Adaptive multiple graph regularized semi-supervised extreme learning machine

Semi-supervised extreme learning machine (SSELM) was proposed as an effective algorithm for machine learning and pattern recognition. However, the performance of SSELM heavily depends on whether the underlying geometrical structure of the data can be well exploited. Though many techniques have been utilized for constructing graph to represent the data structure, which of them can best reflect the intrinsic distribution of complicated input data is still needed to be verified. Aiming to solve this problem, we propose a novel algorithm called adaptive multiple graph regularized semi-supervised extreme learning machine (AMGR-SSELM). The contributions of the proposed algorithm are as follows: (1) AMGR-SSELM employs multiple graph structures extracted from training samples to characterize the structure of input data. Since these graphs are constructed based on different principles and complementary with each other, the underlying data distribution can be well exploited through combining them. (2) A nonnegative weight vector is introduced into AMGR-SSELM to adaptively combine the multiple graphs for representing different data. (3) An explicit classifier can be learnt in our algorithm, which overcomes the 'out of sample' problem. (4) A simple and efficient iterative update approach is also proposed to optimize AMGR-SSELM. In addition, we compare the proposed approach with other classification methods and some extreme learning machine variants on five benchmark image databases (Yale, Extended YaleB, CMU PIE, AR and FKP). The results of extensive experiments show the advantages and effectiveness of the proposed approach.