Projected fuzzy C-means with probabilistic neighbors

In recent years, graph optimization dimensionality reduction methods have become a research hotspot in machine learning. The main challenge of these methods is how to choose proper neighbors for graph construction. For high-dimensional data clustering tasks, most methods often conduct a dimensionality reduction method at first and then perform a clustering method in sequence. However, such a sequential strategy may not be optimal because the reduced data obtained in the first stage may not be suitable for clustering. In this article, a novel method called Projected Fuzzy c-means with Probabilistic Neighbors(PFCM), which unifies graph optimization and Fuzzy c-means, is proposed. Our model projects the data into an optimal subspace at first and then learns the sparse weights matrix by considering probabilistic neighbors and membership matrix together on the projected data. The above two steps run iteratively until the algorithm converges. Especially, L₀-norm constraints are employed on the weights matrix to avoid the obstacles caused by outliers. An optimization procedure is designed to solve the proposed model effectively. We conducted numerous experiments on eight benchmark data sets. The experimental results show that the performance of the proposed method is better than some available dimensionality reduction algorithms for clustering tasks.