PaperlayerView exact revision on arXiv

Source-linked AI summary

CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching

Xingjian Wu, Xiangfei Qiu, Zhengyu Li, Yihang Wang, Jilin Hu, Chenjuan Guo, Hui Xiong, Bin Yang

arXiv:2410.12261v5cs.LGcs.AI

TL;DR

Heterogeneous subsequence anomalies and varying channel correlations make multivariate time-series anomaly detection difficult for methods using coarse frequency modeling or fixed channel strategies. CATCH patches the frequency domain and uses a Channel Fusion Module with a patch-wise mask generator, masked attention, and bi-level optimization. Across 24 multivariate datasets, the authors report state-of-the-art performance.

  • Problem

    Multivariate time-series anomaly detection is challenged by subsequence anomalies that require fine-grained frequency modeling and channel correlations that vary across frequency bands.

  • Method

    CATCH patchifies the frequency domain and uses a Channel Fusion Module with a patch-wise mask generator, masked attention, and bi-level multi-objective optimization.

  • Results

    CATCH achieves state-of-the-art performance across 24 multivariate real-world and synthetic datasets.

  • Takeaways & Limitations

    CATCH simultaneously detects point and subsequence anomalies while adaptively clustering relevant channels and isolating irrelevant-channel effects.

Abstract

from arXiv · show

Anomaly detection in multivariate time series is challenging as heterogeneous subsequence anomalies may occur. Reconstruction-based methods, which focus on learning normal patterns in the frequency domain to detect diverse abnormal subsequences, achieve promising results, while still falling short on capturing fine-grained frequency characteristics and channel correlations. To contend with the limitations, we introduce CATCH, a framework based on frequency patching. We propose to patchify the frequency domain into frequency bands, which enhances its ability to capture fine-grained frequency characteristics. To perceive appropriate channel correlations, we propose a Channel Fusion Module (CFM), which features a patch-wise mask generator and a masked-attention mechanism. Driven by a bi-level multi-objective optimization algorithm, the CFM is encouraged to iteratively discover appropriate patch-wise channel correlations, and to cluster relevant channels while isolating adverse effects from irrelevant channels. Extensive experiments on 10 real-world datasets and 12 synthetic datasets demonstrate that CATCH achieves state-of-the-art performance. We make our code and datasets available at https://github.com/decisionintelligence/CATCH.

1 INTRODUCTION

CATCH addresses the difficulty of detecting heterogeneous subsequence anomalies by modeling fine-grained frequency bands and adapting channel correlations across those bands. Its experiments report state-of-the-art performance across real-world and synthetic multivariate datasets.

  • Subsequence anomalies can remain within the normal value distribution, making them harder to detect than point anomalies.
  • Frequency-domain anomalies affect distinct bands, but coarse reconstruction may miss high-frequency details needed for heterogeneous subsequence detection.
  • Channel relationships vary by frequency band, making fixed channel-independent or channel-dependent strategies inadequate.
  • CATCH patchifies the frequency domain and uses a Channel Fusion Module with masked attention and bi-level optimization to discover adaptive channel correlations.
  • CATCH enables simultaneous detection of heterogeneous point and subsequence anomalies through frequency patch learning.
  • Experiments on 24 multivariate datasets show that CATCH outperforms state-of-the-art baselines.

2 RELATED WORK

Prior multivariate time-series anomaly detection methods include non-learning, machine-learning, forecasting, reconstruction, and contrastive approaches. Frequency analysis helps expose difficult subsequence anomalies, while CATCH extends frequency-based detection to multivariate settings with adaptive channel modeling.

  • MTSAD methods span non-learning, machine-learning, forecasting-based, reconstruction-based, and contrastive-based approaches.
  • Channel-independent strategies share one model across channels, whereas channel-dependent strategies model channels jointly with greater capacity but greater exposure to irrelevant-channel noise.
  • Frequency-domain analysis can reveal subsequence anomalies involving periodic fluctuations or oscillation patterns that are difficult to detect in the time domain.
  • CATCH is organized into Forward, Channel Fusion, and Time-Frequency Reconstruction modules that patch frequency representations and model channel interrelationships.
  • Earlier frequency-based methods such as SR-CNN and PFT are confined to univariate time series, leaving multivariate channel relationships unaddressed.

3 CATCH

CATCH transforms multivariate time series into fine-grained frequency patches, dynamically models patch-wise channel correlations, and reconstructs signals in time and frequency domains for anomaly scoring.

  • 3.1 STRUCTURE OVERVIEW: CATCH applies FFT to retain real and imaginary components, patches each frequency representation, concatenates paired patches, and projects them into a hidden space.The patch count is L = [T − p]/s + 1, with patch size p and stride s.
  • 3.2 CHANNEL FUSION MODULE: The Channel Fusion Module dynamically models channel correlations separately within each fine-grained frequency patch.It processes projected patches in parallel and outputs hidden representations for subsequent reconstruction.
  • 3.2 CHANNEL FUSION MODULE: The CFM uses a patch-wise Mask Generator to produce binary channel-correlation masks that filter irrelevant channels while allowing relationships between relevant channels.The masks are generated from patch representations through linear projections and Bernoulli resampling, with diagonal entries retained.
  • 3.2 CHANNEL FUSION MODULE: Masked attention uses the generated masks to model fine-grained interrelationships among relevant channels while retaining transformer normalization, skip connections, and multi-head attention.The masked attention matrix combines attention scores with the binary mask, assigning −∞ to masked relationships.
  • 3.2 CHANNEL FUSION MODULE: Channel Correlation Discovering optimizes the masks and attention by clustering channels marked as relevant, separating irrelevant channels, and using regularization to avoid an all-ones mask.The clustering objective reuses attention calculations, while the regularization objective constrains the number of relevant channels.
  • 3.5 ANOMALY SCORING: CATCH combines temporal and frequency reconstruction errors, averaging frequency errors across overlapping patches that contain each time point for fine-grained anomaly scoring.This patch-wise scoring addresses the limitation of assigning one coarse frequency score across an entire input window.

4 EXPERIMENTS

CATCH is evaluated against 15 baselines across real-world and synthetic multivariate datasets, achieving strong overall anomaly-detection performance while exposing clear module, parameter, and dual-domain scoring behavior.

  • 4.1 MAIN RESULTS: CATCH achieves state-of-the-art results on most benchmark datasets for Affiliated-F1 and obtains the highest AUC-ROC on most datasets.The evaluation covers 12 real-world datasets and six synthetic anomaly types; the method handles both point and subsequence anomalies, with greater improvement for subsequence anomalies.
  • 4.1 MAIN RESULTS: CATCH cannot effectively capture continuous SWAT abnormal segments that exceed the reconstruction model’s look-back window.
  • 4.2 MODEL ANALYSIS: Removing channel-correlation discovery, frequency objectives, frequency patching, or bi-level optimization consistently reduces performance.The largest ablation decline occurs after removing frequency loss, while replacing patching with a window-based approach substantially reduces performance.
  • 4.2 MODEL ANALYSIS: The score weight is mostly stable from 0.01 to 0.1, while training and testing patch-size sensitivity remains stable across extensive datasets.Performance can still depend on data patterns; for example, training patch size 8 performs better for MSL and testing patch size 32 for CICIDS.
  • 4.2 MODEL ANALYSIS: Temporal scores dominate point anomalies, whereas elevated frequency scores track subsequence intervals and their boundaries.The final anomaly score combines both domains to capture point and subsequence anomalies.

5 CONCLUSION

The conclusion presents CATCH as a framework for jointly detecting point and subsequence anomalies through frequency patching, adaptive channel correlations, and bi-level optimization. Comprehensive real-world and synthetic experiments are reported to show state-of-the-art performance.

  • 5 CONCLUSION: CATCH jointly detects point and subsequence anomalies using frequency patching, adaptive channel-correlation discovery, and bi-level optimization.
  • 5 CONCLUSION: Comprehensive experiments on real-world and synthetic datasets demonstrate that CATCH achieves state-of-the-art performance.

A.1 DATASETS

The dataset suite contains 12 real-world and 12 synthetic multivariate time series spanning nine domains and broad ranges of anomaly ratios, feature dimensions, and sequence lengths.

  • A.1 DATASETS: The evaluation uses 12 real-world and 12 synthetic multivariate datasets spanning nine domains.
  • A.1 DATASETS: Anomaly ratios range from 0.17% to 11.07%, feature dimensions from 3 to 72, and sequence lengths from 5,040 to 1,416,825.

A.2 METRICS

The paper organizes evaluation metrics into label-based and score-based categories, covering classification, range-aware, affiliated, precision-recall, and ROC measures.

  • A.2 METRICS: Label-based metrics include Accuracy, Precision, Recall, F1-score, range-aware metrics, Precision@k, and affiliated precision, recall, and F1.
  • A.2 METRICS: Score-based metrics include the Area Under the Precision-Recall Curve and the Area Under the Receiver Operating Characteristics Curve.

A.3 IMPLEMENTATION DETAILS

The experiments standardize baseline evaluation and training settings, while using a bi-level gradient procedure to update model and mask-generator parameters.

  • Evaluation protocol: Testing disables Drop Last for all baselines to avoid errors related to test batch size.This setting is applied to ensure fair comparison.
  • Runtime settings: Training uses PyTorch, Adam, batch size 32, and an optional reduction to 8 under out-of-memory conditions.Experiments run on an NVIDIA Tesla-A800 GPU.
  • Baseline settings: Baseline comparisons follow original-paper hyperparameters and additional searches select optimal configurations for fair assessment.The search covers multiple parameter sets for each baseline.
  • Optimization: Bi-level optimization alternates outer mask-generator updates with inner model updates using a combined reconstruction, clustering, and regularization loss.The loss combines time-domain reconstruction, frequency-domain reconstruction, clustering, and regularization terms.

A.6 IMPLEMENTATION DETAILS OF SCORING

The scoring implementation computes frequency-based patch losses and aligns patch-level scores back to individual time points, including padding when needed.

  • Frequency scoring: Frequency-enhanced scoring uses overlapping inference patches and a frequency loss to produce patch-level anomaly scores.Patch size, stride, sequence length, patch count, and padding length determine the patch layout.
  • Patch construction: The implementation reshapes patch outputs and unfolds target sequences with the configured patch size and stride for aligned comparison.These operations organize patches across batches, windows, and channels.
  • Point-granularity alignment: Overlapping patch losses are expanded across their covered indices and aggregated into point-granularity scores.The procedure separately accounts for the remaining padded portion when the window is not fully covered.

A.7 COMMAND USED FOR GENERATING THE SYNTHETIC DATASETS

The synthetic-data procedure adapts the TODS generator to create longer series with specified anomaly behaviors, and Figure 6 visualizes anomaly-score comparisons on TODS datasets.

  • TODS synthesis: The synthetic generator is based on the original TODS implementation, with only the length parameter adjusted to produce longer time series.The stated purpose is to maintain a fair comparison.
  • TODS synthesis: The generator configures five dimensions with alternating sine and cosine behaviors and specified frequency, coefficient, offset, and noise settings.The base values and behavior types are explicitly set in the command.
  • Anomaly generation: Anomalies are added according to selected anomaly types, including seasonal anomalies and collective seasonal outliers.The command specifies anomaly-related frequency, level, ratio, and factor parameters.
  • Visualization: Figure 6 compares anomaly scores from recent SOTA methods on TODS datasets.The figure is used for an intuitive comparison of detection accuracy.

C FULL EXPERIMENTAL RESULTS

The full experimental results report multiple accuracy families across real-world and synthetic datasets, while synthetic tests target anomalies with different frequency characteristics.

  • Full results: The reported evaluation covers accuracy, ROC, PR, pointwise, range-based, and affiliated metrics across the full MTSAD results.Tables 5–10 organize these metric families across datasets.
  • Full results: Table 10 reports average affiliated precision, recall, and F1 across all datasets, with best and second-best results marked.The table caption does not provide the underlying cell values.
  • Synthetic evaluation: Table 11 reports average AUC-ROC and affiliated F1 for the four synthetic anomaly types.Best and second-best results are identified in the table caption, but their values are not supplied here.
  • Synthetic evaluation: Synthetic evaluation uses four datasets representing low-, medium-, and high-frequency anomalies, plus anomalies without clear frequency-band separation.The experiments are designed to test fine-grained frequency-characteristic capture.
Loading 2410.12261v5…