Robust Graph Local Coordinate Factorization

With the rapid development of computer and network communication technology,people come into contact with more and more data.The visual information has changed people's way of life,such as music,pictures and text.However,visual information is usually high-dimensional data that analyzed and handle difficulty.How to dig out the useful knowledge from the visual information becomes a problem that researchers need to solve.In recent years,non-negative matrix factorization has been widely used in computer vision and pattern recognition.The purpose of non-negative matrix factorization is to find the product of two nonnegative matrices to approximate the original matrix,and then obtain the low dimensional representation of the data.The non-negativity is closer to the recognition process of the human brain,and meets the requirements of the pixels in the image and the text in the document statistics.Therefore,the research on the nonnegative matrix factorization and its variants has attracted the attention of many researchers.An important variant of nonnegative matrix factorization is Nonnegative Local Coordinates Factorization?NLCF?.In this algorithm,the standard non-negative matrix factorization and local constraints are unified in the same framework.Specifically,we require that the learned basis vectors are linearly combined by a few close anchor points.However,the nonnegative local coordinate factorization algorithm is very sensitive to noise and outliers in practical application,and can not effectively express the geometric structure of the data.In order to solve the problem,we propose a unified algorithm called Robust Graph Local Coordinate Factorization?RGLCF?.The new algorithm uses the nearest neighbor graph to encode the geometric structure of the data in the local coordinate factorization algorithm,and uses more robust?_{2 1,}norm instead of the?₂ norm to form a new objective function.In this way,it can not only keep the local constraints and the row sparse,but also be more robust.In this paper,we give the product update rule of the new algorithm and prove the convergence of the algorithm.Experiments on ORL and Yale face database verify the effectiveness of the algorithm and analyze the sensitivity and convergence of the algorithm.