Nonlinear Model-Based Method for Clustering Periodically Expressed Genes

Algorithm 1

Algorithm for nonlinear model-based clustering.

(1) Select an initial partition for given the number of clusters, 𝐾

(2) Iteration (𝑡=1,2,…):

 (a) estimate the parameter Θ^𝑡 based on the present partition by using (2.11);

 (b) generate a new partition by assigning each sequence 𝑥 to cluster 𝑘 for which the

value of 𝑠²=∑^𝑚𝑖=1[𝑥(𝑖)−𝑎^𝑡𝑘̂cos(𝑖Δ𝜔^𝑡𝑘)−𝑏̂^𝑡𝑘sin(𝑖Δ𝜔^𝑡𝑘)]² is minimum.

(3) Stop if the improvement of the cost function (2.10) is below a given threshold, the

cluster memberships of time series do not change.