Factorization-Based Methods
Learn about factorization-based knowledge graph embedding methods.
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Factorization
Factorization-based methods learn representations of entities and relations in a knowledge graph by factorizing a large sparse matrix of entity-relation pairs. We aim to find two matrices (one for entities and one for relation) so that the product of both matrices approximates the original graph structure. Some of the factorization-based methods include the following.
RESCAL
The RESCAL method is based on tensor factorization. The idea here is to express the graph as a three-way tensor so that , where is the number of entities and is the number of relations. The tensor holds value , denoting the presence of a relation between the entities, and if there are none.
Note: A tensor is a multidimensional array. In other words, a vector is a first-order tensor, and a matrix is a second-order tensor. If the order is greater than two, we just call it a high-order tensor or simply a tensor.
First, the algorithm initializes a tensor and then updates the matrices iteratively by minimizing the difference between the product of the matrices and the original tensor.
The algorithm can be denoted with the following equation:
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