node2vec: Scalable Feature Learning for Networks

node2vec: Scalable Feature Learning for Networks Aditya Grover Jure Leskovec

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node2vec: Scalable Feature Learning for Networks 2016 KDD / arXiv 10.1145/2939672.2939754 1607.00653 grover2016-node2vec grover2016-node2vec.txt, the project's staged copy 2fb851e3163865b0fad01a6e9699b3dbc4b70a56 arxiv-open network-science

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them method Quotation withheld because this record is not cleared for redistribution. network feature learning (node embeddings) Quotation withheld because this record is not cleared for redistribution. system-or-tool-building system-or-tool-building Quotation withheld because this record is not cleared for redistribution. mechanisms biased (2nd-order) random-walk sampling of node neighborhoods Quotation withheld because this record is not cleared for redistribution. Reusing walk samples across source nodes trades statistical purity for efficiency and can bias the procedure. what this limits: every sampled walk and the estimates built on it: SAMPLE REUSE CAN INTRODUCE SOME BIAS IN THE OVERALL PROCEDURE Quotation withheld because this record is not cleared for redistribution. When the search phase does not matter for a given network, node2vec collapses to the DeepWalk baseline and offers no gain. what this limits: 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 Quotation withheld because this record is not cleared for redistribution. The paper does not explain why the Hadamard edge operator works best, nor give equivalence notions for edges. what this limits: 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 Quotation withheld because this record is not cleared for redistribution. 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. what this limits: 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 Quotation withheld because this record is not cleared for redistribution. 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. what this limits: 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 Quotation withheld because this record is not cleared for redistribution. Prior methods are criticised for assuming a particular relationship between network structure and the prediction task, with spectral clustering named as an example. what this limits: 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 Quotation withheld because this record is not cleared for redistribution. the Skip-gram word-embedding architecture (word2vec), applied to graph nodes Quotation withheld because this record is not cleared for redistribution. node2vec measured against state-of-the-art feature-learning algorithms on the same multi-label classification and link-prediction tasks eliminates: an improvement that is really a difference in task, data or metric - the named prior methods are run on the same problems · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. random walk random walk Quotation withheld because this record is not cleared for redistribution. node classification node classification Quotation withheld because this record is not cleared for redistribution. homophily homophily Quotation withheld because this record is not cleared for redistribution. structural equivalence structural equivalence Quotation withheld because this record is not cleared for redistribution. network neighborhood network neighborhood Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. 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 Quotation withheld because this record is not cleared for redistribution. builds-on → the Skip-gram (word2vec) model from NLP Quotation withheld because this record is not cleared for redistribution. builds-on → the Skip-gram model of Mikolov et al. [21] (and its network use in [24]) Quotation withheld because this record is not cleared for redistribution. extends → DeepWalk [24] Quotation withheld because this record is not cleared for redistribution. extends → DeepWalk [24] and LINE [28] (rigid sampling strategies) Quotation withheld because this record is not cleared for redistribution. homophily —contrasted-with→ structural equivalence homophily structural equivalence strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. network neighborhood —operationalised-as→ random walk network neighborhood random walk strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. 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. Quotation withheld because this record is not cleared for redistribution. node2vec beats prior state-of-the-art techniques on multi-label classification and link prediction across several real-world networks. about this quote: 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. Quotation withheld because this record is not cleared for redistribution. Skip-gram model Skip-gram model about this quote: 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. Quotation withheld because this record is not cleared for redistribution. Breadth-first Sampling Breadth-first Sampling Quotation withheld because this record is not cleared for redistribution. Depth-first Sampling Depth-first Sampling Quotation withheld because this record is not cleared for redistribution. p-value p-value about this quote: 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. Quotation withheld because this record is not cleared for redistribution. regression regression Quotation withheld because this record is not cleared for redistribution. sample-size sample-size Quotation withheld because this record is not cleared for redistribution. statistical-significance statistical-significance about this quote: 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. Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1145/2939672.2939754.