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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Learning Regularized LDA by Clustering
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Learning Regularized LDA by Clustering

机译：通过聚类学习正规化的LDA

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摘要

As a supervised dimensionality reduction technique, linear discriminant analysis has a serious overfitting problem when the number of training samples per class is small. The main reason is that the between- and within-class scatter matrices computed from the limited number of training samples deviate greatly from the underlying ones. To overcome the problem without increasing the number of training samples, we propose making use of the structure of the given training data to regularize the between- and within-class scatter matrices by between- and within-cluster scatter matrices, respectively, and simultaneously. The within- and between-cluster matrices are computed from unsupervised clustered data. The within-cluster scatter matrix contributes to encoding the possible variations in intraclasses and the between-cluster scatter matrix is useful for separating extra classes. The contributions are inversely proportional to the number of training samples per class. The advantages of the proposed method become more remarkable as the number of training samples per class decreases. Experimental results on the AR and Feret face databases demonstrate the effectiveness of the proposed method.
机译：作为一种有监督的降维技术，当每类训练样本的数量较少时，线性判别分析会出现严重的过拟合问题。主要原因是，从数量有限的训练样本计算出的类间和类内散布矩阵与基础散布矩阵有很大差异。为了在不增加训练样本数量的情况下克服该问题，我们建议利用给定训练数据的结构分别通过聚类之间和聚类内部散布矩阵同时调整类之间和聚类内部散布矩阵的规则。集群内部和集群之间的矩阵是从无监督的集群数据中计算出来的。集群内散布矩阵有助于编码类内的可能变化，并且集群间散布矩阵可用于分离额外的类。贡献与每个班级的训练样本数量成反比。随着每类训练样本数量的减少，该方法的优势变得更加明显。在AR和Feret人脸数据库上的实验结果证明了该方法的有效性。

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