A New Fuzzy Logic-Based Similarity Measure Applied to Large Gap Imputation for Uncorrelated Multivariate Time Series

Abstract

The completion of missing values is a prevalent problem in many domains of pattern recognition and signal processing. Analyzing data with incompleteness may lead to a loss of power and unreliable results, especially for large missing subsequence(s). Therefore, this paper aims to introduce a new approach for filling successive missing values in low/uncorrelated multivariate time series which allows managing a high level of uncertainty. In this way, we propose using a novel fuzzy weighting-based similarity measure. The proposed method involves three main steps. Firstly, for each incomplete signal, the data before a gap and the data after this gap are considered as two separated reference time series with their respective query windows Q b and Q a. We then find the most similar subsequence (Q b s) to the subsequence before this gap Q b and the most similar one (Q a s) to the subsequence after the gap Q a. To find these similar windows, we build a new similarity measure based on fuzzy grades of basic similarity measures and on fuzzy logic rules. Finally, we fill in the gap with average values of the window following Q b s and the one preceding Q a s. The experimental results have demonstrated that the proposed approach outperforms the state-of-the-art methods in case of multivariate time series having low/noncorrelated data but effective information on each signal.