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Optimality of Spectrum Pursuit for Column Subset Selection Problem: Theoretical Guarantees and Applications in Deep Learning
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  • Mohsen Joneidi ,
  • Saeed Vahidian ,
  • Ashkan Esmaeili ,
  • Siavash Khodadadeh
Mohsen Joneidi
University of Central Florida

Corresponding Author:[email protected]

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Saeed Vahidian
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Ashkan Esmaeili
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Siavash Khodadadeh
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We propose a novel technique for finding representatives from a large, unsupervised dataset. The approach is based on the concept of self-rank, defined as the minimum number of samples needed to reconstruct all samples with an accuracy proportional to the rank-$K$ approximation. Our proposed algorithm enjoys linear complexity w.r.t. the size of original dataset and simultaneously it provides an adaptive upper bound for approximation ratio. These favorable characteristics result in filling a historical gap between practical and theoretical methods in finding representatives.