Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data
<|reference_start|>Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data: The canonical polyadic (CP) tensor decomposition decomposes a multidimensional data array into a sum of outer products of finite-dimensional vectors. Instead, we can replace some or all of the vectors with continuous functions (infinite-dimensional vectors) from a reproducing kernel Hilbert space (RKHS). We refer to tensors with some infinite-dimensional modes as quasitensors, and the approach of decomposing a tensor with some continuous RKHS modes is referred to as CP-HiFi (hybrid infinite and finite dimensional) tensor decomposition. An advantage of CP-HiFi is that it can enforce smoothness in the infinite dimensional modes. Further, CP-HiFi does not require the observed data to lie on a regular and finite rectangular grid and naturally incorporates misaligned data. We detail the methodology and illustrate it on a synthetic example.<|reference_end|>
@article{larsen2024tensor,
    title={Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and
  Misaligned Data},
    author={Brett W. Larsen, Tamara G. Kolda, Anru R. Zhang, Alex H. Williams},
    journal={arXiv preprint arXiv:2408.05677},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.05677},
    primaryClass={math.NA cs.LG cs.NA}
}