Robust Low Rank Representation Learning For Image Clustering And Classification

The swift advancement of image representation learning methods over the past two decades can be attributed to the increasing complexities of image data,marked by a proliferation of samples and dimensions.Among the various techniques,the subspace approach of low-rank representation（LRR）has gained increased attention recently due to its potential to handle corrupt data.As described below,this dissertation addresses the challenges in learning an accurate block diagonal clustering structure by traditional methods with two proposed methods from single and multiview perspectives.The dissertation also tackles the problem of inefficient preservation of image edges for improving discriminability between images with a third proposed method for robust subspace learning.Firstly,for the traditional LRR approaches,the low-rank subspace structure is mainly used as data prior to predefining a similarity matrix for subspace clustering in a sequential two-step spectral post-processing procedure.In other words,a fault in the previous step potentially affects the succeeding step.As a result,most existing methods still face difficulty learning an accurate block diagonal clustering structure,which is desired for excellent clustering performance.To tackle this,we propose the first approach in this dissertation which extends the classical LRR to include a k-block diagonal manifold recovery structure to further correct inadequacies in the low-rank representation of data.The manifold structure is then used to find an ideal similarity matrix that directly denotes the clustering structure with a rank constraint on its normalized Laplacian matrix.Moreover,a coupling regularization term is added to allow the clustering structure to adaptively approximate the low-rank representation towards finding more optimal solutions.In this way,the conventional two-step procedure is avoided to obtain superior clustering performance.Several experiments using eight popular benchmark image datasets demonstrate that the proposed approach outperforms state-of-the-art methods in six evaluation metrics.Furthermore,a second approach is proposed to tackle the above problem from the multiview perspective.Firstly,to collectively capture the diversity and correlation among different views and improve clustering performance,a constraint is imposed on each view’s low-rank representation such that it is a combination of two-component matrices:the view-specific representation and shared representation.An₁-norm regularization is also imposed to encourage sparsity of the view-specific ones to capture the diversity in different views more effectively.Then,similar to the first approach,a unified clustering structure is obtained through the manifold recovery structure of each view.Therefore,by allowing the shared low-rank representation and the unified clustering structure to guide themselves adaptively,cleaner low-rank matrices are obtained in different views,leading to a better clustering structure.An investigation of the proposed method’s effectiveness reveals its superiority over twelve compared multiview techniques.Finally,traditional low rank methods overlook residuals as corruptions in data.However,we discovered that low-rank residuals actually keep structural information such as image edges for improving clustering and classification performance.Therefore,this dissertation also presents a solution to this limitation by exploiting the structure of low-rank residuals.Hence,a third approach,entitled image edge preservation via low-rank residuals for robust subspace learning,is proposed,which regards residuals as another view of data to find image subspace projections.Consequently,fusing the optimal low-rank representation and edge-preserved subspace projections,the proposed framework simultaneously achieves robust linear dimensionality reduction and noise suppression.Extensive experiments in classification and clustering tasks show that it has clear advantages over state-of-the-art linear dimensionality reduction methods.In summary,the first and second proposed approaches in this dissertation address the difficulty faced by traditional LRR methods in learning an accurate block diagonal clustering structure from a single and multi-view perspective,respectively.The third method tackles the problem of inefficient preservation of image edges by low-rank methods in order to improve clustering and classification performance.