Nested nonnegative cone analysis

Lingsong Zhang, Shu Lu and J.S. Marron

Computational Statistics & Data Analysis, 2015, vol. 88, issue C, 100-110

Abstract: Motivated by the analysis of nonnegative data objects, a novel Nested Nonnegative Cone Analysis (NNCA) approach is proposed to overcome some drawbacks of existing methods. The application of traditional PCA/SVD method to nonnegative data often cause the approximation matrix leave the nonnegative cone, which leads to non-interpretable and sometimes nonsensical results. The nonnegative matrix factorization (NMF) approach overcomes this issue, however the NMF approximation matrices suffer several drawbacks: (1) the factorization may not be unique, (2) the resulting approximation matrix at a specific rank may not be unique, and (3) the subspaces spanned by the approximation matrices at different ranks may not be nested. These drawbacks will cause troubles in determining the number of components and in multi-scale (in ranks) interpretability. The NNCA approach proposed in this paper naturally generates a nested structure, and is shown to be unique at each rank. Simulations are used in this paper to illustrate the drawbacks of the traditional methods, and the usefulness of the NNCA method.

Keywords: Constrained inference; Functional data analysis; Nested learning; Nonnegative matrix factorization; Object-oriented data; Principal component analysis (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:88:y:2015:i:c:p:100-110

DOI: 10.1016/j.csda.2015.01.008

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