# Discovery of Important Subsequences in Electrocardiogram Beats Using the Nearest Neighbour Algorithm

## TL;DR

This paper introduces a method to identify key subsequences in ECG data that influence classification outcomes using a nearest neighbor approach with DTW, aiding interpretability and abnormality detection.

## Contribution

It presents a novel approach to find minimal relevant subsequences affecting classification, enhancing interpretability of time series analysis in medical data.

## Key findings

- Identified important ECG subsequences related to cardiac abnormalities.
- Enabled distinction between healthy and sick patients based on subsequence relevance.
- Provided a measure for the relevance of each time point in classification.

## Abstract

The classification of time series data is a well-studied problem with numerous practical applications, such as medical diagnosis and speech recognition. A popular and effective approach is to classify new time series in the same way as their nearest neighbours, whereby proximity is defined using Dynamic Time Warping (DTW) distance, a measure analogous to sequence alignment in bioinformatics. However, practitioners are not only interested in accurate classification, they are also interested in why a time series is classified a certain way. To this end, we introduce here the problem of finding a minimum length subsequence of a time series, the removal of which changes the outcome of the classification under the nearest neighbour algorithm with DTW distance. Informally, such a subsequence is expected to be relevant for the classification and can be helpful for practitioners in interpreting the outcome. We describe a simple but optimized implementation for detecting these subsequences and define an accompanying measure to quantify the relevance of every time point in the time series for the classification. In tests on electrocardiogram data we show that the algorithm allows discovery of important subsequences and can be helpful in detecting abnormalities in cardiac rhythms distinguishing sick from healthy patients.