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Recently, with the explosive increase in Internet data, the traditional Graph-based Semi-Supervised Learning (GSSL) model is not suitable to deal with large scale data as the high computation complexity. Besides, GSSL models perform classification on a fixed input data graph. The quality of initialized graph has a great effect on the classification result. To solve this problem, in this paper, we propose a novel approach, named optimal bipartite graph-based SSL (OBGSSL). Instead of fixing the input data graph, we learn a new bipartite graph to make the result more robust. Based on the learned bipartite graph, the labels of the original data and anchors can be calculated simultaneously, which solves co-classification problem in SSL. Then, we use the label of anchor to handle out-of-sample problem, which preserves well classification performance and saves much time. The computational complexity of OBGSSL is O(ndmt + nm2), which is a significant improvement compared with traditional GSSL methods that need O(n2d + n3) , where n, d, m and t are the number of samples, features anchors and iterations, respectively. Experimental results demonstrate the effectiveness and efficiency of our OBGSSL model. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) clustering is very important in remote sensing applications. However, most graph-based clustering models are not suitable for dealing with large HSI due to their computational bottlenecks: the construction of the similarity matrix $\boldsymbol {W}$ , the eigenvalue decomposition of the graph Laplacian matrix $\boldsymbol {L}$ , and $k$ -means or other discretization procedures. To solve this problem, we propose a novel approach, scalable graph-based clustering with nonnegative relaxation (SGCNR), to cluster the large HSI. The proposed SGCNR algorithm first constructs an anchor graph and then adds the nonnegative relaxation term. With this, the computational complexity can be reduced to $O(nd\log m+nK^{2}+nKc+K^{3})$ , compared with traditional graph-based clustering algorithms that need at least $O(n^{2}d+n^{2}K)$ or $O(n^{2}d+n^{3})$ , where $n$ , $d$ , $m$ , $K$ , and $c$ are, respectively, the number of samples, features, anchors, classes, and nearest neighbors. In addition, the SGCNR algorithm can directly obtain the clustering indicators, without resort to $k$ -means or other discretization procedures as traditional graph-based clustering algorithms have to do. Experimental results on several HSI data sets have demonstrated the efficiency and effectiveness of the proposed SGCNR algorithm. [ABSTRACT FROM AUTHOR]