Discrete mathematics

Equivalence (formal languages)

Mathematics

Domain (mathematical analysis)

Algorithm

Mathematical analysis

Artificial intelligence

Equivalence relation

Computer science

Theoretical computer science

Notation

Artificial neural network

Fuzzy logic

Arithmetic

IEEE Transactions on Fuzzy Systems

In unsupervised domain adaptation (UDA), a classifier for a target domain is trained with labeled source data and unlabeled target data. Existing UDA methods assume that the source data come from the same source domain (i.e., single-source scenario) or from multiple source domains, whose feature spaces have the same dimension ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">homogeneous</i> ) but different distributions (i.e., multihomogeneous-source scenario). However, in the real world, for a specific target domain, we probably have multiple different-dimension ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">heterogeneous</i> ) source domains, which do not satisfy the assumption of existing UDA methods. To remove this assumption and move forward to a realistic UDA problem, this article presents a shared-fuzzy-equivalence-relation neural network (SFERNN) for addressing the multisource heterogeneous UDA problem. The SFERNN is a five-layer neural network containing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c$</tex-math></inline-formula> source branches and one target branch. The network structure of the SFERNN is first confirmed by a novel fuzzy relation called multisource shared fuzzy equivalence relation. Then, we optimize parameters of the SFERNN via minimizing cross-entropy loss on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c$</tex-math></inline-formula> source branches and the distributional discrepancy between each source branch and the target branch. Experiments distributed across eight real-world datasets are conducted to validate the SFERNN. This testing regime demonstrates that the SFERNN outperforms the existing single-source heterogeneous UDA methods, especially when the target domain contains few data.

Multisource Heterogeneous Unsupervised Domain Adaptation via Fuzzy Relation Neural Networks