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.
['Weiling Cai']
A dimension reduction algorithm preserving both global and local clustering structure