Convolution Neural Networks on Graphs are important generalization and extension of classical CNNs. While previous works generally assumed that the graph structures of samples are regular with unified dimensions, in many applications, they are highly diverse or even not well defined. Under some circumstances, e.g. chemical molecular data, clustering or coarsening for simplifying the graphs is hard to be justified chemically. In this paper, we propose a more general and flexible graph convolution network (EGCN) fed by batch of arbitrarily shaped data together with their evolving graph Laplacians trained in supervised fashion. Extensive experiments have been conducted to demonstrate the superior performance in terms of both the acceleration of parameter fitting and the significantly improved prediction accuracy on multiple graph-structured datasets.
Recently, @cite_19 investigated a similar problem as ours by learning edge-conditioned feature weight matrix from edge features using a separate filter-generating network @cite_22 , while @cite_19 's application is on point cloud classification. There are other studies about learning on graph data such as @cite_5 that proposed a kernel embedding methods on feature space for graph-structured data. Another similar work is @cite_17 , but their models do not fall into the kingdom of feed-forward CNN analogs on graphs.
@cite_19 @cite_5 @cite_22 @cite_17
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Recognizing fine-grained categories (e.g., bird species) highly relies on discriminative part localization and part-based fine-grained feature learning. Existing approaches predominantly solve these challenges independently, while neglecting the fact that part localization (e.g., head of a bird) and fine-grained feature learning (e.g., head shape) are mutually correlated. In this paper, we propose a novel part learning approach by a multi-attention convolutional neural network (MA-CNN), where part generation and feature learning can reinforce each other. MA-CNN consists of convolution, channel grouping and part classification sub-networks. The channel grouping network takes as input feature channels from convolutional layers, and generates multiple parts by clustering, weighting and pooling from spatially-correlated channels. The part classification network further classifies an image by each individual part, through which more discriminative fine-grained features can be learned. Two losses are proposed to guide the multi-task learning of channel grouping and part classification, which encourages MA-CNN to generate more discriminative parts from feature channels and learn better fine-grained features from parts in a mutual reinforced way. MA-CNN does not need bounding box part annotation and can be trained end-to-end. We incorporate the learned parts from MA-CNN with part-CNN for recognition, and show the best performances on three challenging published fine-grained datasets, e.g., CUB-Birds, FGVC-Aircraft and Stanford-Cars. Feature learning on point clouds has shown great promise, with the introduction of effective and generalizable deep learning frameworks such as pointnet++. Thus far, however, point features have been abstracted in an independent and isolated manner, ignoring the relative layout of neighboring points as well as their features. In the present article, we propose to overcome this limitation by using spectral graph convolution on a local graph, combined with a novel graph pooling strategy. In our approach, graph convolution is carried out on a nearest neighbor graph constructed from a point’s neighborhood, such that features are jointly learned. We replace the standard max pooling step with a recursive clustering and pooling strategy, devised to aggregate information from within clusters of nodes that are close to one another in their spectral coordinates, leading to richer overall feature descriptors. Through extensive experiments on diverse datasets, we show a consistent demonstrable advantage for the tasks of both point set classification and segmentation. Our implementations are available at https: github.com fate3439 LocalSpecGCN. We present a simple and general framework for feature learning from point cloud. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point cloud are irregular and unordered, thus a direct convolving of kernels against the features associated with the points will result in deserting the shape information while being variant to the orders. To address these problems, we propose to learn a X-transformation from the input points, which is used for simultaneously weighting the input features associated with the points and permuting them into latent potentially canonical order. Then element-wise product and sum operations of typical convolution operator are applied on the X-transformed features. The proposed method is a generalization of typical CNNs into learning features from point cloud, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks. We present a novel approach to learning a point-wise, meaningful embedding for point-clouds in an unsupervised manner, through the use of neural-networks. The domain of point-cloud processing via neural-networks is rapidly evolving, with novel architectures and applications frequently emerging. Within this field of research, the availability and plethora of unlabeled point-clouds as well as their possible applications make finding ways of characterizing this type of data appealing. Though significant advancement was achieved in the realm of unsupervised learning, its adaptation to the point-cloud representation is not trivial. Previous research focuses on the embedding of entire point-clouds representing an object in a meaningful manner. We present a deep learning framework to learn point-wise description from a set of shapes without supervision. Our approach leverages self-supervision to define a relevant loss function to learn rich per-point features. We train a neural-network with objectives based on context derived directly from the raw data, with no added annotation. We use local structures of point-clouds to incorporate geometric information into each point's latent representation. In addition to using local geometric information, we encourage adjacent points to have similar representations and vice-versa, creating a smoother, more descriptive representation. We demonstrate the ability of our method to capture meaningful point-wise features through three applications. By clustering the learned embedding space, we perform unsupervised part-segmentation on point clouds. By calculating euclidean distance in the latent space we derive semantic point-analogies. Finally, by retrieving nearest-neighbors in our learned latent space we present meaningful point-correspondence within and among point-clouds.