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.

中文翻译：

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LLE和随机LEM的融合用于波斯手写数字识别

本文提出了一种新的局部流形学习方法。我们提出的名为FSLL的方法是基于局部线性嵌入（LLE）和新的随机Laplacian特征图（SLEM）的融合。SLEM与常见的LEM技术相同，但是每个数据点与其邻居之间的系数是通过随机过程计算的。SLEM的系数构成一个概率质量函数方案，并将其熵设置为某个值。熵值是每个数据点周围位置的估计值。将基于相互邻域概念提出两个标准，以确定熵值。在LLE中，每个数据点都基于其相邻点进行线性重构，然后通过保留这些线性重构系数来提取嵌入式数据流形。LLE和SLEM通过两种不同的局部结构信息提取并学习嵌入式数据流形。在FSLL中，通过重写成本函数来融合两个局部ML方法SLEM和LLE，而无需任何投影空间。这两种技术的融合在高维空间提供了更多的结构信息，可用于提取嵌入的低维数据。同样，在这项研究中，将通过组合HMAX特征向量和基于PCA的特征向量来呈现特征向量。在图像和特征空间中，对波斯手写数字IFHCDB和IPHD数据库进行了评估。结果证明了FSLL和SLEM的性能。在大多数维度上，识别率提高了约4％。也，