  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.
