Spectral embedding of regularized block models
This work provides theoretical insights for graph data representation, but it is incremental as it builds on existing regularization techniques.
The paper tackles the impact of complete graph regularization on spectral embedding in a simple block model, showing that it forces the embedding to focus on the largest blocks and reduces sensitivity to noise, with improvements demonstrated on synthetic and real data through standard clustering scores.
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we explain on a simple block model the impact of the complete graph regularization, whereby a constant is added to all entries of the adjacency matrix. Specifically, we show that the regularization forces the spectral embedding to focus on the largest blocks, making the representation less sensitive to noise or outliers. We illustrate these results on both on both synthetic and real data, showing how regularization improves standard clustering scores.