A Semi-supervised manifold alignment algorithm and an evaluation method based on local structure preservation

NEUROCOMPUTING

卷:224

Article

Li, Xiaojie¹  Lv, Jiancheng²  Wu, Xi¹  Yu, Xin³ 

[1] Chengdu Univ Informat Technol, Coll Comp Sci, Chengdu, Peoples R China

[2] Sichuan Univ, Coll Comp Sci, Chengdu, Peoples R China

[3] Chinese Acad Sci, Inst Comp Technol, State Key Lab Comp Architecture, Beijing, Peoples R China

关键词: Manifold alignment;    Structural stability;    Local structure;   

DOI  :  10.1016/j.neucom.2016.11.002

来源: Elsevier

【 摘 要 】

Manifold alignment is the process of aligning the shared intrinsic structure extracted from multiple manifolds. The criteria of manifold alignment are 2-fold. First, the alignment should minimize the distance between manifolds, ensuring high alignment accuracy. Second, the original structure should be preserved. Currently, most alignment algorithms focus on alignment accuracy, whereas structure preservation has received little attention. This paper proposes a new semi-supervised alignment method that combines locally linear reconstructions in each manifold. The shared intrinsic structure is obtained by solving an optimization problem with a closed-form solution, which simultaneously matches the corresponding instances and preserves the local geometry of each manifold. Furthermore, a new method is presented to evaluate the local structure preservation. The structural stability is defined as a metric of the local structure preservation property. It is shown that the proposed method preserves the local geometry of the original dataset well. It is also found that better structural stability gives higher alignment accuracy, but the converse is not true. Experimental results on both synthetic and real datasets demonstrate the effectiveness and efficiency of our method.

【 授权许可】

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