Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built on gaussian Laplacian matrices, which is sensitive to parameters. We propose a novel parameter-free distance-consistent locally linear embedding. The proposed distance-consistent LLE can promise that edges between closer data points are heavier. We also propose a novel improved spectral clustering via embedded label propagation. Our algorithm is built on two advancements of the state of the art. First is label propagation, which propagates a node's labels to neighboring nodes according to their proximity. We perform standard spectral clustering on original data and assign each cluster with -nearest data points and then we propagate labels through dense unlabeled data regions. Second is manifold learning, which has been widely used for its capacity to leverage the manifold structure of data points. Extensive experiments on various data sets validate the superiority of the proposed algorithm compared to state-of-the-art spectral algorithms.

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