# Simultaneous Partitioning of a Sequence of Graphs using a Spectral Tensor Method

**Lars Eldén
**

Department of Mathematics

Linköping University

Linköping

### Abstract:

Spectral graph partitioning is a method for clustering data organized
as undirected graphs, and it has numerous applications in information
sciences. The method is based on the computation of eigenvectors of
the graph Laplacian. In many areas one wants to cluster data from a
sequence of graphs. Such data can be organized as a large sparse
tensor. A few attempts have been made to generalize spectral
partitioning to the tensor case. Unfortunately there is no natural way
to set up the Laplacian of a sparse tensor.

We will present a spectral method for tensor partitioning based on the
computation of the best rank-(2,2,2) aproximation of the tensor. A few
applications are briefly discussed.