Missing Data Imputation via Neighbor Data Feature-Enriched Neural Ordinary Differential Equations

Abstract

Missing values, a frequently encountered problem in time series due to network failures, device malfunctions. Such incomplete time series pose significant challenges to subsequent analysis of temporal data and hinder further investigations. Nevertheless, several counter measures are taken to impute missing values based on the historical data, ignoring spatial similarity or similar rate of change among variables of neighboring devices. To comprehensively consider both temporal and neighboring information, a Neighbor Incorporating Ordinary Differential Equation (NIODE) model is proposed for imputing missing data at arbitrary time points. Specifically, the encoder adopts a graph learning model to adaptively extract a graph adjacency matrix. Utilizing a K-nearest neighbor approach, the encoder identifies and incorporates the top-K nearest neighbors into a unified graph. A graph convolution network is then employed to learn adjacent information of neighboring variables. The temporal information is captured by applying a gate recurrent unit module, thereby obtaining a spatiotemporal prior. The decoder introduces an ordinary differential equation module to generate a series of continuous time latent states. These latent states are decoded by a linear network to fill in missing values. Extensive experiments on real-world datasets demonstrate the superior performance of NIODE against state-of-the-art methods.