Conditional Network Embeddings
Network Embeddings (NEs) map the nodes of a given network into -dimensional Euclidean space . Ideally, this mapping is such that *similar* nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if *similar* means being *more likely to be connected*) or classification (if *similar* means *being more likely to have the same label*). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.
 This paper studied learning unsupervised node embeddings by considering the structural properties of networks. Experimental results on a few data sets prove the effective of the proposed approaches over existing state-of-the-art approaches for unsupervised node embeddings. Strength: - important problem and interesting idea - the proposed approach seems to be effective according to the experiments Weakness: - some parts of the paper are quite unclear - the complexity of the proposed algorithm seems to be very high - the data sets used in the experiments are very small Details: -In the introduction, "it is in general impossible to find an embedding in R^d such that ...", why do we have to make v and v*(and u, and u*) far from each other? - In Equation (2), How is P_ij defined exactly, are they parameters? I am quite confused about this part - In Equation (6), the posterior distribution should be P(X|G) since X is the latent variable to be inferred, right？ - In Table 2 and 3, how are the degree and block information leveraged into the model?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Conditional Network Embeddings
Network Embeddings (NEs) map the nodes of a given network into -dimensional Euclidean space . Ideally, this mapping is such that *similar* nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if *similar* means being *more likely to be connected*) or classification (if *similar* means *being more likely to have the same label*). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper studied learning unsupervised node embeddings by considering the structural properties of networks. Experimental results on a few data sets prove the effective of the proposed approaches over existing state-of-the-art approaches for unsupervised node embeddings. Strength: - important problem and interesting idea - the proposed approach seems to be effective according to the experiments Weakness: - some parts of the paper are quite unclear - the complexity of the proposed algorithm seems to be very high - the data sets used in the experiments are very small Details: -In the introduction, "it is in general impossible to find an embedding in R^d such that ...", why do we have to make v and v*(and u, and u*) far from each other? - In Equation (2), How is P_ij defined exactly, are they parameters? I am quite confused about this part - In Equation (6), the posterior distribution should be P(X|G) since X is the latent variable to be inferred, right？ - In Table 2 and 3, how are the degree and block information leveraged into the model?
assistant
 This paper studied learning unsupervised node embeddings by considering the structural properties of networks. Experimental results on a few data sets prove the effective of the proposed approaches over existing state-of-the-art approaches for unsupervised node embeddings. Strength: - important problem and interesting idea - the proposed approach seems to be effective according to the experiments Weakness: - some parts of the paper are quite unclear - the complexity of the proposed algorithm seems to be very high - the data sets used in the experiments are very small Details: -In the introduction, "it is in general impossible to find an embedding in R^d such that ...", why do we have to make v and v*(and u, and u*) far from each other? - In Equation (2), How is P_ij defined exactly, are they parameters? I am quite confused about this part - In Equation (6), the posterior distribution should be P(X|G) since X is the latent variable to be inferred, right？ - In Table 2 and 3, how are the degree and block information leveraged into the model?