Name
Abstract | ||
|---|---|---|
We propose a new low-rank tensor factorization where one mode is coded as a sparse linear combination of elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces r-rank approximations of data tensors via outer products of vectors in each dimension of the data. The SCTD model can leverage prior knowledge about the shape of factors along a given mode, for example in tensor data where one mode represents time. By constraining the vector in the temporal dimension to known analytic forms which are selected from a large set of candidate functions, more readily interpretable decompositions are achieved and analytic time dependencies discovered. The SCTD method circumvents traditional flattening techniques where an N-way array is reshaped into a matrix in order to perform a singular value decomposition. A clear advantage of the SCTD algorithm is its ability to extract transient and intermittent phenomena which is often difficult for SVD-based methods. We motivate the SCTD method using several intuitively appealing results before applying it on a real-world data set to illustrate the efficiency of the algorithm in extracting interpretable spatio-temporal modes. With the rise of data-driven discovery methods, the decomposition proposed provides a viable technique for analyzing multitudes of data in a more comprehensible fashion. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1109/DSAA.2019.00044 | 2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA) |
Keywords | Field | DocType |
CANDECOMP/PARAFAC decomposition,sparsity,overcomplete dictionaries,optimization | Linear combination,Singular value decomposition,Flattening,Tensor,Computer science,Matrix (mathematics),Algorithm,Approximations of π,Tensor factorization,Tensor decomposition | Conference |
ISSN | ISBN | Citations |
2472-1573 | 978-1-7281-4494-8 | 0 |
PageRank | References | Authors |
0.34 | 18 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lusch, Bethany | 1 | 25 | 1.99 |
| Eric C. Chi | 2 | 1 | 1.03 |
| J. Nathan Kutz | 3 | 225 | 47.13 |