Research On Local Linear Embedding Algorithm And Its Application

Local Linear Embedding Algorithm(LLE)is a kind of feature extraction method,which can solve the "dimension disaster" problem,and combines the characteristics of nonlinear method and the advantages of linear method,so it is popular among scholars.However,LLE has the following problems:(1)If the sample points are sparsely distributed or uneven,LLE may lead to uneven distortion and folding;(2)It is greatly affected by outliers,which may lead to the failure of low-dimensional coordinate embedding;(3)Lack of capacity to process new samples;(4)The effect of dimensionality reduction is affected by the number of nearest neighbors and regularization parameters;(5)Traditional LLE uses Euclidean distance,which may lead to short circuit.Aiming at the above problems,the local linear embedding algorithm is studied.The main work is as follows:1.Local Linear Embedding Algorithm Based on Dynamic Neighborhood SelectionThe neighborhood size and the selection of the nearest neighbor are improved.To solve the problem of uneven distribution density of sample points,the calculation formula of distance between sample points and nearby points is modified to make the density of sample points tend to be uniform.Secondly,according to the prior category information of data points,the category information can be fully utilized in the first dimension reduction by adding a category label when calculating the distance.Thirdly,ascending order is carried out according to the change of the distance between sample points and their nearest neighbors before and after the projection,and then the corresponding nearest neighbors are arranged in the same order to form a set of candidate nearest neighbors.Then the size of the neighborhood is determined dynamically according to the curvature of the manifold.Finally,the second dimension reduction is carried out.2.Reconstruction weight local linear embedding algorithm based on Kernel rank-order distanceThe structure information is added and the influence of outliers and short circuit points is reduced.First,the sample points are mapped to a higher dimensional space through the kernel function to increase their linear separability and make the selection of the nearest neighbor points more scientific and effective.Secondly,the weighted reconstruction weight is modified by adding the reconstruction weight coefficient to make the weighted reconstruction weight more reasonable.The reconstruction weight coefficient has two advantages:(1)the correlation between the two points is positively correlated with the reconstruction contribution to reduce the error of mistaken outliers for nearest neighbors;(2)The ratio of the Euclidean distance to the geodesic distance between any two sample points is used as the structural coefficient to correct the weight vector,and the interference of the short circuit point can be significantly reduced;Third,keep the corrected weighted reconstruction weight unchanged,minimize the error function,and output the target dimension coordinates.3.Local Linear Embedding Algorithm Based on Low Rank ConstraintTo increase the global information,enhance the robustness to noise and select the optimal target dimension.The optimal dimension reduction effect is improved by selecting the optimal dimension reduction effect,and the global information is constrained by low rank to increase the robustness to noise,so that the LLE can maintain the local structure and global information well in the process of dimension reduction,and has better robustness to noise.