  Matrix factorization is at the heart of many machine learning algorithms, for
example, dimensionality reduction (e.g. kernel PCA) or recommender systems
relying on collaborative filtering. Understanding a singular value
decomposition (SVD) of a matrix as a neural network optimization problem
enables us to decompose large matrices efficiently while dealing naturally with
missing values in the given matrix. But most importantly, it allows us to learn
the connection between data points' feature vectors and the matrix containing
information about their pairwise relations. In this paper we introduce a novel
neural network architecture termed Similarity Encoder (SimEc), which is
designed to simultaneously factorize a given target matrix while also learning
the mapping to project the data points' feature vectors into a similarity
preserving embedding space. This makes it possible to, for example, easily
compute out-of-sample solutions for new data points. Additionally, we
demonstrate that SimEc can preserve non-metric similarities and even predict
multiple pairwise relations between data points at once.
