Research On Feature Selection Algorithm Based On Adaptive Nearest Neighbor Graph Model And Local Discriminant Analysis

With the development of storage technology and the diversification of information collection,the cost of information acquisition has become lower.However,in addition to important features,high-dimensional data may also contain a lot of noise and redundant features,which leads to the problem of"cruse of dimensionality".Data dimensionality reduction technology is the most effective way to solve the"dimension of dimensionality"by finding the low-dimensional representation of high-dimensional space.Feature selection is an important data dimensionality reduction technique,which selects feature subsets from the original high-dimensional space without changing feature values and units.In recent years,the sparse regularization techniques have been introduced into the feature selection method,which performs feature selection through the optimized sparse model and obtains the sparse representation of the data.Among them,the structured sparsity-inducing feature selection methods based on linear discriminant analysis?LDA?is simple and efficient,which have attracted wide attention.However,such methods are often based on the Gaussian distribution assumption,thus ignoring the local geometric structure of the data,resulting in suboptimal performance on complex distributed data sets that are common in the real world.In order to obtain the local geometric structure of data,many researchers choose to pre-define a graph structure in the original space to represent the data relationship between samples,and rely on the preset graph structure for subsequent dimensionality reduction tasks.The original space may contain a lot of noise and redundant features,leading to the pre-defined graph structure is often inaccurate or even wrong,which in turn makes the final selected features not optimal.This thesis proposes two supervised feature selection methods for the above shortcomings.The main contributions are as follows:?1?We proposed Self-weighted locality discriminant feature selection algorithm?SLD-FS?,which adds a l21 norm to the projection matrix as a penalty term based on the trace ratio criterion of linear discriminant analysis to obtain a projection with row-sparse properties matrix.For complex distribution problems,this method adaptively assigns weights to within-class points based on the distance to obtain the local geometric structure of the data,so that pairs of samples closer in the subspace have larger weight,and vice versa.In order to reduce the influence of redundant features and noise in the original space,we adaptively adjust the weights between samples according to the change of the projection matrix,so as to obtain a better graph structure.In addition,we propose an iterative optimization algorithm to solve the objective function,and we prove that the objective function value monotonically converges in theory and in experiments.?2?We proposed Adaptive neighborhood discriminant feature selection algorithm?AND-FS?,which adaptively selects the k closest within-class samples in the subspace for all samples as neighborhood samples to obtain the local structure of the data.In addition,by constantly iteratively adjusting the subspace and graph structure to reduce noise interference,and by restricting the number of neighboring points to ensure that the edge connections between within-class samples have a certain sparseness.Inspired by TRLN^[1],a fast iterative solution algorithm for the objective function is proposed,and the optimization algorithm is demonstrated convergence fast by experiment results.