Graph-dual Laplacian principal component analysis

Principal component analysis is the most widely used method for linear dimensionality reduction, due to its effectiveness in exploring low-dimensional global geometric structures embedded in data. To preserve the intrinsic local geometrical structures of data, graph-Laplacian PCA (gLPCA) incorporates Laplacian embedding into PCA framework for learning local similarities between data points, which leads to significant performance improvement in clustering and classification. Some recent works showed that not only the high dimensional data reside on a low-dimensional manifold in the data space, but also the features lie on a manifold in feature space. However, both PCA and gLPCA overlook the local geometric information contained in the feature space. By considering the duality between data manifold and feature manifold, graph-dual Laplacian PCA (gDLPCA) is proposed, which incorporates data graph regularization and feature graph regularization into PCA framework to exploit local geometric structures of data manifold and feature manifold simultaneously. The experimental results on four benchmark data sets have confirmed its effectiveness and suggested that gDLPCA outperformed gLPCA on classification and clustering tasks.