Efficient and Effective Optimal Transport-Based Biclustering: Supplementary Material

Z that represents some transfer of mass between elements of w and v . The proof is the same for W . Proposition 2. Suppose that the target row and column representative distributions are the same, The the Kantorovich OT problem and whose rank is at most min(rank(Z), rank( W)) . Proof of proposition 2. From linear algebra, we have that Proof of proposition 3. We suppose that The optimal transport problem can be formulated and solved as the Earth Mover's Distance (EMD) We report the biclustering performance on the synthetic datasets in table 2. At least one of our models finds the perfect partition in all cases. The gene-expression matrices used are the Cumida Breast Cancer and Leukemia datasets. Their characteristics are shown in Table 3. Table 3: Characteristics of the gene expression datasets.