Implicit consensus clustering from multiple graphs

Abstract

Dealing with relational learning generally relies on tools modeling relational data. An undirected graph can represent these data with vertices depicting entities and edges describing the relationships between the entities. These relationships can be well represented by multiple undirected graphs over the same set of vertices with edges arising from different graphs catching heterogeneous relations. The vertices of those networks are often structured in unknown clusters with varying properties of connectivity. These multiple graphs can be structured as a three-way tensor, where each slice of tensor depicts a graph which is represented by a count data matrix. To extract relevant clusters, we propose an appropriate model-based co-clustering capable of dealing with multiple graphs. The proposed model can be seen as a suitable tensor extension of mixture models of graphs, while the obtained co-clustering can be treated as a consensus clustering of nodes from multiple graphs. Applications on real datasets and comparisons with multi-view clustering and tensor decomposition methods show the interest of our contribution.

Tensor-based Graph Modularity for Text Data Clustering

“…, 𝑣 described in the previous section as part of a tensor X of size 𝑛 × 𝑛 × 𝑣. This tensor is used as input to tensor-based clustering techniques which are PARAFAC [17], TUCKER [30], TSPLBM 3 [6][7][8] and our proposed algorithm TGM.…”

“…A suitable way of combining the different available representations consists in using them as part of a 3-way tensor model representation [25] or 3-way similarity tensor [7]. To achieve the latter for a given dataset, we first compute different representation matrices (using BOW, static and contextual embeddings, and entity linking).…”

Spectral partitioning of large and sparse 3‐tensors using low‐rank tensor approximation

“…for some n 1 ≤ n. (We here use the prime notation to indicate that (18) corresponds to the first case in Example 2 and (19) corresponds to the third case. If, in (19), n 1 = n and  1 = 0, then each 3-slice represents a bipartite graph.…”

“…Moreover, as our method is based on perturbation theory, it is natural to define a measure using norms of the tensor blocks after permutations. For instance, when the permuted tensor is approximately of type (18),…”

“…Example 5. We constructed a tensor close to a general (1,2)-reducible structure (18). For visibility reasons we do not give a spy plot of the tensor but of two slices, see Figure )…”