Multi-view Clustering Via Multiple Kernel Concept Factorization And Its Fast Optimization Method

Data objects in the era of big data can be usually represented from multiple sources or can be observed from different perspectives.These data are called multi-view data.Compared with traditional machine learning methods,current learning methods bring new challenges and new opportunities in multi-view data processing and analysis tasks.Mining and using multi-view data have become hot research topics at this stage.In recent years,clustering analysis has attracted widespread attention as a key technology to find the internal structure of data.Clustering analysis for multi-view data is called multi-view clustering.The goal of the multi-view clustering task is to take advantage of the consistency and complementary information between multiple views to fuse the data from different views and carry out a consensus representation,so as to construct a clustering model that is more accurate and efficient than the traditional single-view clustering methods,and at the same time improve the universality of the algorithms to solve practical problems in various fields.This thesis focuses on multi-view cluster analysis,and the main contributions and innovations are as follows:(1)Multi-view clustering via multiple kernel concept factorizationThe kernel function can map the input data from the original space to the feature space.This low-dimensional to high-dimensional mapping effectively deals with linearly inseparable data.The proposed model explores a matrix factorization technique called concept factorization,which learns the potential representation of the original data in the subspace through concept factorization,assigns different weights to different views,and automatically updates the weights during the optimization process.At the same time,local manifold regularization is introduced,so that the algorithm not only considers the global geometric structure of the data space,but also retains the local inherent geometric structure.The model also introduces multi-kernel learning,which is an improvement of the kernel method.The original data is mapped by a combination of multiple kernel functions.The model assigns weights to each kernel function,and the kernel weights are automatically updated in the iterative process,making them suitable for different data distributions.This algorithm solves the problem of the difficulty in selecting kernel function in single-kernel clustering tasks,so that the kernel function can not only process specific types of data.(2)Nesterov-based multi-view clustering via multiple kernel concept factorization based on Nesterov iterationThe calculation amount of multi-view clustering tasks is often several times that of single-view clustering tasks.In order to effectively alleviate the large number of calculations faced by multi-view clustering tasks,this thesis proposes an algorithm called Nesterov-based multi-view clustering via multiple kernel concept factorization by introducing and combing the Nesterov iteration method,random projection method and random subspace iteration method.The generated random Gaussian matrix is used to compress the kernel matrix reasonably,and the alternate iterative optimization algorithm is used to optimize the objective function,which successfully avoids redundant calculations during the optimization process and accelerates the convergence of the algorithm.Experiments on multiple real data sets show that the proposed algorithm has higher clustering quality and faster convergence speed than other popular multi-view clustering algorithms and fast matrix factorization algorithms.In summary,this thesis studies about multi-view data and uses concept factorization,local manifold regularization,multi-kernel learning,Nesterov iteration method,random subspace iteration method to solve problems in multi-view clustering and fast optimization methods.It concerns several key problems in clustering tasks and proposed effective solutions.