# Tensor Decomposition with Unaligned Observations

arXiv: https://arxiv.org/abs/2410.14046 · HTML: https://mlsanity.com/paper/2410.14046/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 61 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Tensor Decompositions for temporal knowledge base completion](https://mlsanity.com/paper/2004.04926/) (2020)
- [Generalized Canonical Polyadic Tensor Decomposition](https://mlsanity.com/paper/1808.07452/) (2018)
- [Stochastic Gradients for Large-Scale Tensor Decomposition](https://mlsanity.com/paper/1906.01687/) (2019)
- [Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration](https://mlsanity.com/paper/2010.02482/) (2020)
- [A least-squares method for sparse low rank approximation of multivariate functions](https://mlsanity.com/paper/1305.0030/) (2013)
- [Guaranteed Functional Tensor Singular Value Decomposition](https://mlsanity.com/paper/2108.04201/) (2021)
- [Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Data](https://mlsanity.com/paper/2408.05677/) (2024)
- [Dictionary-based Tensor Canonical Polyadic Decomposition](https://mlsanity.com/paper/1704.00541/) (2017)
- [High-dimensional Log-Error-in-Variable Regression with Applications to Microbial Compositional Data Analysis](https://mlsanity.com/paper/1811.11709/) (2018)
- [Non-negative Tensor Factorization for Human Behavioral Pattern Mining in Online Games](https://mlsanity.com/paper/1702.05695/) (2017)
- [Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks](https://mlsanity.com/paper/2210.03828/) (2022)

## Built on by (most cited first, 1 of 1)

- [Adaptive Subspace Modeling With Functional Tucker Decomposition](https://mlsanity.com/paper/2603.25530/) (2026)

## Abstract (arXiv)

This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a versatile loss function that effectively accounts for various types of data, including binary, integer-valued, and positive-valued types. Additionally, we propose an optimization algorithm for computing tensor decompositions with unaligned observations, along with a stochastic gradient method to enhance computational efficiency. A sketching algorithm is also introduced to further improve efficiency when using the ℓ2 loss function. To demonstrate the efficacy of our methods, we provide illustrative examples using both synthetic data and an early childhood human microbiome dataset.