Incremental commute time and its online applications

Nguyen Lu Dang Khoa, Yang Wang, Sanjay Chawla

Research output: Contribution to journalArticlepeer-review


Commute time is a robust measure on graphs based on random walks. It has been successfully applied in many application domains including personalized search, collaborative filtering and network intrusion detection. However, the computation of the commute time is expensive since it involves the eigen decomposition of the graph Laplacian matrix. There has been effort to approximate the commute time but they only work in an offline mode. In this work, an accurate and efficient approximation for computing the commute time is proposed in an incremental fashion in order to facilitate online applications. Using the incremental commutime, we design an online anomaly detection application where the commute time of each new arriving data point to any point in the current graph can be estimated in constant time. The proposed approach shows its high accuracy and efficiency in synthetic and real datasets for online applications. It takes only 8 milliseconds on average to detect anomalies online on the DBLP graph which has more than 600,000 nodes and 2 millions edges. We also discuss the use of incremental commute time for other online applications such as classification, graph ranking and clustering.

Original languageEnglish
Pages (from-to)101-112
Number of pages12
JournalPattern Recognition
StatePublished - Apr 2019
Externally publishedYes


  • Anomaly detection
  • Commute time
  • Manifold learning
  • Online learning
  • Random walks


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