DBSCAN of Multi-Slice Clustering for Third-Order Tensors

Several methods for triclustering three-dimensional data require as hyperparameters the cluster size set or the number of clusters in each dimension. These methods raise an issue since, for real datasets, those inputs cannot be known without extreme cost. Recently introduced, the Multi-Slice Clustering (MSC) tackles this issue by using a threshold parameter to perform the data clustering. The MSC finds signal slices that lie in a lower dimensional subspace of 3rd-order rank-1 tensor datasets. The present work addresses an extension of this algorithm, namely the MSC-DBSCAN, that extracts several slice clusters that lie in different subspaces, when the 3rd-order dataset is a sum of r 1 rank-1 tensors. Our algorithm uses the same input as the MSC algorithm and reduces to the same cluster solution for rank-1 tensor dataset.