node2vec：网络中的规模化特征学习

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"本文主要介绍了node2vec，这是一种在图网络中进行大规模特征学习的方法，旨在自动学习节点的特征表示，以捕捉网络中的多样连接模式。通过优化在低维特征空间中保持节点邻域的概率来生成节点的连续特征表示。作者提出了一种灵活的节点邻域定义，并设计了一种偏差随机游走策略，可以有效地探索不同的邻域。" 在机器学习和数据挖掘领域，网络分析已经成为一种强大的工具，特别是在社交网络、生物网络、信息网络等复杂系统的研究中。然而，传统的预测任务通常需要手动工程化特征，这既耗时又限制了模型的泛化能力。为了解决这个问题，研究人员开始探索表示学习（representation learning）的方法，自动从原始数据中学习有意义的特征。 "node2vec"是Aditya Grover和Jure Leskovec在2016年提出的一种创新框架，它结合了word2vec的思想，将其应用于网络节点的表示学习。word2vec是一种用于自然语言处理的著名方法，它能够学习单词在文本中的上下文关系，从而生成词向量。在node2vec中，节点被映射到一个低维度的特征空间，这样做的目标是最大化保留网络中节点邻域的可能性。在node2vec的核心，是一种可调整的邻域定义，它引入了两个关键参数：p和q。这两个参数控制了随机游走的返回概率（return probability, p）和转移概率（in-out probability, q），使得算法能够在不同的邻域结构之间进行权衡。返回概率p决定了游走回到起点的频率，而转移概率q则影响了游走在邻居节点之间的偏好。通过调整这两个参数，node2vec能够灵活地捕获一阶邻域（直接相连的节点）和二阶邻域（间接相连的节点）的信息，以适应各种网络的拓扑结构。在实际应用中，node2vec的偏差随机游走策略可以高效地生成节点的采样序列，这些序列随后用于训练 Skip-gram 模型，这是word2vec中用于生成词向量的模型。通过最大化节点邻域的条件概率，node2vec学习到的特征向量能够保留网络的结构信息，从而在节点分类、链接预测等任务上展现出良好的性能。总结起来，node2vec是一个具有广泛影响力的网络表示学习方法，它通过灵活的邻域定义和优化的随机游走策略，实现了对网络中节点的高效、丰富的特征表示，为网络分析提供了强大的工具。这种方法不仅提高了预测任务的准确性，而且减少了特征工程的工作量，推动了网络科学和机器学习领域的交叉发展。

node2vec: Scalable Feature Learning for Networks

Aditya Grover

Stanford University

adityag@cs.stanford.edu

Jure Leskovec

Stanford University

jure@cs.stanford.edu

ABSTRACT

Prediction tasks over nodes and edges in networks require careful

effort in engineering features used by learning algorithms. Recent

research in the broader ﬁeld of representation learning has led to

signiﬁcant progress in automating prediction by learning the fea-

tures themselves. However, present feature learning approaches

are not expressive enough to capture the diversity of connectivity

patterns observed in networks.

Here we propose node2vec, an algorithmic framework for learn-

ing continuous feature representations for nodes in networks. 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,

which efﬁciently explores diverse neighborhoods. Our algorithm

generalizes prior work which is based on rigid notions of network

neighborhoods, and we argue that the added ﬂexibility in exploring

neighborhoods is the key to learning richer representations.

We demonstrate the efﬁcacy of node2vec over existing state-of-

the-art techniques on multi-label classiﬁcation and link prediction

in several real-world networks from diverse domains. Taken to-

gether, our work represents a new way for efﬁciently learning state-

of-the-art task-independent representations in complex networks.

Categories and Subject Descriptors: H.2.8 [Database Manage-

ment]: Database applications—Data mining; I.2.6 [Artiﬁcial In-

telligence]: Learning

General Terms: Algorithms; Experimentation.

Keywords: Information networks, Feature learning, Node embed-

dings, Graph representations.

1. INTRODUCTION

Many important tasks in network analysis involve predictions

over nodes and edges. In a typical node classiﬁcation task, we

are interested in predicting the most probable labels of nodes in

a network [33]. For example, in a social network, we might be

interested in predicting interests of users, or in a protein-protein in-

teraction network we might be interested in predicting functional

labels of proteins [25, 37]. Similarly, in link prediction, we wish to

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DOI: http://dx.doi.org/10.1145/2939672.2939754

predict whether a pair of nodes in a network should have an edge

connecting them [18]. Link prediction is useful in a wide variety

of domains; for instance, in genomics, it helps us discover novel

interactions between genes, and in social networks, it can identify

real-world friends [2, 34].

Any supervised machine learning algorithm requires a set of in-

formative, discriminating, and independent features. In prediction

problems on networks this means that one has to construct a feature

vector representation for the nodes and edges. A typical solution in-

volves hand-engineering domain-speciﬁc features based on expert

knowledge. Even if one discounts the tedious effort required for

feature engineering, such features are usually designed for speciﬁc

tasks and do not generalize across different prediction tasks.

An alternative approach is to learn feature representations by

solving an optimization problem [4]. The challenge in feature learn-

ing is deﬁning an objective function, which involves a trade-off

in balancing computational efﬁciency and predictive accuracy. On

one side of the spectrum, one could directly aim to ﬁnd a feature

representation that optimizes performance of a downstream predic-

tion task. While this supervised procedure results in good accu-

racy, it comes at the cost of high training time complexity due to a

blowup in the number of parameters that need to be estimated. At

the other extreme, the objective function can be deﬁned to be inde-

pendent of the downstream prediction task and the representations

can be learned in a purely unsupervised way. This makes the op-

timization computationally efﬁcient and with a carefully designed

objective, it results in task-independent features that closely match

task-speciﬁc approaches in predictive accuracy [21, 23].

However, current techniques fail to satisfactorily deﬁne and opti-

mize a reasonable objective required for scalable unsupervised fea-

ture learning in networks. Classic approaches based on linear and

non-linear dimensionality reduction techniques such as Principal

Component Analysis, Multi-Dimensional Scaling and their exten-

sions [3, 27, 30, 35] optimize an objective that transforms a repre-

sentative data matrix of the network such that it maximizes the vari-

ance of the data representation. Consequently, these approaches in-

variably involve eigendecomposition of the appropriate data matrix

which is expensive for large real-world networks. Moreover, the

resulting latent representations give poor performance on various

prediction tasks over networks.

Alternatively, we can design an objective that seeks to preserve

local neighborhoods of nodes. The objective can be efﬁciently op-

timized using stochastic gradient descent (SGD) akin to backpro-

pogation on just single hidden-layer feedforward neural networks.

Recent attempts in this direction [24, 28] propose efﬁcient algo-

rithms but rely on a rigid notion of a network neighborhood, which

results in these approaches being largely insensitive to connectiv-

ity patterns unique to networks. Speciﬁcally, nodes in networks

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