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Self-training is a commonly semi-supervised learning Algorithm framework. How to select the high-confidence samples is a crucial step for algorithms based on self-training framework. To alleviate the impact of noise data, researchers have proposed many data editing methods to improve the selection quality of high-confidence samples. However, the state-of-the-art data editing methods have high time complexity, which is not less than O (n 2) , where n denotes the number of samples. To improve the training speed while ensuring the quality of the selected high-confidence samples, inspired by Ball- k -means algorithm, we propose a fast semi-supervised self-training Algorithm based on data editing (EBSA), which defines ball-cluster partition and editing to improve the quality of high-confidence samples. The time complexity of the proposed EBSA is O (t 2 kn + n log n + n + k 2 ) , where k denotes the number of centers, t denotes the number of iterates. k is far less than n , EBSA has linear time complexity with respect to n. A large number of experiments on 20 benchmark data sets have been carried out and the experimental results show that the proposed Algorithm not only ran faster, but also obtained better classification performance compared with the comparison algorithms. [ABSTRACT FROM AUTHOR]

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, L 0 -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. [ABSTRACT FROM AUTHOR]