  Graph is a fundamental mathematical structure in characterizing relations
between different objects and has been widely used on various learning tasks.
Most methods implicitly assume a given graph to be accurate and complete.
However, real data is inevitably noisy and sparse, which will lead to inferior
results. Despite the remarkable success of recent graph representation learning
methods, they inherently presume that the graph is homophilic, and largely
overlook heterophily, where most connected nodes are from different classes. In
this regard, we propose a novel robust graph structure learning method to
achieve a high-quality graph from heterophilic data for downstream tasks. We
first apply a high-pass filter to make each node more distinctive from its
neighbors by encoding structure information into the node features. Then, we
learn a robust graph with an adaptive norm characterizing different levels of
noise. Afterwards, we propose a novel regularizer to further refine the graph
structure. Clustering and semi-supervised classification experiments on
heterophilic graphs verify the effectiveness of our method.
