Active learning based on locally linear reconstruction

Lijun Zhang, Chun Chen, Jiajun Bu, Deng Cai, Xiaofei He, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review


We consider the active learning problem, which aims to select the most representative points. Out of many existing active learning techniques, optimum experimental design (OED) has received considerable attention recently. The typical OED criteria minimize the variance of the parameter estimates or predicted value. However, these methods see only global euclidean structure, while the local manifold structure is ignored. For example, I-optimal design selects those data points such that other data points can be best approximated by linear combinations of all the selected points. In this paper, we propose a novel active learning algorithm which takes into account the local structure of the data space. That is, each data point should be approximated by the linear combination of only its neighbors. Given the local reconstruction coefficients for every data point and the coordinates of the selected points, a transductive learning algorithm called Locally Linear Reconstruction (LLR) is proposed to reconstruct every other point. The most representative points are thus defined as those whose coordinates can be used to best reconstruct the whole data set. The sequential and convex optimization schemes are also introduced to solve the optimization problem. The experimental results have demonstrated the effectiveness of our proposed method.

Original languageEnglish (US)
Article number5708150
Pages (from-to)2026-2038
Number of pages13
JournalIEEE transactions on pattern analysis and machine intelligence
Issue number10
StatePublished - 2011
Externally publishedYes


  • Active learning
  • experimental design
  • local structure
  • reconstruction.

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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