This paper proposes Regularized Semi-Supervised ISOmetric MAPping (Reg-SS-ISOMAP) algorithm to solve the problem that ISOmetric MAPping (ISOMAP) algorithm is unsupervised and can not generate explicit mapping function. At first, this algorithm creates K-Connectivity Graph (K-CG) by labeled samples in training samples to get geodesic distance between approximate samples and takes it as feature vector substituting for original data. Then, it takes the geodesic distance as kernel and processes feature vector through semi-supervised regularization not MultiDimensional Scaling (MDS) algorithm. At last, it constructs objective function by regularization regression model which is low dimension and explicit mapping. The algorithm is simulated on different data sets, results show that it is stable in dimension reduction and high recognition rate.
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