On Biased Random Walks, Corrupted Intervals, and Learning Under Adversarial Design

Learning Representations using Spectral-Biased Random Walks on Graphs

Several state-of-the-art neural graph embedding methods are based on short random walks (stochastic processes) because of their ease of computation, simplicity in capturing complex local graph properties, scalability, and interpretibility. In this work, we are interested in studying how much a probabilistic bias in this stochastic process affects the quality of the nodes picked by the process. In particular, our biased walk, with a certain probability, favors movement towards nodes whose neighborhoods bear a structural resemblance to the current node's neighborhood. We succinctly capture this …

node2vec 或三角偏向随机游走：平稳性、正则性与复发性

node2vec or triangle-biased random walks: stationarity, regularity & recurrence

本文研究了node2vec随机游走的长期行为，通过提升到有向边和有向楔的状态空间，揭示其正则性和复发性条件，区分其与非回溯随机游走的差异。

Graph Node Embeddings using Domain-Aware Biased Random Walks

The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms for mapping graph data to real-valued vector spaces has become an active area of research. Existing graph embedding approaches are based purely on structural information and ignore any semantic information from the underlying domain. In this paper, we demonstrate that semantic information can play a useful role in computing graph embeddings. Specifically, we …

BiasedWalk: Biased Sampling for Representation Learning on Graphs

Network embedding algorithms are able to learn latent feature representations of nodes, transforming networks into lower dimensional vector representations. Typical key applications, which have effectively been addressed using network embeddings, include link prediction, multilabel classification and community detection. In this paper, we propose BiasedWalk, a scalable, unsupervised feature learning algorithm that is based on biased random walks to sample context information about each node in the network. Our random-walk based sampling can behave as Breath-First-Search (BFS) and Depth-First-S…

Accurately Modeling Biased Random Walks on Weighted Graphs Using $\textit{Node2vec+}$

Node embedding is a powerful approach for representing the structural role of each node in a graph. $\textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph. However, $\textit{node2vec}$ does not consider edge weights when computing walk biases. This intrinsic limitation prevents $\textit{node2vec}$ from leveraging all the information in weighted graphs and, in turn, limits its application to many real-world networks that are weighted and dense. Here, we naturally extend $\textit{node2vec}$ to $\textit{n…

GlobalWalk: Learning Global-aware Node Embeddings via Biased Sampling

Popular node embedding methods such as DeepWalk follow the paradigm of performing random walks on the graph, and then requiring each node to be proximate to those appearing along with it. Though proved to be successful in various tasks, this paradigm reduces a graph with topology to a set of sequential sentences, thus omitting global information. To produce global-aware node embeddings, we propose GlobalWalk, a biased random walk strategy that favors nodes with similar semantics. Empirical evidence suggests GlobalWalk can generally enhance global awareness of the generated embeddings.