An Improved Robust Sparse Convex Clustering

Clustering is a very basic and important problem in machine learning.Clustering divides data sets into different clusters in order to minimize the similarity between clusters and maximize the similarity within clusters.Clustering based on prototype is the most typical clustering method,which mainly realizes the optimal partition of unlabeled data by minimizing or maximizing a objective function model that can describe the similar relationship between data points.The selection of objective function model decides the clustering performance.Convex clustering transforms the clustering problem into a convex optimization problem and overcomes the shortcoming that the non-convex target-based clustering model is easy to fall into the local optimal solution.However,the general convex clustering model is based on Euclidean distance,which ignores the influence of non-standard outlier features and treats different features of data points equally.In view of this problem,the research work and arrangement of this thesis are as follows:This thesis introduces a new norm as the penalty term and proposes a new convex clustering model,which fully considers the factor that different features have different effects.Specifically,the idea of the method is to divide the data matrix into two parts: central matrix and outlier characteristic matrix.On the one hand,the central matrix is fitted with the data points which has been removed the influence of outliers;On the other hand,for each eigenvector,a specific non-singular matrix is applied to generate a new norm as a penalty term.The model can also learn the central matrix and identifying outlier features.In addition,this thesis select alternate minimization algorithm and apply Newton’s method with second-order convergence to solve subproblem.For the numerical experiment,the results show that the clustering model can greatly improve the clustering performance of data sets with outlier characteristics.This thesis is arranged as follows: The first chapter describes the research background and significance of convex clustering,and puts forward the necessity.The second chapter gives the preliminary knowledge,introduces the concept of clustering and a common classification,and summarizes the research content on convex clustering.The third chapter constructs a robust sparse convex clustering model,which is based on outlier features,and gives algorithm framework and convergence analysis.In chapter 4,the feasibility and effectiveness of the model are verified by numerical experiments.