phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | network feature learning (node embeddings)— “We formulate feature learning in networks as a maximum likelihood optimization problem.” | |
| claim-type | method— “Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks.” | |
| method — evidence | — “Datasets and a reference implementation of node2vec are available on the project page: http://snap.stanford.edu/node2vec.” | |
| transfer | from linguistics (natural language processing): the Skip-gram word-embedding architecture (word2vec), applied to graph nodes— “We proceed by extending the Skip-gram architecture to networks” | transfers[0] |
| mechanism | biased (2nd-order) random-walk sampling of node neighborhoods— “We use a 2nd order random walk approach to generate (sample) network neighborhoods for nodes” | mechanisms[0] |
| builds-on | the Skip-gram (word2vec) model from NLP— “Inspired by the Skip-gram model” | claim_relations[0] |
| builds-on | the Skip-gram model of Mikolov et al. [21] (and its network use in [24])— “We proceed by extending the Skip-gram architecture to networks [21, 24].” | claim_relations[1] |
| extends | DeepWalk [24]— “The sampling strategy in DeepWalk can be seen as a special case of node2vec with p = 1 and q = 1.” | claim_relations[2] |
| extends | DeepWalk [24] and LINE [28] (rigid sampling strategies)— “Our algorithm node2vec overcomes this limitation by designing a flexible objective that is not tied to a particular sampling strategy and provides parameters to tune the explored search space (see Section 3).” | claim_relations[3] |
| sense | node similarity - AS HOMOPHILY: two nodes count as alike when they sit in the same tightly knit community, which is one of the two organising principles the paper says networks mix— “nodes in networks could be organized based on communities they belong to (i.e., homophily); in other cases, the organization could be based on the structural roles of nodes in the network (i.e., structural equivalence)” | senses[0] |
| sense | node similarity - AS STRUCTURAL EQUIVALENCE: two nodes count as alike when they play the same role, EVEN IN DIFFERENT COMMUNITIES - the paper's own figure has u alike to s1 under the first sense and alike to s6 under this one, so the two senses pick out different pairs— “For instance, in Figure 1, we observe nodes u and s1 belonging to the same tightly knit community of nodes, while the nodes u and s6 in the two distinct communities share the same structural role of a hub node” | senses[1] |
| sense | network neighborhood - AS A SAMPLED SET, NOT A RADIUS: not restricted to immediate neighbours, and its shape changes with the sampling strategy, so the neighbourhood is a design choice rather than a property of the graph— “The neighborhoods NS(u) are not restricted to just immediate neighbors but can have vastly different structures depending on the sampling strategy” | senses[2] |
| control | node2vec measured against state-of-the-art feature-learning algorithms on the same multi-label classification and link-prediction tasks — held — rules out an improvement that is really a difference in task, data or metric - the named prior methods are run on the same problems— “We contrast the performance of node2vec with state-of-the-art feature learning algorithms [24, 28].” | controls[0] |
| edge | homophily —contrasted-with→ structural equivalence— “nodes in networks could be organized based on communities they belong to (i.e., homophily); in other cases, the organization could be based on the structural roles of nodes in the network (i.e., structural equivalence)” | concept_edges[0] |
| edge | network neighborhood —operationalised-as→ random walk— “We use a 2nd order random walk approach to generate (sample) network neighborhoods for nodes” | concept_edges[1] |
| outcome (stated by the tagger, no quotation) | control — held | controls[0] |
| for which use | limitation — every sampled walk and the estimates built on it: SAMPLE REUSE CAN INTRODUCE SOME BIAS IN THE OVERALL PROCEDURE— “Note that sample reuse can introduce some bias in the overall procedure.” | limitations[0] |
| for which use | limitation — the claim that the search strategy contributes: IN THE WORST CASE, THE SEARCH PHASE HAS LITTLE BEARING ON LEARNED REPRESENTATIONS IN WHICH CASE NODE2VEC IS EQUIVALENT TO DEEPWALK— “In the worst case, the search phase has little bearing on learned representations in which case node2vec is equivalent to DeepWalk.” | limitations[1] |
| for which use | limitation — the recommendation of the Hadamard operator: WE WOULD LIKE TO EXPLORE THE REASONS BEHIND THE SUCCESS OF HADAMARD OPERATOR OVER OTHERS - it performs best and the paper cannot say why— “As a future work, we would like to explore the reasons behind the success of Hadamard operator over others, as well as establish interpretable equivalence notions for edges based on the search parameters.” | limitations[2] |
| for which use | limitation — the learned embeddings as a model of a network neighbourhood: the likelihood is factorised by assuming each neighbourhood node is observed independently of every other one given the source, and the paper adopts this to make the optimisation tractable— “In order to make the optimization problem tractable, we make two standard assumptions: • Conditional independence. We factorize the likelihood by assuming that the likelihood of observing a neighborhood node is independent of observing any other neighborhood node given the feature representation of the source” | limitations[3] |
| for which use | limitation — node2vec read as word2vec applied to graphs: the neighbourhood in language is a sliding window over consecutive words, which the paper states does not transfer because networks are not linear, so the neighbourhood is redefined as a sampled set— “Feature learning methods based on the Skip-gram architecture have been originally developed in the context of natural language [21]. Given the linear nature of text, the notion of a neighborhood can be naturally defined using a sliding window over consecutive words. Networks, however, are not linear, and thus a richer notion of a neighborhood… | limitations[4] |
| for which use | limitation — a comparison against spectral clustering or similar baselines: those methods assume a specific relationship between network structure and the task - graph cuts being useful for classification - which the paper calls reasonable in many scenarios but unsatisfactory for generalising across diverse networks— “For instance, spectral clustering makes a strong homophily assumption that graph cuts will be useful for classification [29]. Such assumptions are reasonable in many scenarios, but unsatisfactory in effectively generalizing across diverse networks” | limitations[5] |
| replication | untested | |
| limitation | Reusing walk samples across source nodes trades statistical purity for efficiency and can bias the procedure.— “Note that sample reuse can introduce some bias in the overall procedure.” | limitations[0] |
| limitation | When the search phase does not matter for a given network, node2vec collapses to the DeepWalk baseline and offers no gain.— “In the worst case, the search phase has little bearing on learned representations in which case node2vec is equivalent to DeepWalk.” | limitations[1] |
| limitation | The paper does not explain why the Hadamard edge operator works best, nor give equivalence notions for edges.— “As a future work, we would like to explore the reasons behind the success of Hadamard operator over others, as well as establish interpretable equivalence notions for edges based on the search parameters.” | limitations[2] |
| limitation | The likelihood is factorised by assuming each neighbourhood node is observed independently of the others given the source, and the paper gives tractability as the reason.— “In order to make the optimization problem tractable, we make two standard assumptions: • Conditional independence. We factorize the likelihood by assuming that the likelihood of observing a neighborhood node is independent of observing any other neighborhood node given the feature representation of the source” | limitations[3] |
| limitation | The construct borrowed from language does not carry over, and the paper says why: text is linear and networks are not, so the neighbourhood had to be redefined.— “Feature learning methods based on the Skip-gram architecture have been originally developed in the context of natural language [21]. Given the linear nature of text, the notion of a neighborhood can be naturally defined using a sliding window over consecutive words. Networks, however, are not linear, and thus a richer notion of a neighborhood… | limitations[4] |
| limitation | Prior methods are criticised for assuming a particular relationship between network structure and the prediction task, with spectral clustering named as an example.— “For instance, spectral clustering makes a strong homophily assumption that graph cuts will be useful for classification [29]. Such assumptions are reasonable in many scenarios, but unsatisfactory in effectively generalizing across diverse networks” | limitations[5] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | node2vec maps nodes into a low-dimensional feature space chosen to keep their network neighborhoods as likely as possible, sampled with a biased random walk.— “In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node’s network neighborhood and design a biased random walk procedure” | content_tags.findings[0] |
| finding | node2vec beats prior state-of-the-art techniques on multi-label classification and link prediction across several real-world networks. Quotation withheld — our stored copy of this sentence carries a text-extraction fault (two words run together), so it is not what the paper says. The tag itself stands; the sentence is being re-fetched. | content_tags.findings[1] |
| evidence status note | finding — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.findings[1] |
| definition | Skip-gram model— “the Skip-gram model [21] aims to learn continuous feature representations for words by optimizing a neighborhood preserving” | content_tags.definitions[0] |
| evidence status note | definition — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.definitions[0] |
| definition | Breadth-first Sampling | content_tags.definitions[2] |
| definition | Depth-first Sampling | content_tags.definitions[3] |
| key-terms | node2vec, network, feature, embedding, neighborhood, random walk, nodes, representation, biased |
| concept | random walk | concepts[1] |
| concept | node classification | concepts[4] |
| concept | homophily | concepts[5] |
| concept | structural equivalence | concepts[6] |
| concept | network neighborhood Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[7] |
| p-value p | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[0] |
| evidence status note | p-value — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[0] |
| regression β | as written: logistic regression Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
| sample-size n/N | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[2] |
| statistical-significance | as written: statistically significant Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[3] |
| evidence status note | statistical-significance — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[3] |
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