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Erschienen in:
2020 | OriginalPaper | Buchkapitel
Nonnegative Tensor Train Factorizations and Some Applications
verfasst von : Elena Shcherbakova, Eugene Tyrtyshnikov
Erschienen in: Large-Scale Scientific Computing
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Abstract
Nowadays as the amount of available data grows, the problem of managing information becomes more difficult. In many applications data can be represented as a multidimensional array. However, in the big data case and as well as when we aim at discovering some structure in the data, we are often interested to construct some low-rank tensor approximations, for instance, using tensor train (TT) decomposition. If the original data is nonnegative, we may be interested to guarantee that an approximant keeps this property. Nonnegative tensor train factorization is an utterly nontrivial task when we cannot afford to see each data element because it may be too expensive in the case of big data.
A natural solution is to build tensor trains with all carriages (cores) to be nonnegative. This means that skeleton decompositions (approximations) have to be constructed nonnegative. Nonnegative factorizations can be used as models for recovering suitable structures in data, e.g., in machine learning and image processing tasks. In this work we suggest a new method for nonnegative tensor train factorizations, estimate its accuracy and give numerical results for different problems.