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A dimension reduction algorithm preserving both global and local clustering structure

机译：保留全局和局部聚类结构的降维算法

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By combining linear discriminant analysis and Kmeans into a coherent framework, a dimension reduction algorithm was recently proposed to select the most discriminative subspace. This algorithm utilized the clustering method to generate cluster labels and after that employed discriminant analysis to do subspace selection. However, we found that this algorithm only considers the information of global structure, and does not take into account the information of local structure. In order to overcome the shortcoming mentioned above, this paper presents a dimension reduction algorithm preserving both global and local clustering structure. Our algorithm is an unsupervised linear dimension reduction algorithm suitable for the data with cloud distribution. In the proposed algorithm, the Kmeans clustering method is adopted to generate the clustering labels for all data in the original, space. And then, the obtained clustering labels are utilized to describe the global and local clustering structure. Finally, the objective function is established to preserve both the local and global clustering structure. By solving this objective function, the projection matrix and the corresponding subspace are yielded. In this way, the global and local information of the clustering structure are integrated into the process of the subspace selection, in fact, the structure discovery and the subspace selection are performed simultaneously in our algorithm. Encouraging experimental results are achieved on the artificial dataset, real-life benchmark dataset and AR face dataset. (C) 2016 Elsevier B.V. All rights reserved.
机译：通过将线性判别分析和Kmeans组合到一个一致的框架中，最近提出了降维算法以选择最具判别力的子空间。该算法利用聚类方法生成聚类标签，然后使用判别分析进行子空间选择。但是，我们发现该算法仅考虑全局结构的信息，而没有考虑局部结构的信息。为了克服上述缺点，本文提出了一种同时保留全局和局部聚类结构的降维算法。我们的算法是适用于云分布数据的无监督线性降维算法。在提出的算法中，采用Kmeans聚类方法为原始空间中的所有数据生成聚类标签。然后，将获得的聚类标签用于描述全局和局部聚类结构。最后，建立目标函数以保留本地和全局聚类结构。通过求解该目标函数，可以得出投影矩阵和相应的子空间。这样，聚类结构的全局信息和局部信息被集成到子空间选择的过程中，实际上，在我们的算法中结构发现和子空间选择是同时执行的。在人工数据集，现实基准数据集和AR人脸数据集上获得了令人鼓舞的实验结果。 （C）2016 Elsevier B.V.保留所有权利。

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