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Predicting pairwise relations with neural similarity encoders

Horn F., Müller K. R.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

Vol. 66, nr 6

821--830

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.

Adaptive test selection for factorization-based surrogate fitness in genetic programming

Krawiec K., Liskowski P.

Foundations of Computing and Decision Sciences

2017

Vol. 42, No. 4

339--358

Genetic programming (GP) is a variant of evolutionary algorithm where the entities undergoing simulated evolution are computer programs. A fitness function in GP is usually based on a set of tests, each of which defines the desired output a correct program should return for an exemplary input. The outcomes of interactions between programs and tests in GP can be represented as an interaction matrix, with rows corresponding to programs in the current population and columns corresponding to tests. In previous work, we proposed SFIMX, a method that performs only a fraction of interactions and employs non-negative matrix factorization to estimate the outcomes of remaining ones, shortening GP’s runtime. In this paper, we build upon that work and propose three extensions of SFIMX, in which the subset of tests drawn to perform interactions is selected with respect to test difficulty. The conducted experiment indicates that the proposed extensions surpass the original SFIMX on a suite of discrete GP benchmarks.

A factor graph based genetic algorithm

Helmi B. H., Rahmani A. T., Pelikan M.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 3

621--633

We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems are provided as support for the mathematical analysis of the approach. The experiments show that FGGA is capable of learning linkages and solving the optimization problems in polynomial time with a polynomial number of evaluations.