  The area of graph embeddings is currently dominated by contrastive learning
methods, which demand formulation of an explicit objective function and
sampling of positive and negative examples. This creates a conceptual and
computational overhead. Simple, classic unsupervised approaches like
Multidimensional Scaling (MSD) or the Laplacian eigenmap skip the necessity of
tedious objective optimization, directly exploiting data geometry.
Unfortunately, their reliance on very costly operations such as matrix
eigendecomposition make them unable to scale to large graphs that are common in
today's digital world. In this paper we present Cleora: an algorithm which gets
the best of two worlds, being both unsupervised and highly scalable. We show
that high quality embeddings can be produced without the popular step-wise
learning framework with example sampling. An intuitive learning objective of
our algorithm is that a node should be similar to its neighbors, without
explicitly pushing disconnected nodes apart. The objective is achieved by
iterative weighted averaging of node neigbors' embeddings, followed by
normalization across dimensions. Thanks to the averaging operation the
algorithm makes rapid strides across the embedding space and usually reaches
optimal embeddings in just a few iterations. Cleora runs faster than other
state-of-the-art CPU algorithms and produces embeddings of competitive quality
as measured on downstream tasks: link prediction and node classification. We
show that Cleora learns a data abstraction that is similar to contrastive
methods, yet at much lower computational cost. We open-source Cleora under the
MIT license allowing commercial use under https://github.com/Synerise/cleora.
