  In this paper, we propose a scalable algorithm for spectral embedding. The
latter is a standard tool for graph clustering. However, its computational
bottleneck is the eigendecomposition of the graph Laplacian matrix, which
prevents its application to large-scale graphs. Our contribution consists of
reformulating spectral embedding so that it can be solved via stochastic
optimization. The idea is to replace the orthogonality constraint with an
orthogonalization matrix injected directly into the criterion. As the gradient
can be computed through a Cholesky factorization, our reformulation allows us
to develop an efficient algorithm based on mini-batch gradient descent.
Experimental results, both on synthetic and real data, confirm the efficiency
of the proposed method in term of execution speed with respect to similar
existing techniques.
