Trusted and Interactive Clustering for Time-Series Data

The fact that paper [1] also employs a contrastive learning technique combining the time- and frequency- domain lead to your misunderstanding that we should place more emphasis on citing [1]. This also have influenced reviewer wHWj's comments. We would like to address this matter in our urgent response.

A1.1: About contribution

Our paper makes two key different contributions:

1. Quantifying the uncertainty of clustering results from both the time and frequency domains (Contribution 2).
2. Proposing an interactive clustering framework (Contribution 3).

These contributions are entirely unrelated to [1]. Reviewer nLrp recognized these as ''...novel directions...''.

A1.2: We treat [1] as a baseline

We included the method from [1], TFC, as a baseline for comparison (see Table 4 and Table 8). Our method significantly outperformed TFC across benchmark datasets on two common tasks—classification and anomaly detection.

A1.3: Significant technical differences

Our similarity with [1] lies in the use of contrastive learning from both the time and frequency domains. However, the essence of our work is fundamentally different. To clarify, we will explain this distinction through the construction of positive and negative pairs.

Let $z_i^{time}$, $z_i^{freq}$, $\tilde{z}_i^{time}$, and $\tilde{z}_i^{freq}$ denote the embeddings (from time and frequency domains) of a sample $x_i^{time}$ and its augmentation $\tilde{x}_i^{time}$.

• Positive pairs in [1]: $(z_i^{time}, \tilde{z}_i^{time})$, $(z_i^{freq}, \tilde{z}_i^{freq})$, $\boldsymbol{(z_i^{time}, z_i^{freq})}$, $\boldsymbol{(\tilde{z}_i^{time}, \tilde{z}_i^{freq})}$
• Negative pairs in [1]: $(z_i^{time}, z_j^{time})$, $(\tilde{z}_i^{time}, \tilde{z}_j^{time})$, $(z_i^{freq}, z_j^{freq})$, $(\tilde{z}_i^{freq}, \tilde{z}_j^{freq})$
• Positive pairs in our paper: $(z_i^{time}, \tilde{z}_i^{time})$, $(z_i^{freq}, \tilde{z}_i^{freq})$
• Negative pairs in our paper: $(z_i^{time}, z_j^{time})$, $(\tilde{z}_i^{time}, \tilde{z}_j^{time})$, $(z_i^{freq}, z_j^{freq})$, $(\tilde{z}_i^{freq}, \tilde{z}_j^{freq})$, $\boldsymbol{(z_i^{freq}, \tilde{z}_j^{freq})}$, $\boldsymbol{(z_i^{time}, \tilde{z}_j^{time})}$

The bold part highlight where our approach diverges from [1], where [1] includes two additional positive pairs, and our paper includes two additional negative pairs.

• In [1], additional positive pairs are constructed to enforce the model to learn better embeddings based on the idea of ''time-frequency consistency''. In this way, they fuse the information from time and frequency domains.
• We fuse the results of FC layers from time and frequency domains, and achieve better embeddings by ''enabling interactive learning between the fused clustering results and the pseudo-labels generated by k-means''. This is fundamentally different from the core idea of [1].
• We construct more negative pairs to enhance the separation between clusters, thereby achieving more distinguishable clustering results.

A1.4: Different focus

The focus of our work is entirely different from [1]. While [1] studies pre-training for time-series models, we address time-series clustering.

A1.5: Combining time- and frequency-domain contrastive learning is a very basic technique used in earlier papers.

It could be illogical to claim that our work originates from [1].

• The use of data augmentation techniques in both time and frequency domains has been well-established, e.g., [2-3].
• Combining time and frequency domains in representation learning existed prior to [1], as demonstrated by works in [4-6]. Does this mean that [1]'s method is not original?

In [1], the authors claimed to be the first to apply frequency-domain data augmentation techniques in contrastive learning for solving the pre-training problem of time-series models. Similarly, we clearly stated in Contribution 1 that we are the first to apply frequency-domain data augmentation techniques to time-series clustering.

Reference

[1] Zhang X, Zhao Z, Tsiligkaridis T, et al. Self-supervised contrastive pre-training for time series via time-frequency consistency. Neurips, 2022.

[2] Cui X, Goel V, Kingsbury B, et al. Data augmentation for deep convolutional neural network acoustic modeling. ICASSP, 2015.

[3] Wen Q, Sun L, Yang F, et al. Time series data augmentation for deep learning: A survey. * arXiv:2002.12478*, 2020.

[4] Liu D, Wang T, Liu S, et al. Contrastive self-supervised representation learning for sensing signals from the time-frequency perspective. ICCCN, 2021.

[5] Woo G, Liu C, Sahoo D, et al. CoST: Contrastive learning of disentangled seasonal-trend representations for time series forecasting. ICLR, 2022.

[6] Yang L, Hong S, et al. Unsupervised time-series representation learning with iterative bilinear temporal-spectral fusion. ICML, 2022.

A3.1: K-means is a particularly efficient algorithm.

In our paper, the total complexity of k-means is approximately $O(I \times N \times K \times L)$, where $N$ is the number of samples, $L$ is the length of the time series, $I$ is the number of iterations, and $K$ is the number of clusters.

The complexity of training our model (which includes two transformers and two 3-layer fully connected modules) is $O(N \times L \times (L \times 128 \times K)^2)$, where $K$ is the number of clusters and the term $(L \times 128 \times K)$ represents the number of neurons. The complexity of k-means is much smaller than that of the training models.

A3.2: We have made specific designs for runtime efficiency.

As mentioned in the Interactive Learning Module section (line 272), we stated: "Run k-means every $t$ epochs." In the experiments section (line 387), $t$ is set to 20.

This design was also appreciated by Reviewer nLrp: "Figure 5 very well demonstrates the need to avoid frequent updates using k-Means..."

A3.3: We provide the proportion of runtime that k-means occupies throughout the entire training process.

It can be observed that the runtime of k-means occupies a very small proportion across all benchmark datasets.

It may be subjective to say our paper is "rather confusing and difficult to follow.

A2.1: About the "Uncertainty Quantification" section.

We kindly request that you carefully review the Uncertainty Quantification section (lines 198–208, lines 216–232) again. In summary, we utilize Subjective Logic [1] to associate the parameters of the Dirichlet distribution, $\alpha_c, c=1,2,\cdots,C$, with the output of the FC layer, $**p**_{\rm{T}}$

$=[p_{1}^{\rm{T}}, p_{2}^{\rm{T}}, \cdots, p_{C}^{\rm{T}}]$

Then, the parameter $\alpha_c$ is calculated as:

The mass function $**m** = [m_1, m_2, \cdots, m_C, m_{\Omega}]$ is determined as follows:

Thanks for your detailed answers.

I admit that I missed some of the results presented in the experimental section and that I might have not understood some parts of the uncertainty quantification section. As such, I will slightly raise my score and lower my confidence.

With that said, I still find that the method is rather (perhaps unnecessary) complex and difficult to follow, especially for a reader like me who is not familiar with Subjective Logic, Dempster's rule, etc...

Most importantly, the contrastive learning part based on temporal and frequency components is not your contribution, while the paper clearly suggests otherwise. I find this is not honest and, as such, I am not comfortable with accepting this work at this time. The paper should be rewritten to make clear what are the novelties and the contributions w.r.t. the existing body of work. For example, you should have included the discussion you provided in your first answer, which shows that the novelty is much more incremental compared to proposing from scratch the time/frequency contrastive learning.

We noticed that due to the similarity between our paper and [1], your rating dropped from 8 to 3, so we are urgently responding to you regarding this issue first.

1. About contribution

Our paper makes two key different contributions:

1. Quantifying the uncertainty of clustering results from both the time and frequency domains (Contribution 2).
2. Proposing an interactive clustering framework (Contribution 3).

These contributions are entirely unrelated to [1]. Reviewer nLrp (rating: 6) recognized these as ''...novel directions...''.

2. We treat [1] as a baseline

We included the method from [1], TFC, as a baseline for comparison (see Table 4 and Table 8). Our method significantly outperformed TFC across benchmark datasets on two common tasks—classification and anomaly detection.

3. Significant technical differences

Our similarity with [1] lies in the use of contrastive learning from both the time and frequency domains, which may lead you and Reviewer UJk1 to believe that we should heavily reference [1]. However, the essence of our work is fundamentally different. To clarify, we will explain this distinction through the construction of positive and negative pairs.

Let $z_i^{time}$, $z_i^{freq}$, $\tilde{z}_i^{time}$, and $\tilde{z}_i^{freq}$ denote the embeddings (from time and frequency domains) of a sample $x_i^{time}$ and its augmentation $\tilde{x}_i^{time}$.

• Positive pairs in [1]: $(z_i^{time}, \tilde{z}_i^{time})$, $(z_i^{freq}, \tilde{z}_i^{freq})$, $\boldsymbol{(z_i^{time}, z_i^{freq})}$, $\boldsymbol{(\tilde{z}_i^{time}, \tilde{z}_i^{freq})}$
• Negative pairs in [1]: $(z_i^{time}, z_j^{time})$, $(\tilde{z}_i^{time}, \tilde{z}_j^{time})$, $(z_i^{freq}, z_j^{freq})$, $(\tilde{z}_i^{freq}, \tilde{z}_j^{freq})$
• Positive pairs in our paper: $(z_i^{time}, \tilde{z}_i^{time})$, $(z_i^{freq}, \tilde{z}_i^{freq})$
• Negative pairs in our paper: $(z_i^{time}, z_j^{time})$, $(\tilde{z}_i^{time}, \tilde{z}_j^{time})$, $(z_i^{freq}, z_j^{freq})$, $(\tilde{z}_i^{freq}, \tilde{z}_j^{freq})$, $\boldsymbol{(z_i^{freq}, \tilde{z}_j^{freq})}$, $\boldsymbol{(z_i^{time}, \tilde{z}_j^{time})}$

The bold part highlight where our approach diverges from [1], where [1] includes two additional positive pairs, and our paper includes two additional negative pairs.

• In [1], additional positive pairs are constructed to enforce the model to learn better embeddings based on the idea of ''time-frequency consistency''. In this way, they fuse the information from time and frequency domains.
• We fuse the results of FC layers from time and frequency domains, and achieve better embeddings by ''enabling interactive learning between the fused clustering results and the pseudo-labels generated by k-means''. This is fundamentally different from the core idea of [1].
• We construct more negative pairs to enhance the separation between clusters, thereby achieving more distinguishable clustering results.

4. Different focus

The focus of our work is entirely different from [1]. While [1] studies pre-training for time-series models, we address time-series clustering.

5. Combining time- and frequency-domain contrastive learning is a very basic technique used in earlier papers.

It could be illogical to claim that our work originates from [1].

• The use of data augmentation techniques in both time and frequency domains has been well-established, e.g., [2-3].
• Combining time and frequency domains in representation learning existed prior to [1], as demonstrated by works in [4-6]. Does this mean that [1]'s method is not original?

In [1], the authors claimed to be the first to apply frequency-domain data augmentation techniques in contrastive learning for solving the pre-training problem of time-series models. Similarly, we clearly stated in Contribution 1 that we are the first to apply frequency-domain data augmentation techniques to time-series clustering.

Reference

[1] Zhang X, Zhao Z, Tsiligkaridis T, et al. Self-supervised contrastive pre-training for time series via time-frequency consistency. Neurips, 2022.

[2] Cui X, Goel V, Kingsbury B, et al. Data augmentation for deep convolutional neural network acoustic modeling. ICASSP, 2015.

[3] Wen Q, Sun L, Yang F, et al. Time series data augmentation for deep learning: A survey. * arXiv:2002.12478*, 2020.

[4] Liu D, Wang T, Liu S, et al. Contrastive self-supervised representation learning for sensing signals from the time-frequency perspective. ICCCN,2021.

[5] Woo G, Liu C, Sahoo D, et al. CoST: Contrastive learning of disentangled seasonal-trend representations for time series forecasting. ICLR, 2022.

[6] Yang L, Hong S, et al. Unsupervised time-series representation learning with iterative bilinear temporal-spectral fusion. ICML, 2022.

We sincerely hope that you could restore your original rating. We will promptly address the other comments and make the necessary revisions.

We are still working on your other comments. And we will respond to you as soon as possible.