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Abstract
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In this paper, a new local manifold learning (ML) method is proposed. Our proposed method, which is named FSLL, is based on the fusion of locally linear embedding (LLE) and a new Stochastic Laplacian Eigenmaps (SLEM). SLEM is the same as a common LEM technique, but the coefficients between each data point and its neighbors are calculated by a stochastic process. The coefficients of SLEM make a probability mass function scheme, and their entropy is set to a certain value. The entropy value is an estimation of the locality around each data point. Two criteria will be presented based on the mutual neighborhood conception to determine the entropy value. In LLE, each data point is linearly reconstructed based on its neighbors and then the embedded data manifold is extracted by preserving these linear reconstruction coefficients. LLE and SLEM extract and learn the embedded data manifold by two different kinds of local structure information. In FSLL, two local ML methods, SLEM and LLE, are fused by rewriting their cost functions without the need for any projection space. Fusion of these two techniques provides more structural information at high-dimensional space that can be applied on extracting the embedded low-dimensional data. Also, in this study, a feature vector will be presented by combining a HMAX feature vector and a PCA-based feature vector. Evaluations of the proposed method are done on Persian handwritten digit IFHCDB and IPHD databases in image and feature spaces. The results demonstrate the performance of FSLL and SLEM. The recognition rates are improved about 4% in most dimensionalities. Also, a method of out-of-sample test data extension is proposed corresponding to the proposed methods.
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