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

Abstract EN

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.