Two-dimensional Ridge Regression Subspace Clustering Method Based On Bilateral Projectio

Clustering is an important data analysis method in fields such as data mining and machine learning.Its goal is to assign unlabeled objects to groups,where similar objects are expected to be assigned to the same group.Traditional clustering algorithms generally consider all dimensions of an input dataset,trying to learn as much as possible about each object being described.In high-dimensional data,however,there is often invalid information,which often adversely affects the learning process.Recently,subspace clustering algorithms have been developed and shown effective for high-dimensional data,among which the spectral clustering-based ones are typical.Subspace clustering,as well as general clustering algorithms,has found various applications for two-dimensional data that contain spatial information,where each example of the data is naturally represented by a matrix.However,most existing subspace clustering methods based on traditional machine learning cannot process such data directly,and common approach is usually to vectorize matrix-type examples before the learning process,which seriously destroys the inherent structural information of the data.To address this problem,a two-dimensional ridge regression subspace clustering method based on bilateral projections,named BVSSC,is proposed in this thesis.The innovations of the thesis are as follows:(1)Considering that most existing subspace clustering methods based on traditional machine learning deal with two-dimensional data by stretching the data matrices into the form of vectors,which inevitably leads to the loss of information about the inherent structure of the data.For this reason,this thesis proposes to use two-dimensional data directly as input in order to exploit the intrinsic structure and relationships of the data.(2)Considering the importance of spatial information on both horizontal and vertical views,the bilateral projection approach is proposed in this thesis introducing projection matrices from the left and right sides of the examples,respectively,which makes it possible to consider the structural information inherent in the data from both the horizontal and vertical views.Compared with unidirectional projection,bilateral projection can retain more structural information in two-dimensional data and help construct the most expressive representation coefficient matrix,so that the learning of projection and representation can mutually enhance each other to obtain the desired clustering performance.(3)Considering that the features of the horizontal and vertical views may have different importance,the number of projection directions in the two projection matrices is used as an optimization variable in this thesis,enabling the model to automatically learn the optimal number of projection directions from the horizontal and vertical views.Given the presence of nonlinear structure in the data,a kernel method is introduced into the model to extend the linear model to a nonlinear model,thus allowing the model to explicitly capture the two-dimensional structure and nonlinear relationships of the data.As a result,all learning tasks are performed simultaneously in a seamlessly integrated framework,allowing to enhance each other and lead to powerful data representation and grouping ability.In general,the two-dimensional ridge regression subspace clustering method based on bilateral projection proposed in this thesis further studies and innovates on the existing subspace clustering methods based on traditional machine learning.Extensive experimental results verify the effectiveness of the proposed method.