We present a new approach for learning graph embeddings, that relies on structural measures of node similarities for generation of training data. The model learns node embeddings that are able to approximate a given measure, such as the shortest path distance or any other. Evaluations of the proposed model on semantic similarity and word sense disambiguation tasks (using WordNet as the source of gold similarities) show that our method yields state-of-the-art results, but also is capable in certain cases to yield even better performance than the input similarity measure. The model is computationally efficient, orders of magnitude faster than the direct computation of graph distances.
The method described in this paper falls into the category of shallow embeddings', meaning that we do not attempt to embed entire communities or neighborhoods: our aim is to approximate distances or similarities between (single) nodes. Existing approaches to solving this task mostly use either factorization of the graph adjacency matrix @cite_35 @cite_22 or random walks over the graph as in @cite_2 and @cite_16 . A completely different approach is taken by , who directly embed the WordNet tree graph into Hamming hypercube binary representations. Their model is dubbed Fast similarity embedding' () and also optimizes one of our objectives, i.e. to provide a much quicker way of calculating semantic similarities based on WordNet knowledge. However, the embeddings are not differentiable, limiting their use in many deep neural architectures, especially if fine-tuning is needed.
@cite_35 @cite_16 @cite_22 @cite_2
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The graph embedding paradigm projects nodes of a graph into a vector space, which can facilitate various downstream graph analysis tasks such as node classification and clustering. To efficiently learn node embeddings from a graph, graph embedding techniques usually preserve the proximity between node pairs sampled from the graph using random walks. In the context of a heterogeneous graph, which contains nodes from different domains, classical random walks are biased towards highly visible domains where nodes are associated with a dominant number of paths. To overcome this bias, existing heterogeneous graph embedding techniques typically rely on meta-paths (i.e., fixed sequences of node types) to guide random walks. However, using these meta-paths either requires prior knowledge from domain experts for optimal meta-path selection, or requires extended computations to combine all meta-paths shorter than a predefined length. In this paper, we propose an alternative solution that does not involve any meta-path. Specifically, we propose JUST, a heterogeneous graph embedding technique using random walks with JUmp and STay strategies to overcome the aforementioned bias in an more efficient manner. JUST can not only gracefully balance between homogeneous and heterogeneous edges, it can also balance the node distribution over different domains (i.e., node types). By conducting a thorough empirical evaluation of our method on three heterogeneous graph datasets, we show the superiority of our proposed technique. In particular, compared to a state-of-the-art heterogeneous graph embedding technique Hin2vec, which tries to optimally combine all meta-paths shorter than a predefined length, our technique yields better results in most experiments, with a dramatically reduced embedding learning time (about 3x speedup). Recently there have been significant advances in image up scaling or image super-resolution based on a dictionary of low and high resolution exemplars. The running time of the methods is often ignored despite the fact that it is a critical factor for real applications. This paper proposes fast super-resolution methods while making no compromise on quality. First, we support the use of sparse learned dictionaries in combination with neighbor embedding methods. In this case, the nearest neighbors are computed using the correlation with the dictionary atoms rather than the Euclidean distance. Moreover, we show that most of the current approaches reach top performance for the right parameters. Second, we show that using global collaborative coding has considerable speed advantages, reducing the super-resolution mapping to a precomputed projective matrix. Third, we propose the anchored neighborhood regression. That is to anchor the neighborhood embedding of a low resolution patch to the nearest atom in the dictionary and to precompute the corresponding embedding matrix. These proposals are contrasted with current state-of-the-art methods on standard images. We obtain similar or improved quality and one or two orders of magnitude speed improvements. The success of neural network methods for computing word embeddings has motivated methods for generating semantic embeddings of longer pieces of text, such as sentences and paragraphs. Surprisingly, (ICLR'16) showed that such complicated methods are outperformed, especially in out-of-domain (transfer learning) settings, by simpler methods involving mild retraining of word embeddings and basic linear regression. The method of requires retraining with a substantial labeled dataset such as Paraphrase Database (, 2013). @PARASPLIT The current paper goes further, showing that the following completely unsupervised sentence embedding is a formidable baseline: Use word embeddings computed using one of the popular methods on unlabeled corpus like Wikipedia, represent the sentence by a weighted average of the word vectors, and then modify them a bit using PCA SVD. This weighting improves performance by about 10 to 30 in textual similarity tasks, and beats sophisticated supervised methods including RNN's and LSTM's. It even improves 's embeddings. This simple method should be used as the baseline to beat in future, especially when labeled training data is scarce or nonexistent. @PARASPLIT The paper also gives a theoretical explanation of the success of the above unsupervised method using a latent variable generative model for sentences, which is a simple extension of the model in (TACL'16) with new "smoothing" terms that allow for words occurring out of context, as well as high probabilities for words like and, not in all contexts. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50).