Name
Abstract | ||
|---|---|---|
The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank r reliably from the fewest possible random entries, and performance in achieving small reconstruction error. We propose a spectral algorithm for these two tasks called MaCBetH (for Matrix Completion with the Bethe Hessian). The rank is estimated as the number of negative eigenvalues of the Bethe Hessian matrix, and the corresponding eigenvectors are used as initial condition for the minimization of the discrepancy between the estimated matrix and the revealed entries. We analyze the performance in a random matrix setting using results from the statistical mechanics of the Hopfield neural network, and show in particular that MaCBetH efficiently detects the rank r of a large n X m matrix from C(r)r √nm entries, where C(r) is a constant close to 1. We also evaluate the corresponding root-mean-square error empirically and show that MaCBetH compares favorably to other existing approaches. |
Year | Venue | Field |
|---|---|---|
2015 | Annual Conference on Neural Information Processing Systems | Discrete mathematics,Combinatorics,Matrix completion,Matrix (mathematics),Hessian matrix,Minification,Initial value problem,Artificial neural network,Mathematics,Eigenvalues and eigenvectors,Random matrix |
DocType | Volume | ISSN |
Journal | abs/1506.03498 | Advances in Neural Information Processing Systems (NIPS 2015) 28,
pages 1261--1269 |
Citations | PageRank | References |
5 | 0.41 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alaa Saade | 1 | 47 | 4.41 |
| Florent Krzakala | 2 | 977 | 67.30 |
| Lenka Zdeborová | 3 | 1190 | 78.62 |