Age estimation based on extended non negative factorization
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This document discusses non-negative matrix factorization (NMF) and its application to age estimation. It introduces NMF, which factors a data matrix into two non-negative matrices. Adding sparseness constraints can make the basis vectors or coefficients sparse. The document then proposes an extended NMF method that imposes orthogonality on the basis matrix and sparsity on the coefficient matrix for age estimation. Experimental results found this approach reduced overlapping between basis images and components.
Age estimation based on extended non negative factorization
- 1. Non-negative Matrix Factorization with Sparseness Constraints Patrik O. Hoyer HIIT Basic Research Unit Department of Computer Science University of Helsinki Finland
- 2. Topics • Introduction • Problem overview • Overall methodology • Integrating NMF with Age estimation problem • Extended NMF • Result found for age estimation • Conclusion
- 3. Non-negative Matrix Factorization • Factor A = WH • A – matrix of data • m non-negative scalar variables • n measurements form the columns of A • W – m x r matrix of “basis vectors” • H – r x n coefficient matrix • Describes how strongly each building block is present in measurement vectors
- 5. Non-negative Matrix Factorization • The image database is regarded as an n*m matrix V, each column of which contains n non-negative pixel values of one of the m facial images • Our purpose is to construct approximate factorizations of the form, where each column of H contains the coefficient vector ht corresponding to the measurement vector, Vt • Written in this form, it becomes apparent that a linear data representation is simply a factorization of the data matrix • Given a data matrix V, the optimal choice of matrices W and H are to be defined to be those nonnegative matrices that minimize the reconstruction error between V and WH • Various error functions have been proposed (Paatero and Tapper, 1994; Lee and Seung, 2001), perhaps the most widely used one is eucledian distance measure •
- 6. Adding sparseness constrains to NMF • The concept of ‘sparse coding’ refers to a representational scheme where only a few units (out of a large population) are effectively used to represent typical data vectors • This implies most units taking values close to zero while only few take significantly non-zero values. • On a normalized scale, the sparsest possible vector (only a single component is non-zero) should have a sparseness of one, whereas a vector with all elements equal zero should have a sparseness of zero. • In this paper, we use a sparseness measure based on the relationship between the L1 norm and the L2 norm:
- 7. NMF with sparseness component • Our aim is to constrain NMF to find solutions with desired degrees of sparseness. • What exactly should be sparse? The basis vectors W or the coefficients H? Depends on scenario • When trying to learn useful features from a database of images, it might make sense to require both W and H to be sparse, pointing that any given object is present in few images and affects only a small part of the image.
- 9. Age Estimation Based on Extended Non-negative Matrix Factorization Ce Zhan, Wanqing Li, and Philip Ogunbona School of Computer Science and Software Engineering University of Wollongong, Australia
- 10. Proposed method : Extended NMF • Extended NMF (ENMF) impose orthogonality constraint on basis matrix W while controlling the sparseness of coefficient matrix H. • To reduce the overlapping between basis images, different bases should be as orthogonal as possible so as to minimize the redundancy • Denote : U=WTW • The orthogonality constraint can be imposed by minimizing • Maximum sparsity in the coefficient matrix makes sure that a basis component cannot be further decomposed into more components, thus the overlapping between basis images is further reduced. • We want :
- 11. Extended NMF • The objective function of the proposed method would be: • β is a small positive constant ENMF is defined as following optimization problem