Parallel Computation of Multi-Slice Clustering of Third-Order Tensors

Machine Learning approaches like clustering methods deal with massive datasets that present an increasing challenge. We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method is based on spectral analysis of the tensor slices and works independently on each tensor mode. Such features fit well in the parallel paradigm via a distributed memory system. We show that our parallel scheme outperforms sequential computing and allows for the scalability of the MSC method.

DBSCAN of Multi-Slice Clustering for Third-Order Tensors

Several methods for triclustering three-dimensional data require the cluster size or the number of clusters in each dimension to be specified. To address this issue, the Multi-Slice Clustering (MSC) for 3-order tensor finds signal slices that lie in a low dimensional subspace for a rank-one tensor dataset in order to find a cluster based on the threshold similarity. We propose an extension algorithm called MSC-DBSCAN to extract the different clusters of slices that lie in the different subspaces from the data if the dataset is a sum of r rank-one tensor (r > 1). Our algorithm uses the same input as the MSC algorithm and can find the same solution for rank-one tensor data as MSC.

Multiway clustering of 3-order tensor via affinity matrix

We propose a new method of multiway clustering for 3-order tensors via affinity matrix (MCAM). Based on a notion of similarity between the tensor slices and the spread of information of each slice, our model builds an affinity/similarity matrix on which we apply advanced clustering methods. The combination of all clusters of the three modes delivers the desired multiway clustering. Finally, MCAM achieves competitive results compared with other known algorithms on synthetics and real datasets.

Multi-Slice Clustering for 3-order Tensor Data

Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the multi-slice clustering (MSC) for a 3-order tensor data set. We analyse, in each dimension or tensor mode, the spectral decomposition of each tensor slice, i.e. a matrix. Thus, we define a similarity measure between matrix slices up to a threshold (precision) parameter, and from that, identify a cluster. The intersection of all partial clusters provides the desired triclustering. The effectiveness of our algorithm is shown on both synthetic and real-world data sets.