Abstract: Deep neural networks have achieved impressive performance on computer vision tasks such as classification, localization, segmentation, captioning, and generation. Applying the same techniques to 3-D point clouds requires a different approach because they are not aligned along a grid that a fixed-size kernel can slide across. We propose treating these point clouds as graphs with connections between nearest neighbors. With this structure, we can define a graph convolution with a fixed-size kernel that can handle variable-size neighborhoods as well as an algebraic graph pooling operation based on graph clustering. With these operations, we build convolutional neural networks for 3-D object classification on the ModelNet dataset, achieving results comparable to the state of the art. We also discuss how sparse implementations of these operations reduce their memory and computational complexity.