Finding Time-Lagged 3D Clusters

Existing 3D clustering algorithms on gene times sample times time expression data do not consider the time lags between correlated gene expression patterns. Besides, they either ignore the correlation on time subseries, or disregard the continuity of the time series, or only validate pure shifting or pure scaling coherent patterns instead of the general shifting and-scaling patterns. In this paper, we propose a novel 3D cluster model, S²D³ Cluster, to address these problems, where S² reflects the shifting-and-scaling correlation and D³ the 3-Dimensional gene times sample times time data. Within the S²D³ Cluster model, expression levels of genes are shifting-and-scaling coherent in both sample subspace and time subseries with arbitrary time lags. We develop a 3D clustering algorithm, LagMiner, for identifying interesting S²D³ Clusters that satisfy the constraints of regulation (gamma), coherence (gamma), minimum gene number (MinG), minimum sample subspace size (MinS) and minimum time periods length (MinT). Experimental results on both synthetic and real-life datasets show that LagMiner is effective, scalable and parameter-robust. While we use gene expression data in this paper, our model and algorithm can be applied on any other data where both spatial and temporal coherence are pursued.