# Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data

arXiv: https://arxiv.org/abs/2408.05677 · HTML: https://mlsanity.com/paper/2408.05677/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 11 Aug 2024.

## Builds on (most cited first, 2 of 2)

- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Guaranteed Functional Tensor Singular Value Decomposition](https://mlsanity.com/paper/2108.04201/) (2021)

## Built on by (most cited first, 5 of 5)

- [Tensor Decomposition with Unaligned Observations](https://mlsanity.com/paper/2410.14046/) (2024)
- [Generalized Least Squares Kernelized Tensor Factorization](https://mlsanity.com/paper/2412.07041/) (2024)
- [Adaptive Subspace Modeling With Functional Tucker Decomposition](https://mlsanity.com/paper/2603.25530/) (2026)
- [Low-rank Distributional Matrix Completion](https://mlsanity.com/paper/2606.04176/) (2026)
- [Kernel Regression with Tensor Trains and Hadamard Overparameterization](https://mlsanity.com/paper/2607.17390/) (2026)

## Abstract (arXiv)

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.