From Similarity to Superiority: Channel Clustering for Time Series Forecasting

Summary

The paper introduces the Channel Clustering Module (CCM), a novel approach to enhance time series forecasting models. CCM addresses the limitations of traditional Channel-Independent (CI) and Channel-Dependent (CD) strategies by dynamically clustering channels based on their intrinsic similarities. This approach allows the model to balance individual channel treatment with capturing essential cross-channel dependencies, leading to improved forecasting performance. CCM is adaptable to various time series models and demonstrates its effectiveness through extensive experiments on multiple real-world datasets.

Strengths

- The originality of CCM lies in its novel approach to channel clustering for time series forecasting, addressing the limitations of existing strategies. - The quality of the work is evident in the well-designed experiments and the clear presentation of results, showcasing the effectiveness of CCM across different datasets and models. - The paper’s clarity in explaining the concept, methodology, and results enhances its readability and understanding.

Weaknesses

- The paper could benefit from more detailed discussions on the selection of similarity metrics and the impact of hyperparameters on performance. - The computational efficiency of CCM, especially in large-scale applications, is not extensively discussed.

Questions

- Where is the official code? - In terms of thinking, the principal component analysis method is actually similar to the proposed method. Please provide a detailed explanation.

Rating

5

Confidence

4

Soundness

2

Presentation

3

Contribution

2

Limitations

The limitation of the Channel Clustering Module (CCM) outlined in the paper includes its scalability to extremely large datasets and the computational overhead introduced by the clustering and embedding processes. While CCM shows improvements in forecasting, its efficiency in real-time forecasting scenarios with limited computational resources remains to be optimized. Additionally, the clustering and embedding processes in CCM introduce additional computational overhead, which could be a concern in scenarios where computational efficiency is critical.

Summary

Time series forecasting has been a topic of interest, with previous studies exploring different strategies. The Channel-Independent (CI) strategy treats channels individually, improving forecasting performance but lacking generalization and ignoring channel interactions. On the other hand, the Channel-Dependent (CD) strategy combines channels indiscriminately, leading to oversmoothing and reduced accuracy. A channel strategy is needed that balances individual treatment and essential interactions. Based on the correlation between performance and channel mixing, a novel Channel Clustering Module (CCM) was developed. CCM groups channels with intrinsic similarities and utilizes cluster information, combining the advantages of CD and CI. Experimental results show that CCM enhances the performance of CI and CD models, enables zero-shot forecasting, and improves interpretability of complex models by uncovering intrinsic patterns among channels.

Strengths

1. The proposed model-agnostic method CCM achieves optimal performance between single-channel and cross-channel modeling, and it can be integrated into existing time series prediction models to enhance their performance. 2. By learning prototypes from clusters, CCM facilitates zero-shot forecasting on unseen samples, whether in univariate or multivariate scenarios. 3. The author integrated CCM into four mainstream time series prediction models on multiple different datasets. The experimental results demonstrate that in most cases, CCM can bring about significant performance improvements.

Weaknesses

1. The experimental section involves a limited number of baseline methods, for example, SOTA LLM-based time series prediction models [1, 2] were not selected. 2. I noticed that CCM introduces additional model complexity, as it has an independent Feed Forward layer for each cluster. When the value of K is large, this may result in an excessive number of Feed Forward layers, leading to a significant increase in space complexity. On the other hand, the time complexity of CCM is linearly related to K and C. For certain datasets with a higher number of channels (e.g., Traffic), CCM may noticeably increase the time complexity of the base model. Some of the results in Figure 5 of the Appendix hint at this issue. 3. According to Table 14, the improvements brought by CCM to the base model are sometimes overshadowed by the perturbation caused by randomness. This may indicate that CCM has certain limitations. [1] Zhou, Tian, et al. "One fits all: Power general time series analysis by pretrained lm." Advances in neural information processing systems 36 (2023): 43322-43355. [2] Jin, Ming, et al. "Time-llm: Time series forecasting by reprogramming large language models." arXiv preprint arXiv:2310.01728 (2023).

Questions

1. Can the author provide the percentage increase in runtime and memory usage after integrating CCM for each method on the Traffic dataset? 2. Can a certain hyperparameter analysis be conducted for the parameter β (i.e., β ∈ {0, 0.25, 0.5, 0.75, 1.0}) to demonstrate the impact of the Cluster Loss on model performance? 3. Can the author provide a significance test (i.e., p-value test) for the experimental results, especially for cases where the values in Table 4 are close? As in some cases, the improvements are minimal, and the observed performance gains might be due to randomness rather than the effectiveness of CCM.

Rating

8

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

The author elaborates on the limitations of their work. The main limitations are as follows: CCM does not outperform CI/CD in a few cases in the long-term forecasting benchmark; CCM’s scalability to extremely large datasets remains to be tested.

Summary

The paper presents a new Channel Clustering Module (CCM) for time series forecasting, which dynamically groups channels based on intrinsic similarities to balance the strengths of Channel-Independent (CI) and Channel-Dependent (CD) strategies. CCM improves forecasting accuracy by enhancing model generalization and capturing essential cross-channel interactions, achieving significant performance gains in both long-term and short-term forecasting. The module also supports zero-shot forecasting and improves the interpretability of complex time series models. Extensive experiments demonstrate CCM's effectiveness and adaptability across various mainstream time series models.

Strengths

1. The paper introduces a new Channel Clustering Module (CCM) that balances individual channel treatment and cross-channel dependencies, combining the strengths of Channel-Independent (CI) and Channel-Dependent (CD) strategies. 2. CCM enables zero-shot forecasting, leveraging learned prototypes to handle unseen samples effectively.

Weaknesses

1. The introduction of CCM increases the model's complexity, particularly for original CD models, which may result in higher computational overhead. 2. The paper acknowledges that the scalability of CCM to extremely large datasets remains untested, which could be a limitation for practical applications requiring the processing of large-scale data.

Questions

1. How can the similarity metric be further refined to enhance the clustering quality and address performance variations across different domains? 2. What strategies can be employed to test and ensure the scalability of CCM for extremely large datasets? 3. How does CCM perform in real-world applications with diverse and dynamic datasets, and what adjustments are necessary to optimize its performance in such scenarios? 4. What techniques can be implemented to mitigate the increased computational overhead introduced by CCM, especially for models with high channel and cluster counts?

Rating

4

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

1. CCM does not outperform CI/CD strategies in a few cases, possibly due to the underlying channel relationships in certain real-world domains not aligning well with the similarity metric used by CCM. 2. The increased model complexity introduced by CCM may lead to higher computational costs, particularly for models with numerous channels and clusters.

Summary

The paper proposes a new Channel Clustering Module and a corresponding Cluster Loss to group similar channels using a cross-attention mechanism. This creates a hybrid between channel independent and channel dependent approaches. Experiments in the paper compare both with and without the proposed module on a variety of existing state of the art methods and are run on time-series datasets in different domains on both short and long-term time horizons and demonstrate that this approach is generally applicable regardless of the domain. These experiments show an improvement in performance over prior work while also enabling zero-shot forecasting. The clustering produced by this module surfaces relationships between channels which are useful for feature analysis and interpretability.

Strengths

The paper is well written and easy to comprehend and has good mathematical background. The CCM and the cluster loss is well motivated and utilizes the Gumbel-softmax to represent cluster assignment in a differentiable manner. The technique is evaluated on a variety of time series datasets across diverse domains in both a short and long-term setting. This demonstrates that the method is useful across different models and generally reduces error. The computational complexity of the CCM in the inference setting is also included.

Weaknesses

The paper is evaluated on a variety of real-world datasets but evaluation on some synthetic data to highlight scenarios where existing methods produce a higher error but adding the clustering module reduces the error would help solidify the claims of the paper.

Questions

- In section 4.1, why shuffle channels in each batch? Channel independent implies each channel is handled individually while the motivating toy experiment here changes the channel every batch. What happens when not shuffling the channels? - How does the prediction error change when the prediction time horizon is changed between training and inference? Is it possible to modify the time horizon after training? - In section D.3, how do you use random and k-means for cluster assignment? Additional details about these experiments would help clarify quality improvement described in the table. - How do you expect the performance of the CCM to change when the channel count is on the order of millions? - What does a cluster ratio of 1.0 mean?

Rating

7

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors list that the work needs to be tested on large datasets and that there is an additional performance overhead of the proposed CCM module.

Rebuttal Summary by Authors

Dear Reviewers, We sincerely appreciate your thorough and valuable feedback on our manuscript. We have provided detailed clarifications and additional experimental results to address all concerns raised. ## I. Contributions We are pleased that many reviewers have offered positive comments, and we would like to highlight our key contributions: - **Generalization and Comprehensive Evaluation:** CCM is a model-agnostic channel strategy that is adaptable to most mainstream time series models. Experiments are thoroughly conducted across multiple different models, datasets, forecasting scenarios. [Reviewers 9puR, rxdY, SRyH] - **Superior Performance Improvement:** Our extensive experiments demonstrate CCM's effectiveness in significantly enhancing base model performance for time series forecasting across multiple benchmarks. [Reviewers 9puR, rxdY] - **Zero-shot Capability:** CCM supports zero-shot forecasting by leveraging learned prototypes, which is crucial for handling challenging scenarios with scarce or limited training data. [Reviewers yXcm, rxdY] - **Clear Motivation and Novelty:** CCM addresses limitations of existing strategies (CD and CI) on suboptimal performance or insufficient channel interactions, through a novel approach to channel clustering for time series forecasting. We appreciate the reviewers' acknowledgment of our manuscript's clarity and readability. [Reviewers 9puR, SRyH] ## II. Common Question We also recognize that there are some common questions from reviewers. We conclude the important clarifications as below. > “CCM’s scalability to extremely large datasets remains to be tested” as mentioned in the Limitation section. - We included **theoretical analysis (Sec 4.3)** and **empirical test (Appendix C.6)** for CCM’s complexity and efficiency. The complexity is linear w.r.t. number of channels. The modest computational overhead on CD models is reasonable and acceptable, as justified by the significant performance improvements achieved. It is worth noting that CCM consistently reduces the model complexity of CI models. - Our current research prioritizes time series benchmarks used in prior works [1,2,3,4]. Our experiments include a traffic dataset comprising 15,122,928 observations and a stock dataset comprising 13,900,000 observations. These datasets represent large-scale real-world datasets widely used in previous research within this domain. - Scalability should not be an issue of CCM in real-world deployment due to several empirical evidence: * Consistent reduction in model complexity for CI models * Linear scaling with respect to the number of channels, enabling efficient handling of high-dimensional data * Maintained performance gains across different dataset sizes ## III. Main modifications in our revised version According to reviewers’ suggestions, we have made the following improvements in our revised version: - We added implementation details of the k-means algorithm in ablation studies in Appendix D.3. - We provided significance tests with p-value for cases where values are close before/after applying CCM. - We conducted ablation studies on the parameter $\beta$ in the loss function to demonstrate CCM’s robustness. We hope these modifications and clarifications address your concerns while highlighting the contributions and significance of our work. We are confident that CCM represents a valuable advancement in time series forecasting and look forward to further constructive discussions. Thank you for your time and consideration. Sincerely,\ Authors [1] TSMixer: An All-MLP Architecture for Time Series Forecasting\ [2] Are Transformers Effective for Time Series Forecasting?\ [3] A Time Series is Worth 64 Words: Long-term Forecasting with Transformers\ [4] TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis