Bernoulli Embeddings for Graphs
نویسندگان
چکیده
Just as semantic hashing [Salakhutdinov and Hinton2009] can accelerate information retrieval, binary valued embeddings can significantly reduce latency in the retrieval of graphical data. We introduce a simple but effective model for learning such binary vectors for nodes in a graph. By imagining the embeddings as independent coin flips of varying bias, continuous optimization techniques can be applied to the approximate expected loss. Embeddings optimized in this fashion consistently outperform the quantization of both spectral graph embeddings and various learned real-valued embeddings, on both ranking and pre-ranking tasks for a variety of datasets.
منابع مشابه
Labeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
متن کاملNonexistence of embeddings with uniformly bounded distortions of Laakso graphs into diamond graphs
Diamond graphs and Laakso graphs are important examples in the theory of metric embeddings. Many results for these families of graphs are similar to each other. In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. The well-known fact that Laakso graphs are uniformly doubling but diamond graphs are not, immediately implies...
متن کاملPrimitive Spatial Graphs and Graph Minors
Robertson, Seymour and Thomas characterized linkless embeddings of graphs by flat embeddings, and determined the obstruction set for linkless embeddings. In this paper, we extend flat embeddings to “primitive embeddings” as linkless embeddings to knotless embeddings. Although the obstruction set for knotless embeddings has not been determined, fundamental theorems and conjectures are obtained.
متن کاملTriangular embeddings of complete graphs
In this paper we describe the generation of all nonorientable triangular embeddings of the complete graphs K12 and K13. (The 59 nonisomorphic orientable triangular embeddings of K12 were found in 1996 by Altshuler, Bokowski and Schuchert, and K13 has no orientable triangular embeddings.) There are 182, 200 nonisomorphic nonorientable triangular embeddings for K12, and 243, 088, 286 for K13. Tri...
متن کاملDynamic Bernoulli Embeddings for Language Evolution
Word embeddings are a powerful approach for unsupervised analysis of language. Recently, Rudolph et al. (2016) developed exponential family embeddings, which cast word embeddings in a probabilistic framework. Here, we develop dynamic embeddings, building on exponential family embeddings to capture how the meanings of words change over time. We use dynamic embeddings to analyze three large colle...
متن کامل