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1、Learning the parts of objects by non-negative matrix factorization,Contents,Professional English,Professional English,NMF,PCA,VQ,Non-negative matrix factorization,Principal components analysis,Vector quantization,Professional English,NMF,PCA,VQ,Its images are localized features that correspond bette
2、r with intuitive notions of the parts of faces,The basis images for PCA are eigenfaces, some of which resemble distorted versions of whole faces,VQ discovers a basis consisting of prototypes, each of which is a whole face,Figure 1,Figure 2,Figure 3,Three methods in a matrix factorization framework,T
3、he r columns of W are called basis images. Each column of H is called an encoding and is in one-to-one correspondence with a face in V.,The differences between PCA, VQ and NMF arise from different constraints imposed on the matrix factors W and H,In VQ, each column of H is constrained to be a unary
4、vector, with one element equal to unity and the other elements equal to zero PCA constrains the columns of W to be orthonormal and the rows of H to be orthonormal to each other NMF does not allow negative entries in the matrix factors W and H,Applying NMF to a completely different problem, the seman
5、tic analysis of text documents.,Vim is the number of times the ith word in the vocabulary appears in the mth document,In each semantic feature, the algorithm has grouped together semantically related words,Figure 4,Although NMF is successful in learning facial parts and semantic topics, this success
6、 does not imply that the method can learn parts from any database, such as images of objects viewed from extremely different viewpoints, or highly articulated objects,A neural network that infers the hidden from the visible variables requires the addition of inhibitory feedback connections.NMF learning is then implemented through plasticity in the synaptic connections.,Thank you,
