for predicting nonstationary data streams with outliers

Data streams online modeling and prediction is an important research direction in the field of data mining. In practical applications, data streams are often of nonstationary nature and containing outliers, hence an online learning algorithm with dynamic tracking capability as well as anti-outlier capability is urgently needed. With this in mind, this paper proposes a novel robust adaptive online sequential extreme learning machine (RA-OSELM) algorithm for the online modeling and prediction of nonstationary data streams with outliers. The RA-OSELM is developed from the famous online sequential extreme learning machine algorithm, but it uses a more robust M-estimation loss function to replace the conventional least square loss function so as to suppress the incorrect online update of the learning algorithm with respect to outliers, and hence enhances its robustness in the presence of outliers. Moreover, the RA-OSELM adopts a variable forgetting factor method to automatically track the dynamic changes of the nonstationary data streams and timely eliminate the negative impacts of the outdated data, so it tends to produce satisfying tracking results in nonstationary environments. The performances of RA-OSELM are evaluated and compared with other representative algorithms with synthetic and real data sets, and the experimental results indicate that the proposed algorithm has better adaptive tracking capability with stronger robustness than its counterparts for predicting nonstationary data streams with outliers.