The Study Of Matrix Recovery Algorithm And Application

Matrices recovery plays a central role in large-scale data analysis and dimensionalityreduction. Especially with the rapid development of the sensor technology,computer net-work and communication technology, the observation data with more complex structures,are becoming very hard to be operated by the traditional one-dimensional data processingmethod. Some two-dimensional data, such as face images and surveillance videos, needto be better described by introducing the matrix structure. And then, matrices recovery asa new method of high-dimensional data processing method has become a hot topic in ma-chine learning, data mining, pattern recognition, and computer vision. Moreover, how torecover these data from the problem of deficiency, loss, or corrupted with noise is also thefocus of attention.Based on IALM, the emphasis of this paper is on the study of matrix recovery algo-rithm and its application. Firstly, a unified matrix recovery model was proposed for diversecorrupted matrices. Resulting from the separable structure of the proposed model, the con-vex optimization problem can be solved efciently by adopting an IALM method. For thefirst time, the IALM was extended to the OP problem. Additionally, a random projectionaccelerated technique was adopted to improve the success rate.The preliminary numerical results on randomly generated matrix recovery problemsdemonstrate that this accelerated technique can save the computational time greatly andachieve satisfactory accuracy, especially when dealing with large-scale data. Moreover,the IALM+RP is combined with Robust PCA and OP problem, and there are a series ofsimulation experiments to recover life pictures and face images. It can be seen that the pro-posed IALM+RP algorithm can quickly find out the right picture in the picture sets. Evenin the case that the absence of characteristic elements was severe polluted, the acceleratedtechnique is still able to efectively restore the original images.