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arXiv · 1810.07845

On Statistical Learning of Simplices: Unmixing Problem Revisited

Amir Najafi·Saeed Ilchi·Amir H. Saberi·Seyed Abolfazl Motahari·Babak H. Khalaj·Hamid R. Rabiee
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Abstract

We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of `spectral unmixing'. We theoretically show that a sufficient sample complexity for reliable learning of a $K$-dimensional simplex up to a total-variation error of $\epsilon$ is $O\left(\frac{K^2}{\epsilon}\log\frac{K}{\epsilon}\right)$, which yields a substantial improvement over existing bounds. Based on our new theoretical framework, we also propose a heuristic approach for the inference of simplices. Experimental results on synthetic and real-world datasets demonstrate a comparable performance for our method on noiseless samples, while we outperform the state-of-the-art in noisy cases.

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Amir Najafi, Saeed Ilchi, Amir H. Saberi, Seyed Abolfazl Motahari, Babak H. Khalaj, Hamid R. Rabiee. 2018-10-18. On Statistical Learning of Simplices: Unmixing Problem Revisited. https://arxiv.org/abs/1810.07845

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