Quantum-inspired algorithm for general minimum conical hull problems

Non-negative Matrix Factorization (NMF) asks to decompose a (entry-wise) non-negative matrix into the product of two smaller-sized nonnegative matrices, which has been shown intractable in general. In order to overcome this issue, separability assumption is introduced which assumes all data points are in a conical hull. This assumption makes NMF tractable and widely used in text analysis and image processing, but still impractical for huge-scale datasets. In this paper, inspired by recent development on dequantizing techniques, we propose a new classical algorithm for separable NMF problem. Our new algorithm runs in polynomial time in the rank and logarithmic in the size of input matrices, which achieves an exponential speedup in the low-rank setting.

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Vibro-acoustic analysis of a cylindrical-conical hull subjected to propeller forces

Applied Ocean Research ◽

10.1016/j.apor.2020.102373 ◽

2020 ◽

Vol 104 ◽

pp. 102373

Author(s):

Zhenkun Lin ◽

Kai Zhou ◽

Zhiwen He ◽

Yong Chen ◽

Zengguang Li ◽

...

Keyword(s):

Acoustic Analysis ◽

Conical Hull

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Hierarchical Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing with Spectral Variability

Remote Sensing ◽

10.3390/rs12142326 ◽

2020 ◽

Vol 12 (14) ◽

pp. 2326 ◽

Cited By ~ 1

Author(s):

Tatsumi Uezato ◽

Mathieu Fauvel ◽

Nicolas Dobigeon

Keyword(s):

Hyperspectral Image ◽

Nonnegative Matrix ◽

Hyperspectral Data ◽

Spectral Variability ◽

Data Set ◽

Sparse Nonnegative Matrix Factorization ◽

Data Driven Modeling ◽

Endmember Variability ◽

Conical Hull ◽

Unmixing Model

Accounting for endmember variability is a challenging issue when unmixing hyperspectral data. This paper models the variability that is associated with each endmember as a conical hull defined by extremal pixels from the data set. These extremal pixels are considered as so-called prototypal endmember spectra that have meaningful physical interpretation. Capitalizing on this data-driven modeling, the pixels of the hyperspectral image are then described as combinations of these prototypal endmember spectra weighted by bundling coefficients and spatial abundances. The proposed unmixing model not only extracts and clusters the prototypal endmember spectra, but also estimates the abundances of each endmember. The performance of the approach is illustrated thanks to experiments conducted on simulated and real hyperspectral data and it outperforms state-of-the-art methods.

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