Related papers: Vertex-reinforced Random Walk for Network Embeddin…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~\cite{mgr, fmk,…
This article studies vertex reinforced random walks that are non-backtracking (denoted VRNBW), i.e. U-turns forbidden. With this last property and for a strong reinforcement, the emergence of a path may occur with positive probability.…
Vertex-Reinforced Random Walk (VRRW), defined by Pemantle (1988a), is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on…
Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
Vertex-reinforced random walk (VRRW), defined by Pemantle in 1988, is a random process that takes values in the vertex set of a graph G, which is more likely to visit vertices it has visited before. Pemantle and Volkov considered the case…
Imbalanced data widely exists in many high-impact applications. An example is in air traffic control, where we aim to identify the leading indicators for each type of accident cause from historical records. Among all three types of accident…
Random walks are at the heart of many existing network embedding methods. However, such algorithms have many limitations that arise from the use of random walks, e.g., the features resulting from these methods are unable to transfer to new…
Given a real-world graph, how can we measure relevance scores for ranking and link prediction? Random walk with restart (RWR) provides an excellent measure for this and has been applied to various applications such as friend recommendation,…
In the last two decades we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs…
Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986, is a random process, which takes values in the vertex set of a graph $G$, and is more likely to cross edges it has visited before. We show that it can be…
We generalize a result from Volkov [Ann. Probab. 29 (2001) 66--91] and prove that, on a large class of locally finite connected graphs of bounded degree $(G,\sim)$ and symmetric reinforcement matrices $a=(a_{i,j})_{i,j\in G}$, the…
Random walks are a fundamental tool for analyzing realistic complex networked systems and implementing randomized algorithms to solve diverse problems such as searching and sampling. For many real applications, their actual effect and…
Random walks find extensive application across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding…
We study Vertex-Reinforced-Random-Walk on the complete graph with weights of the form $w(n)=n^\alpha$, with $\alpha>1$. Unlike for the Edge-Reinforced-Random-Walk, which in this case localizes a.s. on 2 sites, here we observe various phase…
The edge-reinforced random walk (ERRW) is a random process on the vertices of a graph that is more likely to cross the edges it has visited in the past. Depending on the strength of the reinforcement, the ERRW of a single particle can…
Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by…
Network embedding aims to represent a network into a low dimensional space where the network structural information and inherent properties are maximumly preserved. Random walk based network embedding methods such as DeepWalk and node2vec…