  Random feature (RF) has been widely used for node consistency in
decentralized kernel ridge regression (KRR). Currently, the consistency is
guaranteed by imposing constraints on coefficients of features, necessitating
that the random features on different nodes are identical. However, in many
applications, data on different nodes varies significantly on the number or
distribution, which calls for adaptive and data-dependent methods that generate
different RFs. To tackle the essential difficulty, we propose a new
decentralized KRR algorithm that pursues consensus on decision functions, which
allows great flexibility and well adapts data on nodes. The convergence is
rigorously given and the effectiveness is numerically verified: by capturing
the characteristics of the data on each node, while maintaining the same
communication costs as other methods, we achieved an average regression
accuracy improvement of 25.5\% across six real-world data sets.
