Learning Similarity Metrics by Factorising Adjacency Matrices

Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By factorising the adjacency matrix of the relation we are able to learn target vectors for each instance. A regression model can then be constructed that maps instances to these learned targets, resulting in a feature extractor that computes vectors for which the inner product is a meaningful measure of similarity. The primary advantage of our approach is the vastly improved running time compared to other methods that rely on pairwise similarity constraints. We present results demonstrating our method can converge several times faster, while also exhibiting competitive or superior accuracy.