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Issue No. 10 - October (2011 vol. 33)
ISSN: 0162-8828
pp: 2026-2038
Lijun Zhang , Zhejiang University, Hangzhou
Chun Chen , Zhejiang University, Hangzhou
Jiajun Bu , Zhejiang University, Hangzhou
Deng Cai , Zhejiang University, Hangzhou
Xiaofei He , Zhejiang University, Hangzhou
Thomas S. Huang , University of Illinois at Urbana Champaign, Urbana
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.
Active learning, experimental design, local structure, reconstruction.

J. Bu, L. Zhang, T. S. Huang, D. Cai, X. He and C. Chen, "Active Learning Based on Locally Linear Reconstruction," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 33, no. , pp. 2026-2038, 2011.
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