The Study Of Sparse Representation And Its Applications To Clustering

In signal processing,it is possible to understand the characteristics of its time domain or frequency domain which is crucial for revealing the nature of the signal after decomposing or transforming a signal on a certain group of bases or dictionaries.Sparse representation is a branch of research in signal processing which is to obtain a sparse representation of the signal on a set of basis or dictionary vectors.This meaningful and sparse representation can significantly reduce the cost of signal processing,thereby improving signal processing efficiency.Non-negative matrix factorization is an effective method for learning sparse representation of signals.Due to its natural non-negativity,the representation obtained by non-negative matrix factorization has very good physical meaning and interpretability.In addition,sparse constrained non-negative matrix factorization can also learn useful local representation of data.However,non-negative matrix factorization which is an unsupervised learning method is not sufficient for some supervised learning tasks,and the loss of these useful supervised information will directly affect the accuracy of the learning algorithm.Therefore,we can use a semi-supervised non-negative matrix factorization algorithm which is to label a small number of samples to achieve the purpose of improving the learning accuracy and reducing the cost of data annotation.This paper mainly discusses sparse representation and nonnegative matrix factorization theory,and conducts in-depth research on semi-supervised non-negative matrix factorization.Finally,a new dual-constraint non-negative matrix factorization algorithm is creatively proposed to learn low-dimensional representations of images for clustering.In our model,one constraint is used to keep the label feature and the other constraint is utilized to enhance the sparsity of the representations.Meantime,for solving the proposed model,we designed a fast and efficient convergence sequence based on the convex optimization theory to obtain the optimal solution.It is proved that this algorithm achieves a nonlinear convergence rate,much faster than existing methods with linear rate.In the experimental part,we performed image clustering experiments on 3 real image data sets and 1 computer-generated data set for 8 related comparison algorithms including the proposed NMF-DC algorithm.By K-means for multi-category clustering experiments for the representation learning obtained by various algorithms,we found that the proposed NMF-DC outperforms all the comparison algorithms in terms of clustering performance and algorithm speed.