In addition, it refrains from introducing large shifts in time when searching for temporal patterns by applying a lag penalty. It groups time series with correlated changes over time, even if those patterns occur earlier or later in some of the time series. LPWC achieves both of its time series clustering goals. LPWC also identifies clusters with distinct temporal patterns in our yeast osmotic stress response and axolotl limb regeneration case studies. In a simulated dataset based on the biologically-motivated impulse model, LPWC is the only method to recover the true clusters for almost all simulated genes.

We demonstrate the advantages of LPWC versus existing time series and general clustering algorithms. It down-weights aligned profiles based on the length of the temporal lags that are introduced. LPWC aligns time series profiles to identify common temporal patterns. We propose a clustering similarity measure called Lag Penalized Weighted Correlation (LPWC) to group pairs of time series that exhibit closely-related behaviors over time, even if the timing is not perfectly synchronized. In time series datasets generated with high-throughput biological assays, measurements such as gene expression levels or protein phosphorylation intensities are collected sequentially over time, and the similarity score should capture this special temporal structure. The similarity or distance measure used for clustering can generate intuitive and interpretable clusters when it is tailored to the unique characteristics of the data.

Time series clustering