Algorithm 2 Tracking MC with its decomposition

Require: A dataset $\mathcal{X}=\{{\left\{x_{n,t}\right\}}_{n=1}^N\mid t\in 1,\dots ,T\}$, parameters m and L. 1: 2: # Step 1: Estimate lower components. 3: for $t=1$ to $t=T$ do 4:       Estimate ${\widehat{K}}_t$ and ${\left\{{\widehat{g}}_{k,t}\right\}}_{k=1}^{{\widehat{K}}_t}$ from the data ${\left\{x_{n,t}\right\}}_{n=1}^N$ using SDMS. 5:       Calculate ${\mathrm{MC}\left(\mathrm{total}\right)}_t:=\mathrm{MC}\left({\left\{{\widehat{\gamma }}_k\left(x_n\right)\right\}}_{k,n}\right)$. 6: end for 7: 8: # Step 2: Estimate upper components and partition. 9: Estimate the centers ${\tilde{\mu }}_l$ and the partition $Q_{k,t}^{\left(l\right)}$ using fuzzy c-means. 10: 11: # Step 3: Calculate the decomposition of MC. 12: for $t=1$ to $t=T$ do 13:       Calculate ${\mathrm{MC}\left(\mathrm{interaction}\right)}_t$ defined in Section 4.2. 14:       for $l=1$ to $l=L$ do 15:           Calculate $\mathrm{W}(\mathrm{component}l{)}_t$ defined in Section 4.2. 16:           Calculate $\mathrm{MC}(\mathrm{component}l{)}_t$ defined in Section 4.2. 17:     end for 18: end for 19: return ${\left\{{\mathrm{MC}\left(\mathrm{total}\right)}_t\right\}}_{t=1}^T$, ${\left\{{\mathrm{MC}\left(\mathrm{interaction}\right)}_t\right\}}_{t=1}^T$, ${\left\{{\left\{\mathrm{W}(\mathrm{component}l{)}_t\right\}}_{l=1}^L\right\}}_{t=1}^T$, ${\left\{{\left\{\mathrm{MC}(\mathrm{component}l{)}_t\right\}}_{l=1}^L\right\}}_{t=1}^T$.