explores indexing structures, which divides the input point cloud into leaves, and then aggregates node features from leaves to the root. Inspired by the convolution operation, recent methods [@li2018pointcnn; @wang2018dynamic; @xu2018spidercnn] investigate well-designed CNN-like operations to aggregate points in local regions by building local connections with k-neareat-neighbors (kNN).

Capturing the context information inside local regions is very important for the discriminative ability of the learned point cloud representations. KC-Net [@shen2018mining] employs a kernel correlation layer and a graph pooling layer to capture the local patterns of point clouds. ShapeContextNet [@xie2018attentional] extends 2D Shape Context [@belongie2001shape] to the 3D, which divides a local region into small bins and aggregates the bin features. Point2Seqeuce [@liu2019point2sequence] employs an attention-based sequence to sequence architecture to encode the multi-scale area features inside local regions.

In order to alleviate the dependence on the labeled data, some studies have performed unsupervised learning for point clouds. FoldingNet [@yang2018foldingnet] proposes a folding operation to deform a canonical 2D grid onto the suface of a point cloud. 3D-PointCapsNet [@zhao2019pcn] employs a dynamic routing scheme in the reconstruction of input point clouds. However, it is difficult for these methods to capture the local patterns of point clouds. Similar to FoldingNet, PPF-FoldNet 