Name
Abstract | ||
|---|---|---|
Some theoretical difficulties that arise from dimensionality reduction for tensors with non-negative coefficients is discussed in this paper. A necessary and sufficient condition is derived for a low non-negative rank tensor to admit a non-negative Tucker decomposition with a core of the same non-negative rank. Moreover, we provide evidence that the only algorithm operating mode-wise, minimizing the dimensions of the features spaces, and that can guarantee the non-negative core to have low non-negative rank requires identifying on each mode a cone with possibly a very large number of extreme rays. To illustrate our observations, some existing algorithms that compute the non-negative Tucker decomposition are described and tested on synthetic data. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/978-3-319-53547-0_15 | Lecture Notes in Computer Science |
Keywords | Field | DocType |
Non-negative Tucker Decomposition,Non-negative Canonical Polyadic Decomposition,Dimensionality reduction,Non-negative Matrix Factorization | Applied mathematics,Discrete mathematics,Dimensionality reduction,Tensor,Synthetic data,Large numbers,Non-negative matrix factorization,Tucker decomposition,Mathematics | Conference |
Volume | ISSN | Citations |
10169 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 8 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jeremy E. Cohen | 1 | 46 | 8.34 |
| Pierre Comon | 2 | 3856 | 716.85 |
| Nicolas Gillis | 3 | 503 | 39.77 |