Night Vision Processing and Understanding by Lianfa Bai & Jing Han & Jiang Yue

Author:Lianfa Bai & Jing Han & Jiang Yue
Language: eng
Format: epub
ISBN: 9789811316692
Publisher: Springer Singapore

5.1.2 Research on Classification via Semi-supervised Multi-manifold Structure Regularisation (MMSR)

The most popular semi-supervised learning algorithms are transductive learning algorithms and inductive learning algorithms. Gaussian Fields and Harmonic Functions (GFHF), in Zhu et al. (2003), is a typical transductive learning algorithm. However, its properties make it difficult to extend to new samples, limiting its application. Semi-supervised discriminant analysis (SSDA) is a typical inductive learning algorithm. In SSDA, the labelled samples are used to maximise discriminating power, whereas the unlabelled samples are used to estimate the intrinsic geometric structure of the data. SSDA can use the unlabelled samples when establishing the within-class scatter matrix, but it ignores the label information and will influence the performance of SSDA. Then the continuous locality preserving projections (CLPP) is proposed in Cai et al. (2007). In CLPP, the within-class weight matrix obtained by the ordinary algorithm is improved and the constraints are used to modify the neighbourhood relations. CLPP can use the unlabelled samples, but the edges between unlabelled samples remain unchanged. Therefore, it cannot make full use of the unlabelled samples.

To overcome the drawbacks of ordinary manifold-based semi-supervised algorithms, Belkin proposed manifold regularisation (MR) in Cevikalp et al. (2008). The underlying sample distribution information of manifold structures is introduced into the traditional regularisation of MR, which has two regularisation terms. One regularisation term controls the complexity of the classifier and the other controls the complexity, which is measured by the manifold geometry of the sample distribution. Based on MR, many semi-supervised manifold regularisation methods have been proposed: discriminatively regularised least-squares classification in Belkin et al. (2006), semi-supervised discriminative regularisation (SSDR) in Xue et al. (2009) adds a discriminative term to MR and multi-manifold discriminative analysis (multi-MDA) in Wu et al. (2010); sparse regularised least-squares classification (S-RLSC) in Fan et al. (2011), which uses sparse representation to construct the graph in MR, instead of KNN or local and global regression (LGR) (see Zhao et al. 2015), which combines MR and local and global regression.

These algorithms can overcome some of the drawbacks of the original MR. However, when describing the distribution of the unlabelled samples, they cannot use the labelled samples, and discreteness information is ignored during when establishing the weighted matrix. Thus, Sect. 5.​4 introduces a new semi-supervised multi-manifold structure regularisation (MMSR). MMSR considers the discreteness information and uses the distribution of labelled samples to characterise the underlying unlabelled multi-manifold sample distribution when building the weighted matrix. Experimental results on UCI datasets and face datasets further demonstrate the effectiveness of MMSR.

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