Fast and Robust Unsupervised Dimensionality Reduction with Adaptive Bipartite Graphs

Abstract

Recent unsupervised dimension reduction algorithms use similarity graphs between data point pairs to preserve local structure while reducing dimension. However, the time complexity of these methods is proportional to the square of the number of samples, which limits their application to large-scale datasets. Moreover, the square Euclidean calculation criterion between sample point pairs will magnify the bad influence of outliers on the graph. In addition, these methods only preserve the local structure while losing other important structural information. To this end, we propose a fast adaptive unsupervised projection model termed Fast and Robust Unsupervised Dimensionality Reduction with Adaptive Bipartite Graph (FRUDR-ABG), which uses a few anchor points and sample points to build a bipartite graph to preserve the local geometric structure of the data to reduce the running time and improve efficiency. We propose a criterion based on the l2,1 norm to calculate the distance between anchor points and data points to reduce the negative influence of outliers on graph construction. A practical strategy is also proposed to realize joint learning of global and local structures. According to the characteristics of graph construction and dimensionality reduction adaptive learning in the algorithm, we design an iterative reweighting method to solve the model. Experimental results on several benchmark datasets show that FRUDR-ABG has higher efficiency and recognition performance than existing unsupervised dimensionality reduction methods.