Robust Internet of Things Multidimensional Time Series Data Prediction Method

In Internet of Things (IoT) scenarios, data are susceptible to noise during collection and transmission, resulting in outliers and missing data. Existing temporal regularized matrix factorization models typically consider the squared loss as a measure of reconstruction errors, ignoring the fact that the quality of matrix factorization is also a key factor affecting a model's prediction performance when dealing with multidimensional time series in the presence of anomalous data. Therefore, this paper proposes a Time Aware Robust Non-negative Matrix Factorization multidimensional temporal prediction framework (TARNMF) based on the L_{2, log} norm. TARNMF establishes the spatiotemporal correlation of multidimensional time series data through Nonnegative Matrix Factorization (NMF) and autoregressive temporal regular terms with learnable parameters. In the presence of outliers, data obey the Laplace distribution. Based on this assumption, the L_{2, log} norm is used to estimate the error between the original data and the reconstructed matrices in the nonnegative robust matrix factorization to minimize the interference of the anomalous data on the prediction model. The L_{2, log} norm is as robust as existing metric functions, solves the problem of approximating the L₁ loss, and reduces its effect on the objective function by compressing the residuals of the outliers. The paper also proposes a projected gradient descent-based optimization method to optimize the model. Experiments on a high-dimensional Solar dataset show that TARNMF is scalable and robust, and the relative mean absolute error of the suboptimal results is reduced by 8.64%. Meanwhile, results on noisy data verify that TARNMF can efficiently process and predict IoT time series data in the presence of anomalous data.