摘要:流形学习是当今最重要的研究方向之一.约简维度的选择影响着流形学习方法的性能.当约简维度恰好是本征维度时，更容易发现原始数据的内在性质.然而，本征维度估计仍然是流形学习的一个研究难点.在此基础上，提出了一种新的无监督方法，即基于选择聚类集成的相似流形学习（SML-SCE）算法，避免了对本征维度的估计，并且性能表现良好.SML-SCE利用改进的层次平衡K-means（MBKHK）方法生成具有代表性的锚点，高效地构造相似度矩阵.随后计算得到了多个不同维度下的相似低维嵌入，这些低维嵌入是对原始数据的不同表示，而且不同低维嵌入之间的多样性有利于集成学习.因此，SML-SCE采用选择性聚类集成方法作为结合策略.对于通过K-means聚类得到的相似低维嵌入的聚类结果，采用聚类间的归一化互信息（NMI）作为权重的衡量标准.最后，舍弃权重较低的聚类，采用基于权重的选择性投票方案，得到最终的聚类结果.在多个数据集的大量实验结果表明了该方法的有效性.



Abstract:Manifold learning is one of the most important research directions nowadays. The performance of manifold learning methods is affected by the choice of reduced dimension. When the reduced dimension is the intrinsic dimension, it is easily to handle the original data. However, intrinsic dimension estimation is still a challenge of manifold learning. In this study, a novel unsupervised method is proposed, called similar manifold learning based on selective cluster ensemble (SML-SCE), which avoids the estimation of intrinsic dimension and achieves a promising performance. SML-SCE generates representative anchors with modified balanced K-means based hierarchical K-means (MBKHK) to construct similarity matrix efficiently. Moreover, multiple similar low-dimensional embeddings in different dimensions are obtained, which are the different presentations of original data. The diversity of these similar low-dimensional embeddings is benefit to the ensemble learning. Therefore, selective cluster ensemble method is taken advantage of as the combination rule. For the clustering results obtained by K-means in similar low-dimensional embeddings, the normalized mutual information (NMI) is calculated between clusterings as weight. Finally, the low weight clusterings is discarded and a selective vote scheme is adopted based on weight to obtain the final clustering. Extensive experiments on several data sets demonstrate the validity of the proposed method.



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