Hinge-FM2I: An Approach using Image Inpainting for Interpolating Missing Data in Univariate Time Series

TL;DR

Hinge-FM2I is a novel method that improves missing data imputation in univariate time series by combining image inpainting with a hinge-based selection algorithm, outperforming traditional methods on benchmark datasets.

Contribution

The paper introduces Hinge-FM2I, a new approach that enhances FM2I with a hinge-based selection algorithm for more accurate missing data imputation in time series.

Findings

Hinge-FM2I outperforms linear, spline, K-NN, and ARIMA methods.

Achieves an average sMAPE of 5.6% for small gaps.

Effective across various missing data rates and gap sizes.

Abstract

Accurate time series forecasts are crucial for various applications, such as traffic management, electricity consumption, and healthcare. However, limitations in models and data quality can significantly impact forecasts accuracy. One common issue with data quality is the absence of data points, referred to as missing data. It is often caused by sensor malfunctions, equipment failures, or human errors. This paper proposes Hinge-FM2I, a novel method for handling missing data values in univariate time series data. Hinge-FM2I builds upon the strengths of the Forecasting Method by Image Inpainting (FM2I). FM2I has proven effective, but selecting the most accurate forecasts remain a challenge. To overcome this issue, we proposed a selection algorithm. Inspired by door hinges, Hinge-FM2I drops a data point either before or after the gap (left/right-hinge), then use FM2I for imputation, and then select the imputed gap based on the lowest error of the dropped data point. Hinge-FM2I was evaluated on a comprehensive sample composed of 1356 time series, extracted from the M3 competition benchmark dataset, with missing value rates ranging from 3.57\% to 28.57\%. Experimental results demonstrate that Hinge-FM2I significantly outperforms established methods such as, linear/spline interpolation, K-Nearest Neighbors (K-NN), and ARIMA. Notably, Hinge-FM2I achieves an average Symmetric Mean Absolute Percentage Error (sMAPE) score of 5.6\% for small gaps, and up to 10\% for larger ones. These findings highlight the effectiveness of Hinge-FM2I as a promising new method for addressing missing values in univariate time series data.