  The collaborative filtering (CF) problem with only user-item interaction
information can be solved by graph signal processing (GSP), which uses low-pass
filters to smooth the observed interaction signals on the similarity graph to
obtain the prediction signals. However, the interaction signal may not be
sufficient to accurately characterize user interests and the low-pass filters
may ignore the useful information contained in the high-frequency component of
the observed signals, resulting in suboptimal accuracy. To this end, we propose
a personalized graph signal processing (PGSP) method for collaborative
filtering. Firstly, we design the personalized graph signal containing richer
user information and construct an augmented similarity graph containing more
graph topology information, to more effectively characterize user interests.
Secondly, we devise a mixed-frequency graph filter to introduce useful
information in the high-frequency components of the observed signals by
combining an ideal low-pass filter that smooths signals globally and a linear
low-pass filter that smooths signals locally. Finally, we combine the
personalized graph signal, the augmented similarity graph and the
mixed-frequency graph filter by proposing a pipeline consisting of three key
steps: pre-processing, graph convolution and post-processing. Extensive
experiments show that PGSP can achieve superior accuracy compared with
state-of-the-art CF methods and, as a nonparametric method, PGSP has very high
training efficiency.
