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Matlab非负矩阵分解NMF-NMF.ppt

发布时间：2022-05-29 发布人：admin 分类：说明书 资料大小：0.06M 资料格式：ppt 举报 版权申诉
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    Learning the parts of objects by nonnegative matrix factorization D.D. Lee from Bell Lab H.S. Seung from MIT Presenter: Zhipeng Zhao
    Introduction • NMF (Nonnegative Matrix Factorization): Theory: Perception of the whole is based on perception of its parts. • Comparison with another two matrix factorization methods: PCA (Principle Components Analysis) VA (Vector quantization )
    Comparison: • Common features: – Represent a face as a linear combination of basis images. – Matrix factorization: VWH V: nm matrix. Each column of which contains n nonnegative pixel values of one of the m facial images. W: (n r): r columns of W are called basis images. H: (r m): each column of H is called encoding.
    Comparison (cont’d) NMF Representation: parts- Based PCA holistic VQ holistic Basis Image: localized features eigenfaces whole face Constrains on W and H: each face is each column of H is allow multiple basis images to approximated by constrained to be a represent a face, a linear combi- unary vector, every face is approximat- but only additive nation of all combinations the eigenfaces ed by a single basis image.
    Implementation of NMF • Iterative algorithm:
    Implementation (cont’d) • Objective function: Updates: converges to a local maximum of the objective function. ( related to the likelihood of generating the images in V from the basis W and encoding H.
    Network model of NMF
    Semantic analysis of text doc. using NMF • A corpus of documents summarized by matrix V, where Vi is the number of times the ith word in the vocabulary appears in the th document. • NMF algorithm involves finding the approximate factorization of this Matrix VWH into a feature set W and hidden variables H, in the same way as was done for faces.
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