Fuzzy Longest Common Subsequence Matching With FCM Using R

Capturing the interdependencies between real valued time series can be achieved by finding common similar patterns. The abstraction of time series makes the process of finding similarities closer to the way as humans do. Therefore, the abstraction by means of a symbolic levels and finding the common patterns attracts researchers. One particular algorithm, Longest Common Subsequence, has been used successfully as a similarity measure between two sequences including real valued time series. In this paper, we propose Fuzzy Longest Common Subsequence matching for time series.

💡 Research Summary

The paper introduces a novel similarity measure for real‑valued time‑series called Fuzzy Longest Common Subsequence (Fuzzy‑LCS). The authors begin by highlighting the importance of pattern matching in time‑series analysis and noting that conventional techniques such as Dynamic Time Warping (DTW), Symbolic Aggregate approXimation (SAX) combined with LCS, and the classic LCS algorithm each suffer from specific drawbacks. DTW is computationally intensive and sensitive to noise, SAX reduces a continuous series to a discrete symbol string but discards subtle amplitude information, and classic LCS only counts exact symbol matches, making it brittle when the data are perturbed or temporally misaligned.

To overcome these limitations, the authors propose a two‑stage pipeline. First, the raw series are normalized and optionally resampled to a common length. Then, Fuzzy C‑Means (FCM) clustering is applied to the entire dataset, producing a set of c fuzzy clusters (typically 5–10). Each time point i receives a membership vector μ_i = (μ_i^1, …, μ_i^c) where μ_i^k ∈