  Transfer learning can address the learning tasks of unlabeled data in the
target domain by leveraging plenty of labeled data from a different but related
source domain. A core issue in transfer learning is to learn a shared feature
space in where the distributions of the data from two domains are matched. This
learning process can be named as transfer representation learning (TRL). The
feature transformation methods are crucial to ensure the success of TRL. The
most commonly used feature transformation method in TRL is kernel-based
nonlinear mapping to the high-dimensional space followed by linear
dimensionality reduction. But the kernel functions are lack of interpretability
and are difficult to be selected. To this end, the TSK fuzzy system (TSK-FS) is
combined with transfer learning and a more intuitive and interpretable modeling
method, called transfer representation learning with TSK-FS (TRL-TSK-FS) is
proposed in this paper. Specifically, TRL-TSK-FS realizes TRL from two aspects.
On one hand, the data in the source and target domains are transformed into the
fuzzy feature space in which the distribution distance of the data between two
domains is min-imized. On the other hand, discriminant information and
geo-metric properties of the data are preserved by linear discriminant analysis
and principal component analysis. In addition, another advantage arises with
the proposed method, that is, the nonlinear transformation is realized by
constructing fuzzy mapping with the antecedent part of the TSK-FS instead of
kernel functions which are difficult to be selected. Extensive experiments are
conducted on the text and image datasets. The results obviously show the
superiority of the proposed method.
