Further explanations for your three comments
We thank the reviewer for the active feedback and give us the opportunity to further explain to your concerns.
**New Q1**: I do not agree with authors that "the majority of real-world applications … are binary classification tasks". In fact, real-world medical applications must be able to handle multi-class classification.
**New A1**:
1. We highly agree with the reviewer that real-world applications should be able to handle multi-class classification. Although the current dominant trend of AI research for medical time series centers around simple binary tasks [1-4], yet complexity of medical data and the diversity of clinical applications call for more comprehensive approaches.
2. In response to your concern, we have demonstrated the efficacy of our model in addressing multi-classification challenges. We have conducted an additional experiment over a large-scale ECG dataset (PTB-XL, 17596 patients, 191400 samples) with 5 classes (See A4 and R-table 2).
3. We acknowledge it's helpful to have more studies and analyses in terms of multi-class tasks. Will discuss it in our limitations of this paper, and list it as an important future work.
[1] Liang, H., et al., 2019. Evaluation and accurate diagnoses of pediatric diseases using artificial intelligence. Nature medicine,.
[2] Hicks, S.A., et al., 2022. On evaluation metrics for medical applications of artificial intelligence. Scientific reports.
[3] Buch, V.H., et al., 2018. Artificial intelligence in medicine: current trends and future possibilities. British Journal of General Practice.
[4] Soenksen, L.R., et al. 2022. Integrated multimodal artificial intelligence framework for healthcare applications. NPJ digital medicine.
**New Q2**: Refine their notations. In particular, it is quite confusing to use the same notation x to indicate both observation, sample, and trial.
**New A2**:
We appreciate your attention to the notations used in our work.
First, we clarify we didn’t use the same notation to indicate all of observation, sample, and trial. In this paper, our $x$ consistently represents a sample, while $r$ and $p$ stand for trial and patient, respectively.
- Within the sample level, $x_i$ denotes a sample with index $i$, and in the observation level, $x_{i, t}$ signifies an observation within sample $x_i$ at timestamp $t$. The subscripts $_i$ and $_t$ denote the $i$-th sample and the $t$-th observation.
- However, at the patient and trial levels, the subscript $i$ is unnecessary as the sample index doesn't matter here because we mainly care about how the positive/negative sample pairs are formulated. Here, the focus shifts to whether the sample $x$ originates from the same patient or trial. So, to simplify the notations, we omitted the subscript $_i$ in patient and trial levels, Instead, we use superscript $^+$ and $^-$ to denote the positive and negative samples, respectively, to emphasize the sample pair construction is more important than sample index.
Second, we struggled in designing our paper's notation for a long time. We explored various plans, such as using different subscripts and superscripts to represent different levels (e.g., let $x_{s,o}^{p,t}$ denote the $o$-th observation from the $s$-th sample of the $t$-th trial of the $p$-th patient). However, we found such notations are overly complex and difficult to comprehend. Consequently, we opted for a simpler notation scheme (i.e., the one we presented in the paper) to make the whole model easier to follow.
Your attention to our notation design is greatly valued, and we truly welcome any suggestions and advice to help us further polish the notations. We remain committed to refining our notations to ensure they are accessible and intuitive.
**New Q3**: ....Why the former use InfoNCE loss while the later use NT-Xent loss? ...
**New A3**: This is the Q8 of your original comments, which we have answered in rebuttal. Due to the space limitation in response, we have presented the answers to your Q7-Q10 in the global response (prior to the references). For your convenience, we paste our answer here:
- We observed that TS2Vec performs effectively for observation and sample levels. Concurrently, CLOCS introduced contrastive learning on ECG data, utilizing patient-level information, which bears similarity to our implementation at the trial level. Thus, we adopted their loss functions as a foundation for designing our own loss functions across distinct granularities.
- Moreover, we clearly understand InfoNCE and NT-Xent are all derived from NCE loss family. We conducted preliminary experiments to compare using InfoNCE at four granularities, using NT-Xent in all granularities, and exchangeable use InfoNCE or NT-Xent at different granularities. The experimental results show InfoNCE and NT-Xent will lead to very similar outcomes while the NT-Xent can converge a bit faster. We will discuss this in our limitations and future work.