Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or predictions. We present an approach for applying machine learning directly to such graph neighborhoods, yielding predicitons for graph nodes on the basis of the structure of their local neighborhood and the features of the nodes in it. Our approach allows predictions to be learned directly from examples, bypassing the step of creating and tuning an inference model or summarizing the neighborhoods via a fixed set of hand-crafted features. The approach is based on a multi-level architecture built from Long Short-Term Memory neural nets (LSTMs); the LSTMs learn how to summarize the neighborhood from data. We demonstrate the effectiveness of the proposed technique on a synthetic example and on real-world data related to crowdsourced grading, Bitcoin transactions, and Wikipedia edit reversions.
Several approaches have been proposed for summarizing graph structures in feature vectors. The algorithm node2vec @cite_4 enables the construction of feature vectors for graph nodes in such a way that the feature vector optimally represents the node's location in the graph. Specifically, the feature vector maximizes the a-posteriori probability of graph neighborhoods given the feature vector. The resulting feature vector thus summarizes a node's location in a graph, but it does not summarize the original features of the node, or of its neighbors. In contrast, the techniques we introduce allow us to feed to machine learning the node features of an entire graph neighborhood.
@cite_4
2366141641 2962756421 2094325573 2963830382
Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks. Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks. Video summarization helps users obtain quick comprehension of video content. Recently, some studies have utilized local features to represent each video frame and formulate video summarization as a coverage problem of local features. However, the importance of individual local features has not been exploited. In this paper, we propose a novel Bag-of-Importance (BoI) model for static video summarization by identifying the frames with important local features as keyframes, which is one of the first studies formulating video summarization at local feature level, instead of at global feature level. That is, by representing each frame with local features, a video is characterized with a bag of local features weighted with individual importance scores and the frames with more important local features are more representative, where the representativeness of each frame is the aggregation of the weighted importance of the local features contained in the frame. In addition, we propose to learn a transformation from a raw local feature to a more powerful sparse nonlinear representation for deriving the importance score of each local feature, rather than directly utilize the hand-crafted visual features like most of the existing approaches. Specifically, we first employ locality-constrained linear coding (LCC) to project each local feature into a sparse transformed space. LCC is able to take advantage of the manifold geometric structure of the high dimensional feature space and form the manifold of the low dimensional transformed space with the coordinates of a set of anchor points. Then we calculate the l2 norm of each anchor point as the importance score of each local feature which is projected to the anchor point. Finally, the distribution of the importance scores of all the local features in a video is obtained as the BoI representation of the video. We further differentiate the importance of local features with a spatial weighting template by taking the perceptual difference among spatial regions of a frame into account. As a result, our proposed video summarization approach is able to exploit both the inter-frame and intra-frame properties of feature representations and identify keyframes capturing both the dominant content and discriminative details within a video. Experimental results on three video datasets across various genres demonstrate that the proposed approach clearly outperforms several state-of-the-art methods. 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.