Research On Similarity Metric Learning Of Manifold Data Based On Sparse Constraints

In recent years,with the continuous development of modern science and technology,manifold learning has become one of the important research directions in the field of information science.In the real world,there are many high-dimensional manifold data.If you directly manipulate these high-dimensional data,There will be many difficulties,so solving the problems faced by high-dimensional data is the current problem.After continuous research by many scholars,many classic manifold learning methods have been proposed.These manifold learning methods are mainly divided into two types,linear manifold learning algorithms and nonlinear manifold learning algorithms.However,researchers have found that linear learning methods are not suitable for manifold data with high-dimensional nonlinear structures.A new method is to learn a nonlinear mapping on manifold data,so that the data after the mapping still has a manifold structure.Laplacian Eigenmaps(LE)is a graph-based method and a nonlinear dimensionality reduction method.The main idea is to reconstruct the local structural features of the data manifold by constructing an adjacency matrix.From the perspective of considering the relationship of building data,I hope that the structure of the previous data can be maintained after dimensionality reduction,so similar points are as close as possible in the space after dimensionality reduction,that is,similarity of similar data points after dimensionality reduction higher.For manifold data,we usually use the similarity measurement method to obtain the similarity of different sample data.The commonly used traditional similarity measurement methods include cosine similarity,adjusted cosine similarity,Jaccard similarity,and Pearson correlation coefficient.A good similarity measure can not only significantly improve the accuracy of the classification of the algorithm,but also better reflect the structure between the manifold data.If the data sample corresponds to the data point in the space,the distance between the points reflects the sample.The difference between the data,the closer the distance,the greater the similarity,the farther the distance,the smaller the similarity.Therefore,on this basis,this paper proposes a new method for learning the similarity of manifold data.The main idea is to make the sample similarity between the same class as much as possible,and the sample similarity between different classes is smaller.The main research contents of this article are as follows:(1)Research on similarity learning algorithm based on Laplace rank constraint.For high-dimensional data,many features are invalid.We hope to extract valid parts from high-dimensional data to make our results more accurate.Low rank can automatically separate noise and clean data.If you add a low rank to the algorithm,you can obtain more effective data.Based on this theoretical idea,we add rank constraints to the algorithm,and propose a similarity learning algorithm based on Laplacian rank constraints.The iterative solution process of the similarity algorithm was studied,and then experiments were performed on multiple data sets and compared with other algorithms to verify the effectiveness of our algorithm.(2)Research on multi-view similarity learning algorithm based on manifold data.In many real-world applications,the actual data is not represented in a single way,but has multiple expressions.For example,a person can collect different information from different angles when viewed from different angles.Usually for each thing,we can observe from different angles and cannot observe information from another angle.Therefore,in order to understand more comprehensive information about things,we can observe from multiple angles to obtain more information.Compared with the single-view algorithm,the multi-view algorithm that fuses information from multiple views can get better results.Therefore,we propose a multi-view similarity learning algorithm based on manifold data,and introduce the iterative solution process of the algorithm in detail.A lot of experiments have been performed on some data sets and the experimental results of single-view and multi-view algorithms have been compared.Verifying the efficiency and robustness of the multi-view algorithm.(3)Research on multi-view similarity learning algorithm based on Laplace rank constraint.In this work,we combined the ideas of the previous two works,that is,to maintain the diversity of the data and also to maintain the validity of the data.We integrated the low-rank idea into the multi-view similarity algorithm and proposed a method based on pull the multi-view similarity learning algorithm with low rank constraint,and the corresponding algorithm solution process and iterative solution formula are given.Finally,a large number of experiments are performed on multiple data sets to verify the effectiveness of the algorithm.