大规模数据挖掘：Web与网络分析

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"大规模数据挖掘英文版，源自斯坦福大学的课程教材，由Anand Rajaraman、Jure Leskovec和Jeﬀrey D. Ullman合著。该书涵盖了从Web挖掘到大规模网络分析的数据挖掘内容，并包含了实际的大规模数据挖掘项目课程的材料。" 《Mining of Massive Datasets》这本书主要探讨的是在海量数据背景下进行数据挖掘的技术和方法。作者们结合了在斯坦福大学多年教学的经验，将内容进行了精心设计和组织，最初作为一门名为"Web Mining"的研究生课程，后来随着Jure Leskovec的加入，课程内容扩展到了网络分析，并更名为CS246。书中的内容不仅仅局限于数据挖掘，而是特别关注于处理那些无法一次性加载到内存中的超大规模数据。由于这种对规模的强调，书中许多实例都与Web相关或源自Web的数据。这些例子包括但不限于网页链接结构、搜索引擎的工作原理、推荐系统、社交网络分析以及大规模数据集的可视化等。数据挖掘的核心在于从大量无结构或半结构化的数据中发现有价值的信息和模式。书中可能涉及的知识点包括： 1. 数据预处理：清洗、转换和整合数据，处理缺失值和异常值，为挖掘做好准备。 2. 聚类算法：如K-means、层次聚类等，用于将相似数据分组。 3. 分类算法：如决策树、随机森林、支持向量机等，用于预测未知数据的类别。 4. 关联规则学习：如Apriori算法，用于找出项集之间的频繁模式。 5. 社交网络分析：研究用户之间的关系和互动，如社区检测、影响力传播等。 6. 图算法：如PageRank，用于理解网络中的重要性分布。 7. 推荐系统：基于用户行为和物品属性的协同过滤方法。 8. 时间序列分析：处理和预测随时间变化的数据模式。 9. 大规模数据存储和并行计算：如Hadoop和MapReduce，用于处理大数据的基础设施。本书不仅提供了理论知识，还强调了实际应用，通过实际项目帮助读者理解如何在真实世界的大数据场景中应用这些技术。同时，书中可能还包括了一些关于如何评估模型性能、处理数据稀疏性以及优化算法效率的讨论。《Mining of Massive Datasets》是学习大规模数据挖掘领域的宝贵资源，适合对数据科学、计算机科学以及相关领域感兴趣的研究生和高级本科生，同时也为专业人士提供了深入理解和实践大数据挖掘的理论框架。

xvi CONTENTS

10.6.5 Using Fewer Reduce Tasks . . . . . . . . . . . . . . . . . . 375

10.6.6 Exercises for Section 10.6 . . . . . . . . . . . . . . . . . . 375

10.7 Neighborhood Properties of Graphs . . . . . . . . . . . . . . . . . 377

10.7.1 Directed Graphs and Neighborhoods . . . . . . . . . . . . 377

10.7.2 The Diameter of a Gra ph . . . . . . . . . . . . . . . . . . 378

10.7.3 Transitive Closure and Reachability . . . . . . . . . . . . 379

10.7.4 Transitive Closure Via MapReduce . . . . . . . . . . . . . 3 80

10.7.5 Smart Transitive Closure . . . . . . . . . . . . . . . . . . 382

10.7.6 Transitive Closure by Graph Reduction . . . . . . . . . . 384

10.7.7 Approximating the Sizes of Neighborhoods . . . . . . . . 386

10.7.8 Exercises for Section 10.7 . . . . . . . . . . . . . . . . . . 387

10.8 Summary of Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . 3 88

10.9 References for Chapter 10 . . . . . . . . . . . . . . . . . . . . . . 391

11 Dimensionali ty Reduction 395

11.1 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . 395

11.1.1 Deﬁnitions . . . . . . . . . . . . . . . . . . . . . . . . . . 396

11.1.2 Computing Eigenvalues and Eigenvectors . . . . . . . . . 396

11.1.3 Finding Eigenpairs by Power Iteration . . . . . . . . . . . 398

11.1.4 The Matrix of Eigenvectors . . . . . . . . . . . . . . . . . 401

11.1.5 Exercises for Section 11.1 . . . . . . . . . . . . . . . . . . 401

11.2 Principal-Compo nent Analysis . . . . . . . . . . . . . . . . . . . 402

11.2.1 An Illustr ative Exa mple . . . . . . . . . . . . . . . . . . . 403

11.2.2 Using Eigenvectors for Dimensionality Reduction . . . . . 406

11.2.3 The Matrix of Distances . . . . . . . . . . . . . . . . . . . 406

11.2.4 Exercises for Section 11.2 . . . . . . . . . . . . . . . . . . 408

11.3 Singular-Value Decomposition . . . . . . . . . . . . . . . . . . . . 408

11.3.1 Deﬁnition of SVD . . . . . . . . . . . . . . . . . . . . . . 408

11.3.2 Interpretation of SVD . . . . . . . . . . . . . . . . . . . . 410

11.3.3 Dimensionality Reduction Using SVD . . . . . . . . . . . 412

11.3.4 Why Zeroing Low Singula r Values Works . . . . . . . . . 413

11.3.5 Querying Using Concepts . . . . . . . . . . . . . . . . . . 415

11.3.6 Computing the SVD of a Matrix . . . . . . . . . . . . . . 416

11.3.7 Exercises for Section 11.3 . . . . . . . . . . . . . . . . . . 417

11.4 CUR Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 418

11.4.1 Deﬁnition of CUR . . . . . . . . . . . . . . . . . . . . . . 418

11.4.2 Choosing Rows and Columns Proper ly . . . . . . . . . . . 419

11.4.3 Constructing the Middle Matrix . . . . . . . . . . . . . . 421

11.4.4 The Complete CUR Decomposition . . . . . . . . . . . . 422

11.4.5 Eliminating Duplicate Rows and Columns . . . . . . . . . 423

11.4.6 Exercises for Section 11.4 . . . . . . . . . . . . . . . . . . 424

11.5 Summary of Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . 4 24

11.6 References for Chapter 11 . . . . . . . . . . . . . . . . . . . . . . 426

CONTENTS xvii

12 Large-Scale Machine Learning 429

12.1 The Machine-Learning Model . . . . . . . . . . . . . . . . . . . . 430

12.1.1 Training Sets . . . . . . . . . . . . . . . . . . . . . . . . . 430

12.1.2 Some Illustrative Examples . . . . . . . . . . . . . . . . . 430

12.1.3 Approaches to Machine Learning . . . . . . . . . . . . . . 433

12.1.4 Machine-Learning Architecture . . . . . . . . . . . . . . . 434

12.1.5 Exercises for Section 12.1 . . . . . . . . . . . . . . . . . . 437

12.2 Perceptrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

12.2.1 Training a Perceptron with Zero Thresho ld . . . . . . . . 437

12.2.2 Convergence of Perceptrons . . . . . . . . . . . . . . . . . 441

12.2.3 The Winnow Algorithm . . . . . . . . . . . . . . . . . . . 441

12.2.4 Allowing the Threshold to Vary . . . . . . . . . . . . . . . 443

12.2.5 Multiclass Perceptrons . . . . . . . . . . . . . . . . . . . . 4 45

12.2.6 Transforming the Tr aining Set . . . . . . . . . . . . . . . 446

12.2.7 Problems With Perceptrons . . . . . . . . . . . . . . . . . 4 47

12.2.8 Parallel Implementation of Perceptrons . . . . . . . . . . 448

12.2.9 Exercises for Section 12.2 . . . . . . . . . . . . . . . . . . 449

12.3 Support-Ve ctor Machines . . . . . . . . . . . . . . . . . . . . . . 45 1

12.3.1 The Mechanics of an SVM . . . . . . . . . . . . . . . . . . 451

12.3.2 Normalizing the Hyperplane . . . . . . . . . . . . . . . . . 452

12.3.3 Finding Optimal Approximate Separators . . . . . . . . . 454

12.3.4 SVM So lutions by Gradient Descent . . . . . . . . . . . . 457

12.3.5 Stochastic Gradient Descent . . . . . . . . . . . . . . . . . 461

12.3.6 Parallel Implementation of SVM . . . . . . . . . . . . . . 461

12.3.7 Exercises for Section 12.3 . . . . . . . . . . . . . . . . . . 462

12.4 Learning fro m Nearest Neig hbors . . . . . . . . . . . . . . . . . . 462

12.4.1 The Framework for Nea rest-Neighbor Calculations . . . . 463

12.4.2 Learning with One Nearest Neighbor . . . . . . . . . . . . 463

12.4.3 Learning O ne-Dimensional Functions . . . . . . . . . . . . 464

12.4.4 Kernel Regressio n . . . . . . . . . . . . . . . . . . . . . . 467

12.4.5 Dealing with High-Dimensional Euclidean Data . . . . . . 467

12.4.6 Dealing with Non-Euclidean Distances . . . . . . . . . . . 469

12.4.7 Exercises for Section 12.4 . . . . . . . . . . . . . . . . . . 469

12.5 Comparison of Lea rning Methods . . . . . . . . . . . . . . . . . . 470

12.6 Summary of Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . 4 71

12.7 References for Chapter 12 . . . . . . . . . . . . . . . . . . . . . . 473

2 CHAPTER 1. DATA MINING

and standard deviation of this Gaussian distribution completely characterize the

distribution and would become the model of the data. 2

1.1.2 Machine Learning

There are some who regard data mining as synonymous with machine learning.

There is no question that some data mining appr opriately uses algorithms from

machine learning. Machine-learning practitioners use the data as a training set,

to train an algorithm of one of the many types used by machine-learning prac-

titioners, such as Bayes nets, support-vector machines, decision trees, hidden

Markov models, and many o thers.

There are situations where using data in this way makes sense. The typical

case where machine learning is a good approach is when we have little idea of

what we are looking for in the data. For example, it is rather unclear what

it is about movies that makes certain movie-goers like or dislike it. Thus,

in answering the “Netﬂix challenge” to devise an algorithm that pre dicts the

ratings of movies by users, based on a sample of their resp onses, machine-

learning algorithms have proved quite success ful. We shall discuss a simple

form of this type of algorithm in Section 9.4.

On the other hand, machine learning has not proved succes sful in situations

where we can describe the goals of the mining more directly. An interesting

case in point is the attempt by WhizBang! Labs

to use machine learning to

locate people’s resumes on the Web. It was not a ble to do better than algorithms

in the typical resume. Since everyone who has looked at or written a resume has

a pretty good idea of what resumes contain, there was no mystery about what

makes a Web page a resume. Thus, there was no advantage to machine-learning

over the dire ct design of an algorithm to discover resumes.

1.1.3 Computational Approaches to Modeling

More recently, computer scientists have looked at data mining as an algorithmic

problem. In this case, the model of the data is simply the answer to a complex

query about it. For instance, given the set of numbers of Example 1.1, we might

compute their average and standard deviation. Note that these values might

not be the parameters of the Gaussian that best ﬁts the data , although they

will almost certainly be very close if the size of the data is large.

There are many diﬀerent approaches to modeling da ta. We have already

mentioned the possibility of constructing a statistical process whereby the data

could have been g e nerated. Most other approaches to modeling can be desc ribed

as either

1. Summarizing the data succinctly and approximately, or

This startup attempted to use machine learning to mine large-scale data, and hired many

of the top machine-learning people to do so. Unfortunately, it was not able to survive.

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