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考虑了一种带有数据领域知识的降维问题。这里领域知识是指关于数据的一些额外监督信息,如类别标号以及比标号弱的样本间相似性和不相似性约束等。其中,约束可以从标号中产生,但反过来从约束中却得不到标号信息,因而约束比标号更一般。另外,在图像检索等实际应用中,约束比标号更容易获取。鉴于此,本文主要研究基于约束的降维问题。提出了一种有效利用约束进行降维的约束保持嵌入算法(constraint preserving embed-ding,COPE),将其纳入到图嵌入统一框架之中并指出与同类方法的关系。进一步,通过引入无标记样本提出了半监督COPE算法;提出核COPE以揭示数据中的非线性结构。最后,在人脸识别、图像检索及半监督聚类等一系列实验中的结果验证了算法的有效性。
Considered a dimension reduction problem with data domain knowledge. Domain knowledge here refers to some additional supervisory information about the data, such as the category label and sample similarity and dissimilarity constraints that are weaker than the label. Among them, the constraints can be generated from the label, but in turn can not get the label information from the constraint, so the constraint is more general than the label. In addition, in practical applications such as image retrieval, constraints are easier to obtain than labels. In view of this, this paper mainly studies constrained dimensionality reduction. This paper presents a constraint preserving embed-ding (COPE) algorithm that effectively uses constraints to reduce dimensions, which is incorporated into the unified framework of graph embedding and indicates the relationship with similar methods. Further, a semi-supervised COPE algorithm is proposed by introducing unlabeled samples; nuclear COPE is proposed to reveal the nonlinear structure in the data. Finally, the results of a series of experiments, such as face recognition, image retrieval and semi-supervised clustering, verify the effectiveness of the algorithm.