Several methods for tensor clustering require hyperparameters such as the cluster size or the number of clusters per mode.These methods present a challenge because, for real datasets, such inputs cannot be determined without incurring significant costs.Recently, Multi-Slice Clustering (MSC) has addressed this issue by utilizing a threshold parameter to perform data clustering.MSC identifies signal slices that reside in a lower-dimensional subspace within a 3rd-order rank-1 tensor dataset.However, determining the tensor rank remains a complex task.The current work introduces a new approach to tensor clustering that can extract clusters of similar slices and is also capable of finding co-clustering and triclustering in 3rd-order tensors of any rank.Our algorithm is based on the density of the 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.

Group invariants are used in high energy physics to define quantum field theory interactions. In this paper, we present the parallel algebraic computation of special invariants called symplectic and focus on one particular invariant that finds recent interest in physics. Our results will export to other invariants. The cost of performing basic computations on the multivariate polynomials evolves during the computation, as the polynomials get larger and/or have increasing numbers of terms. Interestingly, in some cases, they stay small. Traditionally, high-performance software is optimized by running experiments with sample data sets in order to profile and optimize expected behavior of workloads in practice. Since the (communication and computation) costs depend on the changing behavior of the symplectic invariant calculations, the standard optimization approach is insufficient. Thus, it is necessary to implement online performance tuning methods that can track the algorithm's progress and state, evaluate performance data in situ, and control the parallel resources during execution.