# Kernel distance measures for time series, random fields and other structured data

arXiv: https://arxiv.org/abs/2109.14752 · HTML: https://mlsanity.com/paper/2109.14752/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Spherical Text Embedding](https://mlsanity.com/paper/1911.01196/) (2019)
- [Associative Domain Adaptation](https://mlsanity.com/paper/1708.00938/) (2017)
- [Two-sample Statistics Based on Anisotropic Kernels](https://mlsanity.com/paper/1709.05006/) (2017)
- [A witness function based construction of discriminative models using Hermite polynomials](https://mlsanity.com/paper/1901.02975/) (2019)
- [Bounding the Error From Reference Set Kernel Maximum Mean Discrepancy](https://mlsanity.com/paper/1812.04594/) (2018)

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

- [An unsupervised approach towards promptable defect segmentation in laser-based additive manufacturing by Segment Anything](https://mlsanity.com/paper/2312.04063/) (2023)

## Abstract (arXiv)

This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only overlap over a portion of their region of support. Our proposed measure is inspired by MPdist which has been previously proposed for such datasets and is constructed using Euclidean metrics, whereas kdiff is constructed using non-linear kernel distances. Also, kdiff accounts for both self and cross similarities across the instances and is defined using a lower quantile of the distance distribution. Comparing the cross similarity to self similarity allows for measures of similarity that are more robust to noise and partial occlusions of the relevant signals. Our proposed measure kdiff is a more general form of the well known kernel-based Maximum Mean Discrepancy (MMD) distance estimated over the embeddings. Some theoretical results are provided for separability conditions using kdiff as a distance measure for clustering and classification problems where the embedding distributions can be modeled as two component mixtures. Applications are demonstrated for clustering of synthetic and real-life time series and image data, and the performance of kdiff is compared to competing distance measures for clustering.