C4.5决策树：机器学习中的经典算法解析

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"这篇文档介绍了机器学习中的C4.5决策树算法，包括其基本原理、特点、软件实现、示例应用以及相关的高级主题。C4.5是用于分类问题的一套算法，专注于监督学习，能从属性值数据集中学习到从属性值到类别的映射，以便对新的未知实例进行分类。" 在机器学习领域，C4.5算法是一个重要的决策树构建方法，由Ross Quinlan开发，是对ID3算法的改进。该算法主要用于解决分类问题，特别是在有缺失值和连续属性的数据集上表现优越。 1.1 引言 C4.5算法旨在处理带标签的训练数据，其中每个实例由一组属性特征来描述，并且属于预定义的互斥类别中的一种。它通过学习数据集的模式，构建一个决策树模型，这个模型可以对新的、未见过的实例进行预测。 1.2 算法描述 C4.5算法的核心是通过信息增益或信息增益比来选择最优划分属性，创建决策树。对于连续属性，它会自动进行离散化处理，将它们划分为多个区间。算法会递归地分裂节点，直到所有实例属于同一类别或者没有更多可用于分裂的属性。 1.3 C4.5特性 - **树修剪**：C4.5通过后剪枝策略来防止过拟合，提高泛化能力。 - **连续属性的优化使用**：C4.5可以处理连续属性，并选择最佳分割点来最大化信息增益。 - **处理缺失值**：对于缺失值，C4.5采用不同的策略，如平均值、多数类别等来处理，使得算法更具鲁棒性。 - **规则集诱导**：C4.5不仅构建决策树，还能生成可解释的规则集，这些规则集同样可以用于分类。 1.4 软件实现讨论 C4.5算法有多种软件实现，例如开源的Weka数据挖掘库，它提供了一个易于使用的界面和API，使得研究人员和开发者可以方便地应用C4.5算法。 1.5 举例说明 - **高尔夫数据集**：展示了C4.5如何处理具有多种属性的分类任务，如高尔夫球的天气预测。 - **大豆数据集**：显示了C4.5在处理复杂数据集时的性能，包括连续和离散属性。 1.6 高级话题 - **从二级存储中挖掘**：讨论如何在有限的内存资源下处理大型数据集。 - **倾斜决策树**：允许非垂直划分，提高模型的灵活性和准确性。 - **特征选择**：探讨如何选择最相关的特征来提高模型效率和精度。 - **集成方法**：如随机森林和梯度提升，通过结合多个C4.5决策树来提升模型性能。 - **分类规则**：除了决策树，C4.5还能生成易于理解的分类规则。 - **重描述**：通过寻找数据的不同表示方式来改善模型解释性。 1.7 练习与参考文献章节末尾通常包含练习题以帮助读者巩固理解和进一步研究，以及相关参考文献供深入学习。 C4.5算法在机器学习和数据挖掘领域具有广泛的应用，尤其适用于需要解释性模型的场景。通过理解和掌握这一算法，可以为解决实际问题提供有力工具。

16 C4.5

axes. Apply C4.5 on this dataset and comment on the quality of the induced

trees. Take factors such as accuracy, size of the tree, and comprehensibility into

account.

3. An alternative way to avoid overﬁtting is to restrict the growth of the tree rather

than pruning back a fully grown tree down to a reduced size. Explain why such

prepruning may not be a good idea.

4. Prove that the impurity measure used by C45 (i.e., entropy) is concave. Why is

it important that it be concave?

5. Derive Equation (1.1). As stated in the text, use the normal approximation to

the Bernoulli random variable modeling the error rate.

6. Instead of using information gain, study how decision tree induction would be

affectedif we directly selected the attribute with the highest prediction accuracy.

Furthermore, what if we induced rules with only one antecedent? Hint: Yo u

are retracing the experiments of Robert Holte as described in R. Holte, Very

Simple Classiﬁcation Rules Perform Well on Most Commonly Used Datasets,

Machine Learning, vol. 11, pp. 63–91, 1993.

7. In some machine learning applications, attributes are set-valued,for example,an

object can have multiple colors and to classify the object it might be important to

model color as a set-valued attribute rather than as an instance-valued attribute.

Identify decision tests that can be performed on set-valuedattributes and explain

which can be readily incorporated into the C4.5 system for growing decision

trees.

8. Instead of classifying an instance into a single class, assume our goal is to obtain

a ranking of classes according to the (posterior) probability of membership of

the instance in various classes. Read F. Provost and P. Domingos, Tree Induction

for Probability Based Ranking, Machine Learning, vol. 52, no. 3, pp. 199–215,

2003, who explain why the trees induced by C4.5 are not suited to providing

reliable probability estimates; they also suggest some ways to ﬁx this problem

using probability smoothing methods. Do these same objections and solution

strategy apply to C4.5 rules as well? Experiment with datasets from the UCI

repository.

9. (Adapted from S. Nijssen and E. Fromont, Mining Optimal Decision Trees

from Itemset Lattices, Proceedings of the 13th ACM SIGKDD International

Conference on Knowledge Discovery and Data Mining, pp. 530–539, 2007.)

The trees induced by C4.5 are driven by heuristic choices but assume that our

goal is to identify an optimal tree. Optimality can be posed in terms of various

considerations; two such considerations are the most accurate tree up to a

certain maximum depth and the smallest tree in which each leaf covers at least

k instances and the expected accuracy is maximized over unseen examples.

Describe an efﬁcient algorithm to induce such optimal trees.

10. First-order logic is a more expressive notation than the attribute-value repre-

sentation considered in this chapter. Given a collection of ﬁrst-order relations,

describe how the basic algorithmic approach of C4.5 can be generalized to use

References 17

ﬁrst-order features. Your solution must allow the induction of trees or rules of

the form:

grandparent(X,Z) :- parent(X,Y), parent(Y,Z).

that is, X is a grandparent of Z if there exists Y such that Y is the parent of

X and Z is the parent of Y. Several new issues result from the choice of ﬁrst-

order logic as the representational language. First, unlike the attribute value

situation, ﬁrst-order features (such as parent(X,Y)) are not readily given

and must be generalized from the speciﬁc instances. Second, it is possible to

obtain nonsensical trees or rules if the variables participate in the head of a rule

but not the body, for example:

grandparent(X,Y) :- parent(X,Z).

Describe how you can place checks and balances into the induction process

so that a complete ﬁrst-order theory can be induced from data. Hint: You are

exploring the ﬁeld of inductive logic programming [9], speciﬁcally, algorithms

such as FOIL [29].

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Chapter 2

K-Means

Joydeep Ghosh and Alexander Liu

Contents

2.1 Introduction ............................................................ 21

2.2 The k-means Algorithm ................................................. 22

2.3 Available Software ...................................................... 26

2.4 Examples ............................................................... 27

2.5 Advanced Topics ........................................................ 30

2.6 Summary ............................................................... 32

2.7 Exercises ............................................................... 33

References ................................................................... 34

2.1 Introduction

In this chapter, we describe the k-means algorithm, a straightforward and widely

used clustering algorithm. Given a set of objects (records), the goal of clustering

or segmentation is to divide these objects into groups or “clusters” such that objects

withina grouptendto bemore similartoone anotherascompared toobjects belonging

to different groups. In other words, clustering algorithms place similar points in the

same cluster while placing dissimilar points in different clusters. Note that, in contrast

to supervised tasks such as regression or classiﬁcation where there is a notion of a

target value or class label, the objects that form the inputs to a clustering procedure

do not come with an associated target. Therefore, clustering is often referred to

as unsupervised learning. Because there is no need for labeled data, unsupervised

algorithms are suitable for many applications where labeled data is difﬁcult to obtain.

Unsupervised tasks such as clustering are also often used to explore and characterize

the dataset before running a supervised learning task. Since clustering makes no use

of class labels, some notion of similarity must be deﬁned based on the attributesof the

objects.The deﬁnition ofsimilarityand themethodin which pointsare clustered differ

based on the clustering algorithm being applied. Thus, different clustering algorithms

are suited to different types of datasets and different purposes. The “best” clustering

algorithm to use therefore depends on the application. It is not uncommon to try

several different algorithms and choose depending on which is the most useful.

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