Abstract
Nonnegativity constraint is more consistent with the biological modeling of visual data and often leads to better performance for data representation and graph learning [66]. In this chapter, we present an overview of some recent advances in correntropy with nonnegative constraint. We begin with an introduction of an ℓ 1 regularized nonnegative sparse coding algorithm to learn a nonnegative sparse representation (NSR). Then we show how to use correntropy to learn a robust NSR. Finally, based on the divide and conquer strategy, a two-stage framework is discussed for large-scale sparse representation problems.
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Notes
- 1.
Since β is assumed to be sparse, LCP can be used to efficiently find a sparse active set.
- 2.
According to Theorem 4.2, we can learn that p ≤ 0. By replacing the p with − p, we can get the equivalent minimal problem.
- 3.
- 4.
Subspace U is composed of the eigenvectors computed by principal component analysis [49].
- 5.
- 6.
The source code: http://www.acm.caltech.edu/l1magic/.
- 7.
The source code: http://redwood.berkeley.edu/bruno/sparsenet/.
- 8.
- 9.
The source code: http://www.openpr.org.cn/index.php/All/69-CESR/View-details.html.
- 10.
The source code: http://www4.comp.polyu.edu.hk/~cslzhang.
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He, R., Hu, B., Yuan, X., Wang, L. (2014). Correntropy with Nonnegative Constraint. In: Robust Recognition via Information Theoretic Learning. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-07416-0_6
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