Distance metric learning by minimal distance maximization
Distance metric learning by minimal distance maximization
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DOI：
10.1016/j.patcog.2010.09.019
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发表时间：
2011-03
期刊：
影响因子：
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通讯作者：
Yaoliang Yu;Jiayan Jiang;Liming Zhang
中科院分区：
文献类型：
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作者：
Yaoliang Yu;Jiayan Jiang;Liming Zhang
经典的线性降维（LDR）方法，如主成分分析（PCA）和线性判别分析（LDA），已知对离群值不鲁棒。在统一框架下对多类LDR问题进行了系统的分析之后，我们提出了一种新的算法，称为最小距离最大化（MDM），以解决非鲁棒性问题。MDM背后的原则是最大化输出空间中的最小类间距离。MDM被制定为半定规划（SDP），其对偶问题揭示了“加权”LDR方法的密切联系。一个软版本的MDM，其中LDA被归入作为一个特殊的情况下，也被开发来处理重叠的质心。最后，我们通过以非参数方式扩展MDM中的同方差高斯假设，沿着使用基于梯度的凸近似算法，以显着降低原始SDP的复杂性。在两个UCI数据集和两个人脸数据集上验证了所提方法的有效性。
Classic linear dimensionality reduction (LDR) methods, such as principal component analysis (PCA) and linear discriminant analysis (LDA), are known not to be robust against outliers. Following a systematic analysis of the multi-class LDR problem in a unified framework, we propose a new algorithm, called minimal distance maximization (MDM), to address the non-robustness issue. The principle behind MDM is to maximize the minimal between-class distance in the output space. MDM is formulated as a semi-definite program (SDP), and its dual problem reveals a close connection to “weighted” LDR methods. A soft version of MDM, in which LDA is subsumed as a special case, is also developed to deal with overlapping centroids. Finally, we drop the homoscedastic Gaussian assumption made in MDM by extending it in a non-parametric way, along with a gradient-based convex approximation algorithm to significantly reduce the complexity of the original SDP. The effectiveness of our proposed methods are validated on two UCI datasets and two face datasets.