Local distances preserving based manifold learning

•Defining a local distances preserving based manifold learning method.•Defining a neighborhood graph matrix by better description of the local distances.•Defining a new cost function for graph matrix to find the embedded data manifold.•Low sensitivity to the initialization of the parameters.•Defining a criterion to evaluate the local manifold learning methods. In this paper a local manifold learning method based on the local distances preserving (LDP) is proposed. LDP focuses on extracting and preserving the local distances between the data points. In LDP, the coefficients between each data point and its neighbors are calculated based on the inverse of Euclidean distances between them. Then, a minimization function, which is in accordance with the calculated coefficients, is proposed for calculating the embedded data manifold in the low-dimensional representation space. Matching the way of calculation the coefficients and the proposed minimization function is the main significance of the proposed LDP method. In addition, the proposed LDP method shows less sensitivity to the initial parameters such as the number of neighbors and the value of variance. Also, a stochastic based extension of LDP (SLDP) manifold learning method is proposed. The proposed method is compared with the common manifold learning methods based on the achievable recognition rate and the power of the local distances preserving. The experiments have been done on two different kinds of databases: HODA Persian handwritten character database and ORL face image database. The results demonstrate the suitable performance of LDP and SLDP. Also, the results show the robustness of the proposed method to the number of neighbors and the value of variance parameter. Moreover, the proposed method of calculating the embedded data points in LDP and SLDP has less complexity than the similar local manifold learning methods, Laplacian eigenmaps (LEM) and stochastic LEM (SLEM).