Algorithm 1: PSA-MNMF

Input: Dataset A={a1,…., an}, a set of partitions B of data points B = {b1,b2, ….., bt} such that each partition B consists of a set of clustering Dt= {d1t, d2t, …., dkt} that uses a selected clustering methodology. Output: The set H of B heterogeneous clusterings that included the 10 best and highest F-scores (or performance metrics α) and appeared in all 100 runs when using the exhaustive search method.  Initialization:  Calculate the X-cluster= {The results of each clustering Initialize H= {}. Define the connectivity matric CM as follows:             $C{M}_{ij}\left(b^t\right)=\{\begin{array}{c}1 \left(i,j\right)\in D_k\left(b^t\right)\\ 0 \left(i,j\right)\notin D_k\left(b^t\right) \end{array}$ Define a matrix Nixk such that in each row only “1” can exist and the rest of the values should be zeros. Calculate the NNT. If i belongs to k, the results will equal 1, otherwise they will equal zero. Define L as L = NTN.   Begin  $\mathbf{Step} \mathbf{1}\mathbf{\text{:}} \mathrm{The} \mathrm{optimization} \mathrm{equation} \mathrm{for} \mathrm{PSA}-\mathrm{NMF} \mathrm{is} \mathrm{calculated} \mathrm{using} \mathrm{the} \mathrm{equation}\text{:} \underset{N, L\ge 0}{\min }\left|\right|\widetilde{CM}-\tilde{N}L{\tilde{N}}^T\left|\right|{}^2$, where NTN=1 $\mathbf{Step} \mathbf{2}\mathbf{\text{:}} \mathrm{At} \mathrm{each} \mathrm{iteration}, \mathrm{the} \mathrm{N} \mathrm{value} \mathrm{will} \mathrm{be} \mathrm{updated} \mathrm{using} \mathrm{this} \mathrm{equation}\text{:} N_{oi} \leftarrow N_{oi} \sqrt{\frac{{\left(CM N L\right)}_{oi}}{{\left(N{N}^{T}CM NL\right)}_{oi}}}$ $\mathbf{Step} \mathbf{3}\mathbf{\text{:}} \mathrm{At} \mathrm{each} \mathrm{iteration}, \mathrm{the} L \mathrm{is} \mathrm{updated}\text{:} L_{ie} \leftarrow L_{ie} \sqrt{\frac{{\left(N^{T}CM N\right)}_{ie}}{{\left(N^{T}N L N^{T}N\right)}_{ie}}}$ Step 5: The exhaustive method finds the best performance metric from among the top 10 recorded combinations. Step 4: Steps 1-4 are repeated 100 times. Step 6: The final consensus clustering solution assigns each data point in the input data set to a consensus cluster. Step 7: The algorithm returns H and performance metrics α (including F-score, accuracy, precision, and recall) End