Research On NMF-based Algorithms Applying To Face Recognition

Face recognition is a long hot issue in the field of computer vision; so many scholarshave porposed a variety of solutions for this issue. However, due to the problem existed inface recognition (such as: illumination, angle, occlusion) which still not resolved, Issue onface recognition are still difficulities in the field or computer vision.In this paper, we focus on one difficulity issue in the fild of face recognition whichresearch face recognition algorithm under the complex background. This issue has greattheoretical value and application value. On the aspect of the theoretical value: compared withthe traditional sense of face recognition issue, there is too much complex environmentinterference on the face image, which needs us to be able to grasp the key information moreaccurately in the image. So we need more in intelligent algorithms, more robustness to theoutsider interference, able to adapt to a more complex environment, On the aspect of theapplication value: Taking into account the field of security and surveillance, due to thecomplexity of the environment, the monitoring system can not effectively identify theindividual abnormality in a monitored region, so human force are needed, which isinconvenience to normal individuals, and more wastly. but the face recognition algorithmsbased on the complex environment can effectively improve the recognition rate to identify theabnormal individual in the field or security, thereby reducing the human and materialresources monitoring agencies. By the monitoring system across the country, works suchhunting for fugitive becomes more easy and timely; by improving the recognition rate of facerecognition under the conditions of occlusion and illumation, monitoring agencies can get ridof the heavy manual labor, produce less interference to the normal individuals, and make thesecurity more efficient.In this paper, we have chosen the face recognition technology based on the overall, whosemethods have been chosen as the popular Non-negative Matrix Factorization (NMF)algorithm, and algorithms that based on NMF, then we will make some improvement on it.NMF algorithm is one of the most popular face recognition algorithms, because NMFalgorithm can handle illumation problem and occlusion problem easily, and the algorithm hasthe following two advantages:1. by introducing the non-negative constraint, the calculationresults of the algorithm can simulate the human eye’s visual habits.2. NMF algorithm has thenatural sparsity, which can deal with the illumation and occlusion. Based on these twoadvantages methoned above, in this paper, we have chosen the Non-negative Matrix Factorizaion algorithm, merging with nowadays the more popular face recognition technology,(such as manifold, discriminant, subclass discriminant and those outstanding algorithms ofgradient descent algorithm),to improve the recognition rate of the algorithm effectively.There are5contributions in this paper.1. Due to its non-negative restrictions, we can’t add the discriminant into the traditionNMF algorithm based on the Euclidean distance error function. Because the discriminantneeds to construct two matrixes and to measure the relationship between all samplepoints, especially measuring the relationship within class and between classes. Notice thedefinitions of and need to subtracte the average form the raw data, which leads partsof the elements of and are negative and the other parts are non-negative, sotraditional method for NMF can’t grarantee the non-negative constraints on all the elementsduring its iteration. Aimed on this difficulty, we introduced a self-learning-step gradientdescent algorithm into discrimant Non-negative Matrix Factorization algorithm. Because thesteps of the algorithm don’t need to be set before the algorithm running, instend, they arecalculated, so this algorithm can get rid of the prarmeter selection process. One advantage ofthe proposed algorihm is as follow: because the algorithm chose the largest step which satisifythe situation defined, so iterate process can jump out of the poor local minimum value, untilconvering into a good local minimum value. This advantage can improve the meanrecognition rate under several trials.2. Subclass discrimant method is one ingenious improvement aimed at the traditionaldiscrimant method. Due to the uneven distribution of the face image in the high dimensionalspace, the classification based classification center becomes very difficult. By dividing pointsbelong to one class into two subclasses, the distribution of the points in each subclass aremore even, which will improve the recognition rate. By introducing the subclass discrimantmethod into the algorithm we proposed in1, the new subclass discrimant algorithm willimprove the recognition rate.3. The thinking of manifold is trying to keep the relationship between the sample pointsin the original space with the help of constructing the weight graph, and the relationshipbetween the down-diminition samples points keep similar to the origitional sample points.Most of the traditional weight graph construction methods for Manifold Non-negative MatrixFactorization algorithms are based on the Euclidean distance between two vectors of thevectorilized face images. Also this construction method achieves a lot of successful, but it willbe very sensitive to the background and illumination, in this paper, we improved the weightgraph construction method for Non-negative Matrix Factorization by measuring the Euclideandistance of all the lines of the image, our new construction method will reduce the influenceof the parts of images such as background and illumination. Our new weight graph construction method for Manifold NMF algorithm will preserve more information among allthe points, so the recognition rate will be improved.4. Projvetive Non-negative Matrix Factorization algorithm is an improvement on thecost function of Non-negative matrix Factorization based on the Euclidean distance.Traditional NMF algorithm needs to calculate two target matrix (and), however,Projvetive Non-negative Matrix Factorization algorithm just needs to compute one targetmatrix (). There is little improvement on the Projvetive Non-negative Matrix Factorizationalgorithm. In this paper, we introduced manifold into Projvetive Non-negative MatrixFactorization algorithm, then the convergence of the proposed algorithm are proved.5. In practical applications, we can’t necessarily get all the face images at once, whichmeans that in most practical applications, there are a lot of work on new coming face image,if we rerun the face recognition algorithm, it will cost a lot of time, and the real-time systemcan not be guaranteed. Therefore, how to integrate the new coming face image into the currentface recognition system every time while new face image coming, is a major difficulty in facerecognition system in practical applications. In this paper, we introduced graph Graphregularized Non-negative Matrix Factorization into incremental study, proposed a newIncremental Graph regularized Non-negative Matrix Factorization algorithm for facerecognition, the algorithm can integrate the new coming face image into face recognitionsystem efficiently, with the help of manifold, the relationship between face image points canbe recorded, which will improve the recognition rate. Latter, considering face image alwayscomes in batch, so we improved our algorithm, introducing the Batch Incremental Graphregularized Non-negative Matrix Factorization for face recognition which can deal with manynew coming face images at once.