Direct Discriminant Locality Preserving Projection With Hammerstein Polynomial Expansion
Direct Discriminant Locality Preserving Projection With Hammerstein Polynomial Expansion
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DOI：
10.1109/tip.2012.2219542
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发表时间：
2012-12
影响因子：
10.6
通讯作者：
X. Chen;Jiashu Zhang;Defang Li
中科院分区：
文献类型：
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作者：
X. Chen;Jiashu Zhang;Defang Li
判别保域投影（DLPP）是将判别信息编码到保域投影目标中，提高其分类能力的一种线性方法。为了增强DLPP的非线性描述能力，我们可以优化DLPP在再现核Hilbert空间中的目标函数，形成一个基于核的判别保域投影（KDLPP）。但是，KDLPP存在以下问题：1)计算量较大；2) KDLPP中没有明确的映射函数，将新样本投影到低维子空间时计算量较大；3) KDLPP无法获得最优的判别向量，使得DLPP的目标极度优化。为了克服KDLPP算法的缺点，本文提出了一种直接判别保局域投影与Hammerstein多项式展开（HPDDLPP）。该算法在无矩阵逆的高维二阶Hammerstein多项式空间中直接实现了DLPP的目标，在不增加计算量的情况下提取了DLPP的最优判别向量。在人脸和掌纹识别问题上，与其他经典方法进行了对比，实验结果表明了该方法的有效性。
Discriminant locality preserving projection (DLPP) is a linear approach that encodes discriminant information into the objective of locality preserving projection and improves its classification ability. To enhance the nonlinear description ability of DLPP, we can optimize the objective function of DLPP in reproducing kernel Hilbert space to form a kernel-based discriminant locality preserving projection (KDLPP). However, KDLPP suffers the following problems: 1) larger computational burden; 2) no explicit mapping functions in KDLPP, which results in more computational burden when projecting a new sample into the low-dimensional subspace; and 3) KDLPP cannot obtain optimal discriminant vectors, which exceedingly optimize the objective of DLPP. To overcome the weaknesses of KDLPP, in this paper, a direct discriminant locality preserving projection with Hammerstein polynomial expansion (HPDDLPP) is proposed. The proposed HPDDLPP directly implements the objective of DLPP in high-dimensional second-order Hammerstein polynomial space without matrix inverse, which extracts the optimal discriminant vectors for DLPP without larger computational burden. Compared with some other related classical methods, experimental results for face and palmprint recognition problems indicate the effectiveness of the proposed HPDDLPP.