基于流行的非负矩阵分解算法探讨
流行学习是近年来机器学习及模式识别等领域的一个研究热点，其主要目标是去发现高维观察数据空间的低维光滑流行．非负矩阵分解算法是对已知矩阵 进行分解使之表示成 的形式，且矩阵 和 的每一个元素都满足非负限制，流行的非负矩阵分解算法是使 与 之间的差尽可能小．本文首先介绍了流行非负矩阵的研究背景及意义、流行学习研究中涉及到的相关数学知识．然后介绍了人脸识别的原理以及人脸识别的步骤，人脸识别的步骤是人脸检测、特征提取、特征降维、匹配识别，流行非负矩阵分解主要用于特征降维．其次我们探讨了流行非负矩阵分解算法模型，采用Yale人脸数据库进行了实验，根据非负矩阵分解算法的流程，利用matlab计算出非负矩阵分解后得到的图片与原始图片的对比图、流行非负矩阵分解后得到的图片与原始图片的对比图.
关键词 非负矩阵分解 流行学习 数据降维 人脸识别
Research on Algorithm Based on the Thinking of Manifold
Abstract Manifold learning is a hot topic in the field of machine learning and pattern recognition in recent years and its objective is to find low dimensional data space smooth manifold of the high-dimensional observation. The nonnegative matrix decomposition algorithm is a form in which the known matrix is decomposed to the representation .And each element of the matrix and satisfies the nonnegative restriction.The manifold nonnegative matrix decomposition algorithm is to make the difference between and as small as possible.We first introduces the background and significance of manifold and the related mathematical knowledge involved in manifold learning research in this paper. Then the principle of face recognition and the steps of face recognition are introduced. The steps of face recognition are made of it face detection, feature extraction, feature dimension reduction, matching recognition. Nonnegative matrix factorization is mainly used for feature dimension reduction. Secondly,we discuss manifod nonnegative matrix decomposition algorithm model by using Yale face database as the research object. According to the flow of nonnegative matrix decomposition algorithm,we use matlab to obtain the comparison picture of non-negative matrix decomposition between the new picture and the original picture, and calculate the comparison picture of manifold non-negative matrix decomposition between the new picture and the original picture.
Keywords face recognition, Nonnegative Matrix Factorization, manifold learning, data dimensionality reduction
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