CSTS - Correlation Structures in Time Series

• Repository: https://github.com/isabelladegen/corrclust-validation
• Paper: https://arxiv.org/abs/2505.14596
• Demo: https://colab.research.google.com/github/isabelladegen/corrclust-validation/blob/main/src/utils/hf_tooling/CSTS_HuggingFace_UsageExample.ipynb

Dataset Description

CSTS (Correlation Structures in Time Series) is a comprehensive synthetic benchmarking dataset for evaluating correlation structure discovery in time series data. The dataset systematically models known correlation structures between three different time series variates and enables examination of how these structures are affected by distribution shifting, sparsification, and downsampling. With its controlled properties and ground truth labels, CSTS provides algorithm developers clean benchmark data that bridge the gap between theoretical models and messy real-world data.

Key Applications

• Evaluating the ability of time series clustering algorithms to segment and group segments by correlation structures
• Assessing clustering validation methods for correlation-based clusters
• Investigating how data preprocessing affects correlation structure discovery
• Establishing performance thresholds for high-quality clustering result

Correlation Structures

The dataset contains 23 distinct correlation structures, each representing a valid combination of relationships between three time series variables. These relationships fall into three categories: strong positive ([0.7,1]), negligible ([-0.2,0.2]), and strong negative ([-1,-0.7]) correlations.

These correlation structures vary between segments, modelling a regime-switching time series with stationary segments. Notably, the time series data does not incorporate temporal dependencies such as autocorrelation, trends, or seasonality.

Dataset Structure

CSTS provides two main splits (exploratory and confirmatory) with 30 subjects each, enabling proper statistical validation. The dataset structure includes:

• 12 data variants: 4 generation stages × 3 completeness levels for each split
• Generation stages: raw (unstructured data, i.i.d), correlated (normal-distributed data, not independent), nonnormal (extreme value and negative binomial distribution shifts, not independent, not identically distributed), downsampled (1s→1min, non-normal, not independent, not identically distributed)
• Completeness levels: complete (100% of observations), partial (70% of observations), sparse (10% of observations)

Subjects

In total there are 60 subjects. Each subject contains 100 segments of varying lengths (900-36000), and each segment encodes one of the 23 specific correlation structures. Each subject uses all 23 patterns 4-5 times. For the complete data variants, each subject consists of ~1.26 million observations.

Subjects each have the following information, accessible as subsets:

• a time series data file with three variates (iob, cob, ig) and time stamps (datetime)
• a label file specifying the ground truth segmentation and clustering
• 66 bad clustering label files with controlled degradations (varying numbers of segmentations and/or cluster assignment mistakes) spanning the entire Jaccard Index range [0,1]

Additional Splits

CSTS also includes versions (configured as splits) that allow exploring how cluster and segment counts affect algorithm performance. They follow the same dataset structure (exploratory and confirmatory splits with each 12 data variants subset with each 3 information file subsets). These versions are:

• Reduced cluster count: 11 or 6 instead of 23
• Reduced segment count: 50 or 25 instead of 100

Our accompanying paper provides complete methodological details, baseline findings, and usage guidance. Our GitHub codebase includes the generation, validation and use case code and is configured to automatically load the data.

Usage Guidance

Configuration Concept

The configuration follows the convention: <generation_stage>_<completeness_level>_<file_type> and allows access to a specific subset of the data. The possible values are all combinations of:

<generation_stage>:

• raw: raw data, segmented but not correlated, i.i.d
• correlated: correlated data according to a specific correlation structure, normally distributed, no longer independent
• nonnormal: distribution shifted, correlated data, no longer identically distributed
• downsampled: resampled non-normal data from 1s to 1min

<completeness_level>:

• complete: 100% of the data
• partial: 70% of the data (30% of observations dropped at random)
• sparse: 10% of the data (90% of observations dropped at random)

<file_type>:

• data: the time series data (needed for training algorithms)
• labels: the labels containing the ground truth (perfect) segmentation and clustering (needed for validating the results)
• badclustering_labels: the 66 labels files for a degraded clustering with controlled segmentation and/or cluster assignment mistakes (needed for validating validation methods)

Splits

The main splits are:

• exploratory: for experimentation and training
• confirmatory: for testing and validation Consider that depending on the application and study design, a single subject might be sufficient for training.

Additional splits are:

• reduced_11_clusters(_exploratory or _confirmatory): same data including 11 of the original 23 clusters (selected at random)
• reduced_6_clusters(_exploratory or _confirmatory): same data including 6 of the original 23 clusters (selected at random)
• reduced_50_segments(_exploratory or _confirmatory): same data including 50 of the original 100 segments (selected at random)
• reduced_25_segments(_exploratory or _confirmatory): same data including 25 of the original 100 segments (selected at random)

Quick Start

Steps to load the data and labels for the complete correlated data variant:

1. Load the data for all 30 exploratory subjects for the complete and correlated data variant into pandas df:

import pandas as pd
from datasets import load_dataset
correlated_data = load_dataset("idegen/csts", name="correlated_complete_data", split="exploratory")
df_correlated = correlated_data.to_pandas()
df_correlated.head()

2. Load the ground truth labels for these subjects

import pandas as pd
from datasets import load_dataset
correlated_labels = load_dataset("idegen/csts", name="correlated_complete_labels", split="exploratory")
df_correlated_labels = correlated_labels.to_pandas()
df_correlated_labels.head()

Comprehensive examples can be found in this Google Colab Notebook:

Additional Information

Authors

• Isabella Degen, University of Bristol
• Zahraa S Abdallah, University of Bristol
• Henry W J Reeve, University of Nanjing
• Kate Robson Brown, University College Dublin

Citation Information

Please use the following citation. This is the arXiv preprint version check back for updates:

@misc{degen2025csts,
      title={CSTS: A Benchmark for the Discovery of Correlation Structures in Time Series Clustering}, 
      author={Isabella Degen and Zahraa S Abdallah and Henry W J Reeve and Kate Robson Brown},
      year={2025},
      eprint={2505.14596},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2505.14596}, 
}

Acknowledgements

We would like to thank UK Research and Innovation (UKRI) for funding author ID's PhD research through the UKRI Doctoral Training in Interactive Artificial Intelligence (AI) under grant EP/S022937/1. The authors extend their gratitude to the faculty, staff and colleagues of the Interactive AI Centre for Doctoral Training at Bristol University for their valuable support and guidance throughout this research. We acknowledge the use of Claude 3.7 Sonnet by Anthropic as a research dialogue tool throughout the development of this work, assisting with dataset documentation, iterative refinement of ideas, and evaluating the clarity of our methods and contributions.