Parametric dimensionality reduction methods have gained prominence for their ability to generalize to unseen datasets, an advantage that traditional approaches typically lack. Despite their growing popularity, there remains a prevalent misconception among practitioners about the equivalence in performance between parametric and non-parametric methods. Here, we show that these methods are not equivalent -- parametric methods retain global structure but lose significant local details. To explain this, we provide evidence that parameterized approaches lack the ability to repulse negative pairs, and the choice of loss function also has an impact. Addressing these issues, we developed a new parametric method, ParamRepulsor, that incorporates Hard Negative Mining and a loss function that applies a strong repulsive force. This new method achieves state-of-the-art performance on local structure preservation for parametric methods without sacrificing the fidelity of global structural representation. Our code is available at https://github.com/hyhuang00/ParamRepulsor.
Paper
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Peer review
Summary
The paper focuses on comparing parametric and non-parametric neighborhood embedding methods for dimensionality reduction. Non-parametric methods excel at preserving local data structures but struggle with large datasets. Parametric methods, utilizing neural networks, offer better scalability but often compromise local structure preservation. The paper reveals that parametric methods tend to prioritize global structure preservation at the expense of local details, leading to less distinct cluster boundaries. This is attributed to their inability to effectively repulse negative pairs and sensitivity to the choice of loss function. To address these issues, the authors propose a new parametric method called ParamRepulsor with two key improvements: Hard Negative Mining: This technique focuses on identifying and repulsing the most challenging negative pairs, improving the separation between dissimilar points. Modified Loss Function: The authors use a loss function that applies a stronger repulsive force, particularly on hard negative pairs, leading to better local structure preservation. In experiments, ParamRepulsor is shown to outperform other parametric methods on various datasets.
Strengths
Novel Insight: The paper provides a novel perspective on the differences between parametric and non-parametric dimensionality reduction methods, highlighting the issue of local structure preservation in parametric methods. Technical Contribution: The introduction of ParamRepulsor, a new parametric method with hard negative mining and a modified loss function, is a significant technical contribution. The paper demonstrates its superior performance in preserving local structures compared to other parametric methods. Thorough Evaluation: The paper includes a comprehensive evaluation of ParamRepulsor and other dimensionality reduction methods on a diverse range of datasets, providing strong empirical evidence for the effectiveness of the proposed approach. Clear Presentation: The paper is well-written and easy to read.
Weaknesses
Limited Generalizability: The focus of this paper is on parametric DR methods that utilize shallow neural networks. However, the generalizability of the findings to other parametric models, such as deep neural networks, remains unexplored. This is particularly relevant as the paper's results indicate that all parametric methods tend to better preserve local structures, and the performance differences between algorithms diminish as network depth increases. Insufficient Theoretical Analysis: While the paper offers empirical evidence, it lacks a comprehensive theoretical analysis. It remains unclear why the same algorithm that performs well in its non-parametric version underperforms in the parametric version (loses local structure). Although the authors acknowledge that the limited capacity of shallow neural networks is widely accepted as an explanation for their failure, they dismiss it as the primary cause. Absence of Non-Parametric Repulsor: The paper presents both parametric and non-parametric versions for all algorithms except ParamRepulsor. Including a non-parametric version of ParamRepulsor would provide better intuition into how the modified terms (e.g., including MN terms) affect the results. Additionally, the paper does not theoretically analyze why hard negative mining and the specific loss function are effective. Limited Practical Impact/Advantage: While the paper demonstrates the superior performance of ParamRepulsor compared to other parametric methods in the shallow network case, this advantage might not be significant when deeper networks are used. This limitation could potentially reduce the practical impact and contribution of this work. Evaluation Metrics: The evaluation metrics used in the paper, although standard in the field, may not fully capture all aspects of dimensionality reduction quality, especially for complex datasets.
Questions
Network Depth and Embedding Structure: The paper exclusively focuses on shallow neural networks for parametric dimensionality reduction. It would be valuable to understand the rationale behind this choice. Is there a risk of overfitting with deeper networks? The authors mention that "The shallow parametrization used in NE DR methods ensures that distances in the high-dimensional space remain correlated with those in the low-dimensional embedding." Investigating how the embedding structure changes with increasing network depth could provide valuable context for interpreting the results of this work.
Rating
6
Confidence
3
Soundness
3
Presentation
3
Contribution
2
Limitations
While the authors transparently acknowledge certain limitations, such as the need for further theoretical analysis and computational optimization of ParamRepulsor, other significant limitations remain unaddressed. The paper's exclusive focus on shallow networks limits the generalizability of its findings. The authors do not provide a clear rationale for this choice, nor do they explore the impact of network depth on the preservation of local structures. This is particularly important given the observation that deeper networks might naturally mitigate the issues observed with shallow parametric models. Suggestions to enhance the impact and relevance of this work: Expanding the scope: Investigate the behavior of ParamRepulsor and other parametric methods with deeper networks. Developing Non-Parametric Repulsor: Create a non-parametric version of ParamRepulsor for direct comparison and to isolate the effect of the proposed modifications. Deeper Theoretical Analysis: Conduct a more in-depth analysis to understand the underlying reasons for the performance differences between parametric and non-parametric methods and the impact of network depth on local structure preservation.
Summary
Authors study the effect of parameterization in neighbor embedding algorithms. They aim to improve how these methods capture local structure in the data. To do so they propose a new algorithm building upon PaCMAP with slight modification of its loss with new weights in front of each term.
Strengths
* code is provided. * the experimental section is rich with a good variety of datasets and metrics. Conducted experiments seem to make sense. * section 2 is clear and efficient.
Weaknesses
I am disappointed that this work does not really dive into the effects of amortization on neighbor embeddings. I was expecting more discussions on the effect of batch size, initialization, learning rates etc... Many discussions here also seem to apply to the non parametric setting, we often have the impression to move away from the initial focus of this work. The problem at hand is not correctly introduced in section 3 which makes the paper unclear to follow and understand. Here are some issues: * the sampling procedure to obtain mid-near pair is taken from PACMAP is not a new contribution. * it would be helpful to state more clearly the difference between the proposed objective and the one of PACMAP. From what I understand it amounts to switching the sign of the mid-near term from attraction to repulsion. To me it not clear at all how is this change related to parameterization. It would be interesting to see how the new loss function would perform in the non-parametric setting as well. * About observation 2 in section 3, it is stated that NEG based methods perform better in local structure preservation and : *This is in contrast to both NCE and InfoNCE losses, where each negative pair term is based on all pairs.* . However, reading through : https://arxiv.org/pdf/2206.01816 , I have the understanding than even NEG based algorithms sample negatives pairs uniformly in all pairs. Therefore this point is not clear to me. Also I am wondering why it is related to the parametric setting and not non-parametric as well. * In the experimental part it would also be interesting to compare with non parametric methods which are expected to perform better. This way we could measure how does this paper contribute to closing the gap between parametric and non parametric. * one major drawback of this approach is that there are too many hyperparameters to tune with all the weight terms in the loss. Looking at the code we have : `def paramrepulsor_weight_schedule(epoch): if epoch < 200: w_nn = 4.0 w_fp = 8.0 w_mn = 0.0 else: w_nn = 1.0 w_fp = 8.0 w_mn = -12.0 weight = np.array([w_nn, w_fp, w_mn]) return weight`. How were these values determined ? do they need to be tuned for each dataset ? From the practitioner point of view, I have strong doubts about the practical utility of such machinery. More minor comments: * false negatives should be clearly defined before theorem 4.1 . * theorem 4.1 is an asymptotic result thus it doesn't bring true insights about practical guarantees of the methods. * I wouldn't put Corollary 4.2. in the form of a corollary as there is no associated proof.
Questions
* in the observation 1 section 3 : *all the parametric counterparts (App. F.1) have a smaller FP distance ratio, meaning further pairs are positioned closer together* . Woul you have more insights on why this phenomenon happen ? how robust is this observation to batch size, learning rate and architectures used ? * Do observation 3 and 4 also apply in the non-parametric setting ? Could you discuss more the effect of parametrization on these. * in algorithm 1 we can see that the kNN graphs are constructed once at the beginning. Would there be a way to adapt this construction to the online setting *i.e.* to easily update these graphs during iterations? * did the authors consider using entropic affinity graphs as in TSNE instead of binary kNN graphs ? these affinities can be seen as smooth kNN graphs and they are usually faster to compute that kNN on GPUs as they are highly parallelizable.
Rating
2
Confidence
5
Soundness
1
Presentation
3
Contribution
1
Limitations
/
We strongly disagree with the assessment of our paper. Here's our detailed reply: > The proposed method is limited to PACMAP. > The proposed ParamRepulsor and ParamPaCMAP are minor adaptations of the PACMAP algorithm, which is not among the most widely used neighbor embedding methods. In my view, focusing on enhancing the parametric versions of more popular algorithms like tSNE, UMAP, or LargeVis would have a much greater impact. As a result, the scope of this paper feels very limited. With all due respect, we don’t agree with the reviewer over the contribution of our work, as well as the analysis of the scope. In this work, we have clearly demonstrated the existence of local structure preservation gaps in the parametric NE methods, provided theoretical and empirical analysis over the potential causes, and then applied our methods to create a novel parametric NE DR algorithm. As practitioners ourselves, we believe PaCMAP is more reliable, robust to parameter tuning and simpler than the methods you listed - see [A] as well as the experiment section of this work, which you also found to be “rich” and “make sense”. It also has no parameters that need tuning per dataset, unlike the older methods. Additionally, despite being a more recent method published in 2021, PaCMAP has already garnered 319 citations, a number that compares favorably to LargeVis, which has received 503 citations despite being published five years earlier. This suggests that PaCMAP is gaining significant traction within the community. In terms of impact, we think **designing the best method** ought to have the largest impact. The focus of our work is on creating and improving methods that offer meaningful advances, and we believe that this should be the primary criterion for assessing the scope and impact of our research, **instead of what method we use as a basis**. [A] Huang, et al. "Towards a comprehensive evaluation of dimension reduction methods for transcriptomic data visualization." Communications biology 5.1 (2022): 719.
Thank you for your response, though I feel the tone could have been more respectful. To clarify, I’d like to briefly summarize my point. I have personally implemented and experimented with these algorithms and have also taught them to students on numerous occasions. This experience has led me to understand that PACMAP fundamentally involves three components for near, mid-near, and farther points, which is why I find it requires more tuning than other methods. Each component comes with its own sampling and weighting schedule. Moreover I would like to insist on some points that I believe are incorrect and potentially very misleading: - "They can also handle global structure better than the non-parametric methods." There’s no basis for this claim. - "This is particularly beneficial in longitudinal studies, such as those in computational biology or recommendation systems, where the position of new data in an established embedding space is of significant interest." I strongly believe that statistical analysis should not be conducted based on such parametric embeddings. **Neighbor-embedding methods should be approached with caution**, and I am convinced of the importance of considering different perspectives with various initializations, learning rates, and attraction/repulsion trade-offs. For this reason, I encourage students to compute multiple embeddings, whether using t-SNE, PACMAP, or any other method. Thank you for the discussion. I will not further discuss with authors.
> I have personally implemented and experimented with these algorithms and have also taught them to students on numerous occasions. This experience has led me to understand that PACMAP fundamentally involves three components for near, mid-near, and farther points, which is why I find it requires more tuning than other methods. Each component comes with its own sampling and weighting schedule. We respectfully emphasize that this work is entirely distinct from PaCMAP, and we believe that any **previous biases related to an existing work** should not influence the evaluation of this new work. As noted in our previous response, our approach does not involve more tuning, as reflected in our codespace. It’s important to highlight that, as shown in [A], methods like t-SNE and UMAP often require significant hyperparameter tuning. In contrast, all our experiments were conducted using default parameters across all datasets, as reported in our rebuttal. > "They can also handle global structure better than the non-parametric methods." There’s no basis for this claim. We respectfully disagree with the assertion that there is no basis for our claim. We have provided specific experimental results, particularly in Table 1 and Fig. 4 in the rebuttal PDF, as well as Table 4, 5, and Fig. 5-18 in the original submission. These results clearly demonstrate the better preservation of our method and parametric methods in general in handling global structures. We kindly hope you had the opportunity to thoroughly review our rebuttal, and we are open to further clarifying or expanding upon these findings if needed. > "This is particularly beneficial in longitudinal studies, such as those in computational biology or recommendation systems, where the position of new data in an established embedding space is of significant interest." I strongly believe that statistical analysis should not be conducted based on such parametric embeddings. Non-parametric methods should be approached with caution, and I am convinced of the importance of considering different perspectives with various initializations, learning rates, and attraction/repulsion trade-offs. For this reason, I encourage students to compute multiple embeddings, whether using t-SNE, PACMAP, or any other method. We hope the reviewer can provide more substantial arguments and evidence to support the belief that parametric embedding cannot be applied to parametric embeddings other than personal anecdotes. This is not the consensus of the scientific community. As we mentioned in the previous reply, statistical analysis has already been conducted with parameterized embedding and has inspired scientific discoveries, such as [E, F, G, H, I]. [E] Ding et al. "Interpretable dimensionality reduction of single cell transcriptome data with deep generative models." Nature Communications 2018 [F] Lopez et al. "Deep generative modeling for single-cell transcriptomics." Nature methods 2018 [G] Kulichenko et al. "Uncertainty-driven dynamics for active learning of interatomic potentials." Nature Computational Science 3.3 (2023): 230-239. [H] Wahle et al. "Multimodal spatiotemporal phenotyping of human retinal organoid development." Nature Biotechnology 41.12 (2023): 1765-1775. [I] Islam et al. "Revealing hidden patterns in deep neural network feature space continuum via manifold learning." Nature Communications 14.1 (2023): 8506.
Summary
The paper tackles the problem of Dimensionality Reduction (DR). The authors flag a problem with the current existing parametric DR methods. It is shown with empirical evidence that parametric methods cannot capture all the local details. To mitigate this problem, the paper presents ParamRepulsor, a new parametric method that utilizes Hard Negative Mining. Empirical results show that ParamRepulsor performs strongly against the previously proposed baselines.
Strengths
- DR problem is important as it is the main tool to visualize experiments and getting intuitions. - The paper presents detailed experiments to support the conclusions - The problem tackled is clear and well-motivated
Weaknesses
See below
Questions
- What is the computational time of ParamRepulsor compared to the other methods? - What are the limitations of ParamRepulsor?
Rating
6
Confidence
2
Soundness
3
Presentation
3
Contribution
3
Limitations
NA
Summary
The paper addresses the problem of improving parametric neighborhood embedding (NE) methods -- i.e., techniques that optimize a neural network to project a higher dimensional dataset into a lower dimensional space. The main advantage of these being that they don't have to be recomputed for new samples, as it only involves a projection through the pre-trained encoder. However, they are generally inferior to the traditional NE techniques, the paper argues, mainly because of failing to repulse negative pairs effectively. To address this issue, they propose a method that explicitly factors in an unsupervised hard negative mining cost, to achieve good balance of local and global structure preservation.
Strengths
* The paper is well written generally and easy to follow. The motivation for their method is laid out clearly following the limitations of existing parametric and non parametric methods. * The proposed mid-near sampling to identify hard negatives seems simple to implement, and has a tangible impact in reducing the false negatives. * Good empirical performance from the proposed method supports the argument that including a negative repulsion loss improves local and global structure preservation.
Weaknesses
* One high level comment is that some of the experiments feel incomplete in terms of answering the main hypothesis put forward -- why parametric methods under perform their non parametric counterparts. The paper identified an issue that most parametric methods suffer from -- lack of negative pair repulsion -- and addressed it using mid-near sampling. Does this make the proposed ParamRepulsor or P-PACMAP comparable or better than existing non parametric methods? The experiments only compare parametric methods so this question remains unanswered. * The ablation from Figure 4 on the effect of weight on MN sampling clearly shows a preference for local structure preservation as it is increased -- how does this affect global structure? Every NE algorithm has some form of parameter to trade-off between these two properties. For a fair comparison, they should be ablated together to understand the relative sensitivity of the algorithms towards global and local structure preservation. * MN Sampling utilizes uniform random sampling in high dimensions to identify hard negatives, and finds nearest neighbors presumably using an L2 like metric. I see some issues with these assumptions on data that is locally Euclidean but lives on some unknown curved manifold. Uniform sampling in high dimensions is challenging, and an L2 metric becomes inaccurate very quickly -- does the effect of hard negatives disappear as the dimensionality increases? Ablations on these properties will help the reader understand the limitations more clearly.
Questions
Please see above
Rating
6
Confidence
4
Soundness
3
Presentation
3
Contribution
3
Limitations
Limitations of the proposed method are not entirely clarified -- rather limitations of the field in general are discussed. I think this could be expanded as I have suggested in my comments.
Dear Reviewers, As the discussion period is approaching its conclusion in two days, we would like to kindly remind you that we have addressed your comments in our rebuttal. We would greatly appreciate any additional feedback you may have before the deadline. If you have any further questions or concerns, please do not hesitate to reach out, and we will do our utmost to respond promptly. Thank you for your time and consideration. Best regards, The Authors of Submission 13990
Thank you for the rebuttal. I still have several key concerns regarding this work: **The proposed method is limited to PACMAP.** The proposed ParamRepulsor and ParamPaCMAP are minor adaptations of the PACMAP algorithm, which is not among the most widely used neighbor embedding methods. In my view, focusing on enhancing the parametric versions of more popular algorithms like tSNE, UMAP, or LargeVis would have a much greater impact. As a result, the scope of this paper feels very limited. **The motivations for parametric neighbor embedding are unclear.** Neighbor embedding algorithms are incredibly efficient. Embedding a few million points can be done in a matter of seconds on a GPU using recent implementations of TSNE or LargeVis. However, this efficiency is still far from what we see in other domains like SSL, where scalability and efficiency present interesting research directions. This leads me to question the importance of developing parametric methods for neighbor embedding, particularly when practitioners typically recompute the full embeddings when new data is introduced. I'm curious if the authors can provide references where an amortized, differentiable model for neighbor embedding is crucial. To my knowledge, these methods are primarily used for data exploration rather than being integrated into larger pipelines that would benefit from differentiability, as is common in SSL. This point further limits the scope of the paper. **Lack of theoretical support for the method.** In my view, this method adds unnecessary complexity and introduces numerous steps without sufficient justification. The arguments seem to rely more on intuition than on solid theoretical backing. As a practitioner, I already find PACMAP challenging due to its numerous parameters, and this approach seems to further complicate the field unnecessarily. I strongly disagree with the authors' assertion that other methods have similar parameter complexity. From my experience, the methods that gain practical adoption are those that are straightforward to implement and easy for practitioners to grasp, minimizing the use of tricks and adhering to core principles. This is especially true in unsupervised learning, where evaluating model performance is difficult. While simplicity might come at the cost of slight performance trade-offs on the toy datasets often used in ML research, principled methods tend to perform better on real-world datasets encountered by practitioners. TSNE is a prime example, consistently delivering state-of-the-art results across a wide range of datasets. Similarly, LargeVis, which extends TSNE with negative sampling, is another method that is accessible to ML practitioners. The paper in question takes the opposite approach, which is why I believe it does not contribute value to the field of dimensionality reduction. For these reasons, I am convinced that this work does not meet the bar for NeurIPS, and I am modifying my score accordingly.
> The motivations for parametric neighbor embedding are unclear. > Neighbor embedding algorithms are incredibly efficient. Embedding a few million points can be done in a matter of seconds on a GPU using recent implementations of TSNE or LargeVis. However, this efficiency is still far from what we see in other domains like SSL, where scalability and efficiency present interesting research directions. This leads me to question the importance of developing parametric methods for neighbor embedding, particularly when practitioners typically recompute the full embeddings when new data is introduced. > I'm curious if the authors can provide references where an amortized, differentiable model for neighbor embedding is crucial. To my knowledge, these methods are primarily used for data exploration rather than being integrated into larger pipelines that would benefit from differentiability, as is common in SSL. > This point further limits the scope of the paper. While we agree that nonparametric methods are indeed efficient, we believe that **efficiency is not the only criterion** to consider. Both nonparametric and parametric methods serve important roles in data exploration and analysis. In terms of uses, both nonparametric methods and parametric methods can be used for data exploration as well as analysis. However, parametric methods offer unique advantages, particularly when a map $x\rightarrow y$ between input and output spaces is needed. This capability is crucial for **comparing multiple datasets or adding new data to an existing embedding**, as demonstrated in our experiments. They can also handle global structure better than the non-parametric methods. This is particularly beneficial in **longitudinal studies**, such as those in computational biology or recommendation systems, where the position of new data in an established embedding space is of significant interest. Nonparametric methods, while efficient, lack this capability. Furthermore, while speed is undoubtedly important, the quality of the embedding is paramount. Our work aims to achieve high-quality embeddings that serve the specific needs of the user, even if that means prioritizing aspects other than raw efficiency. We also wish to highlight that in the code we provided, **we also support non-parametric implementations** that are compatible with both CPU and GPU, and can also achieve comparable scalability as other non-parametric GPU implementations.
> Lack of theoretical support for the method. > In my view, this method adds unnecessary complexity and introduces numerous steps without sufficient justification. The arguments seem to rely more on intuition than on solid theoretical backing. We’re not sure what you mean by “theoretical backing”. It’s hard to respond to criticism of this abstract. We provided theoretical backgrounds with the theoretical principles for loss functions in our rebuttal. It's important to note that many widely-used methods in this field, such as t-SNE, are based on **assumptions** rather than strictly theoretical foundations. For instance, there is **no definitive theory** that mandates the use of heavy-tailed Student-t distributions to represent probabilities in low-dimensional space, yet this assumption has proven effective in practice. > As a practitioner, I already find PACMAP challenging due to its numerous parameters, and this approach seems to further complicate the field unnecessarily. I strongly disagree with the authors' assertion that other methods have similar parameter complexity. With all due respect, we must strongly disagree with the assertion that PaCMAP presents excessive parameter complexity. PaCMAP is specifically designed to minimize the need for user intervention in parameter tuning. Its **default parameters** work fine for a wide range of datasets, providing a robust and reliable embedding without requiring the extensive tuning that is often necessary with methods like t-SNE and UMAP. These methods, while powerful, can indeed struggle [B] with preserving global structure unless carefully tuned—an issue PaCMAP addresses effectively. This statement also raises the question of **whether the reviewer has really looked into the implementation of any DR method** as well. Every ML algorithm has lots of parameters, including the DR methods. Even simple algorithms such as k-nearest neighbor methods have parameters - what is the form of the distance metric, how many neighbors, etc. The most popular t-SNE implementation, [openTSNE](https://github.com/pavlin-policar/openTSNE), provides **20** different tunable parameters. [UMAP](https://github.com/lmcinnes/umap) has **27** different tunable hyperparameters. These numbers do not account for the various schedules and automatic hyperparameter selection mechanisms embedded within these implementations. When considering the parametric versions of these methods, the number of hyperparameters increases significantly. [B] Kobak et al., "The art of using t-SNE for single-cell transcriptomics." Nature Communications 10.1 (2019): 5416.
> From my experience, the methods that gain practical adoption are those that are straightforward to implement and easy for practitioners to grasp, minimizing the use of tricks and adhering to core principles. This is especially true in unsupervised learning, where evaluating model performance is difficult. While simplicity might come at the cost of slight performance trade-offs on the toy datasets often used in ML research, principled methods tend to perform better on real-world datasets encountered by practitioners. We agree. PaCMAP’s loss function is much simpler than t-SNE’s or UMAPs. It performs better in our experiments, which you agree to be of “rich variety of datasets and metrics” and “make sense” in your review. > TSNE is a prime example, consistently delivering state-of-the-art results across a wide range of datasets. Similarly, LargeVis, which extends TSNE with negative sampling, is another method that is accessible to ML practitioners. > The paper in question takes the opposite approach, which is why I believe it does not contribute value to the field of dimensionality reduction. There is clearly not much we can say to convince you. While we respect the contributions of t-SNE and LargeVis, we believe it is important to highlight that **newer methods**, such as PaCMAP, **offer significant advantages** in terms of maintaining global structure and simplifying the tuning process. It is not accurate to assert that older methods inherently provide superior results. In fact, PaCMAP's simpler loss function and ability to preserve global structure without extensive tuning have been key factors in its growing adoption. **We also reject the idea that LargeVis as a method is accessible to ML practitioners.** Its official implementation 1. has not been maintained for more than eight years from now, 2. needs to be compiled from scratch, 3. requires platform-specific handling, and 4. does not provide a user-friendly interface that’s compatible to popular ML frameworks, such as scikit-learn. On the other hand, our method instead is fully compatible with existing ML frameworks such as scikit-learn and pytorch. We also believe that parametric methods play an essential role in the field of dimensionality reduction. [C, D] have all garnered hundreds of citations and have inspired various scientific discoveries. We deeply regret your bias towards the parametric DR embeddings. [C] Van Der Maaten L. Learning a parametric embedding by preserving local structure, AISTATS 2009: 384-391. [D] Sainburg, Tim, Leland McInnes, and Timothy Q. Gentner. "Parametric UMAP embeddings for representation and semisupervised learning." Neural Computation 33.11 (2021): 2881-2907.
Thanks for the responses. I will raise my score to 6. Only one comment regarding the confusion about parametric/non-parametric method formulation -- it maybe helpful to formulate the paper slightly differently instead of the current argument on introducing non-parametric --> parametric and then introducing the proposed method while this is the technical argument, i think the introduction can be built to emphasize on parametric methods only to avoid confusion.
Thank you sincerely for taking the time to reassess our paper and for raising the score. We really appreciate your feedback and will revise our paper accordingly! Your input is invaluable to us.
Thank you for your response
I thank the authors for the clarification and the extra figures in their response. I'm raising the score to 6.
Decision
Accept (poster)