Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, December 03, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Saeed Ilchi

Sample Complexity of Learning Simplices

We study the problem of learning a d-dimensional simplex from a set of points uniformly sampled from its interior. This problem has applications in biology and remote sensing, mostly under the name of ``spectral unmixing''. We show that O(d²/ε log d/ε) samples are enough to learn a simplex up to a total-variation error of ε.  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.

Joint work with Amir Najafi, Amirhosssein Saberi, Abolfazl Motahari, Babak Khalaj, and Hamid Rabiee.
Paper: https://arxiv.org/abs/1810.07845

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