Research On Dimensionality Reduction Based On Graph Learning And Discriminant Analysis

In this information age,complicated objects,such as images,are usually required to represent in the high dimensional vectors.However,with the rapid development of information technique,the much higher dimension of the vectors was required to represent the data of an object so that "curse of dimensionality" problem emerges which means much more difficult process for the data.Many researchers have proposed some approaches to overcome this problem,but how to processing these ultra-high dimensional data is still an open topic.Dimensionality reduction(DR)is a prevalent technology to process high dimensional data in pattern recognition,machine learning and face recognition areas.It aims to extract one low-dimensional representation that can well characterize the structure hidden in the high dimensional data,and to filter unnecessary redundant information,so that the computational cost of data process was simplified and the operating speed was increased as well.To obtain a compact and effective low-dimensional representation,recently,most existing discriminant manifold learning methods have integrated manifold learning into discriminant analysis(DA)for extracting the intrinsic structure of data.These methods learn two kinds of adjacency graphs,such as intrinsic graph and penalty graph,to characterize the similarity between samples from intraclass and the pseudo similarity of interclass.However,they treat every sample equally,which results in the following defects:These methods cannot accurately characterize the marginal region among different classes only through penalty graphs;They cannot identify the noisy and outlier samples which reduce the robustness of these methods.This article focuses on graph learning and discriminant analysis methods.The main contributions of this article are:(1)To address these problems,we introduce an adaptive adjacency factor to perform the discriminative based reliability analysis for each sample.By integrating the adjacency factor into discriminant manifold learning methods,we propose a novel method for DA namely discriminant analysis based on reliability of local neighborhood(DA-RoLN).By the introduction of adjacency factor,sample points can be divided into three parts:intraclass samples,marginal samples,and outliers.Therefore,DA-RoLN emphasizes the effect of valid samples and filters the influence of outliers.Also,the adjacency factors were calculated adaptively in low-dimensional space,thus,the margin between different classes in low-dimensional space is emphasized.An iterative algorithm is developed to solve the objective function of DA-RoLN,and it is easy to solve with a low computational cost.(2)To reduce the impact of noisy samples,we clipped the sample data based on the evaluation of all sample points under the adjacency factor learning.And then we proposed a new discriminant analysis method namely regional margin discriminant analysis(RMDA).RMDA not only reduces the impact of noise sample points by clipping samples,but also emphasizes the extraction of regional margin information and intra-class compactness based on the clipped samples,making the algorithm robust in discriminating sample points.