数据挖掘导论：习题解答与高级概念解析

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"数据挖掘导论(完整版)习题答案英文原版，由Pang-Ning Tan, Michael Steinbach, Vipin Kumar三位作者撰写，涵盖了数据挖掘的基础和高级主题，包括数据、分类、关联分析、聚类和异常检测。适合作为教学教材和专业参考书。" 在数据挖掘领域，这本书提供了一个全面的视角，引导读者理解如何将数据挖掘技术应用于实际问题。作者团队由知名学者组成，他们在数据挖掘和相关领域有深厚的学术背景和实践经验。首先，"数据"部分介绍了数据挖掘的基本环境，包括数据预处理、数据清洗和数据转换，这些都是进行有效挖掘前必不可少的步骤。数据的质量和准备对于确保后续分析的准确性和可靠性至关重要。其次，"分类"章节详细讲解了决策树算法，这是数据挖掘中的经典方法，用于预测性建模。同时，书中还探讨了其他分类技术，如神经网络、贝叶斯分类和支持向量机，这些是理解和构建分类模型的关键。 "关联分析"部分阐述了如何发现数据中的频繁模式和关联规则，例如市场篮子分析。从基本概念如Apriori算法到更复杂的高级概念，这部分内容有助于读者理解如何在大规模数据集中寻找有价值的关联。 "聚类"章节则关注无监督学习，讨论了如何通过聚类算法将数据集中的对象分组。从K-means到层次聚类，这些方法帮助识别数据中的自然群体结构。最后，"异常检测"部分介绍了如何识别数据中的离群值或异常行为，这对于欺诈检测、网络入侵检测等场景尤为重要。除了理论知识，书中还包含大量的实例、图表和习题，旨在增强读者的实践能力。这些习题答案可以帮助读者检验和巩固所学知识，确保他们能够应用所学概念解决实际问题。 "数据挖掘导论(完整版)"是一本深度与广度兼具的教材，适合数据挖掘课程的学生和从事相关工作的专业人士。通过阅读此书，读者可以系统地学习数据挖掘的核心概念和技术，并逐步掌握这个领域的高级主题。

12 Chapter 2 Data

x = 0101010001

y = 0100011000

Hamming distance = number of di?erent bits = 3

Jaccard Similarity = number of 1-1 matches /( number of bits - number

0-0 matches) = 2 / 5 = 0.4

(b) Which approach, Jaccard or Hamming distance, is more similar to the

Simple Matching Coe?cient, and which approach is more similar to the

cosine measure? Explain. (Note: The Hamming measure is a distance,

while the other three measures are similarities, but don’ｔlet this confuse

you.)

The Hamming distance is similar to the SMC. In fact, SMC = Hamming

distance / number of bits.

The Jaccard measure is similar to the cosine measure because both

ignore 0-0 matches.

species are in terms of the number of genes they share. Describe which

measure, Hamming or Jaccard, you think would be more appropriate

for comparing the genetic makeup of two organisms. Explain. (Assume

that each animal is represented as a binary vector, where each attribute

is 1 if a particular gene is present in the organism and 0 otherwise.)

Jaccard is more appropriate for comparing the genetic makeup of two

organisms; since we want to see how many genes these two organisms

share.

(d) If you wanted to compare the genetic makeup of two organisms of the

same species, e.g., two human beings, would you use the Hamming

distance, the Jaccard coe?cient, or a di?erent measure of similarity or

distance? Explain. (Note that two human beings share > 99.9% of the

same genes.)

Two human beings share > 99.9% of the same genes. If we want to

compare the genetic makeup of two human beings, we should focus on

their di?erences. Thus, the Hamming distance is more appropriate in

this situation.

19. For the following vectors, x and y, calculate the indicated similarity or dis-

tance measures.

(a) x = (1, 1, 1, 1), y = (2 , 2, 2, 2) cosine, correlation, Euclidean

cos(x, y ) = 1, corr( x , y ) = 0/0 (unde?ned), Euclidean( x, y ) = 2

(b) x = (0, 1, 0, 1), y = (1 , 0, 1, 0) cosine, correlation, Euclidean, Jaccard

cos(x, y ) = 0, corr( x , y ) = - 1, Euclidean( x, y ) = 2, Jaccard( x , y ) = 0

cos(x , y ) = 0, corr( x , y )=0, Euclidean( x, y) = 2

(d) x = (1, 1, 0, 1, 0, 1), y = (1 , 1,1, 0, 0, 1) cosine, correlation, Jaccard

cos(x , y ) = 0.75, corr( x, y) = 0.25, Jaccard( x , y ) = 0.6

(e) x = (2, - 1,0, 2, 0, - 3) , y = (- 1, 1, - 1, 0, 0, - 1) cosine, correlation

cos(x , y ) = 0, corr( x , y ) = 0

20. Here, we further explore the cosine and correlation measures.

(a) What is the range of values that are possible for the cosine measure?

[- 1, 1]. Many times the data has only positive entries and in that case

the range is [0, 1].

(b) If two objects have a cosine measure of 1, are they identical? Explain.

Not necessarily. All we know is that the values of their attributes di?er

by a constant factor.

(Hint: Look at statistical measures such as mean and standard devia-

tion in cases where cosine and correlation are the same and di?erent.)

For two vectors, x and y that have a mean of 0, corr( x , y ) = cos(x , y ).

(d) Figure 2.1(a) shows the relationship of the cosine measure to Euclidean

distance for 100,000 randomly generated points that have been normal-

ized to have an L2 length of 1. What general observation can you make

about the relationship between Euclidean distance and cosine similarity

when vectors have an L2 norm of 1?

Since all the 100,000 points fall on the curve, there is a functional rela-

tionship between Euclidean distance and cosine similarity for normal-

ized data. More speci?cally, there is an inverse relationship between

cosine similarity and Euclidean distance. For example, if two data

points are identical, their cosine similarity is one and their Euclidean

distance is zero, but if two data points have a high Euclidean distance,

their cosine value is close to zero. Note that all the sample data points

were from the positive quadrant, i.e., had only positive values. This

means that all cosine (and correlation) values will be positive.

(e) Figure 2.1(b) shows the relationship of correlation to Euclidean distance

for 100,000 randomly generated points that have been standardized

to have a mean of 0 and a standard deviation of 1. What general

observation can you make about the relationship between Euclidean

distance and correlation when the vectors have been standardized to

have a mean of 0 and a standard deviation of 1?

16 Chapter 2 Data

23. Given a similarity measure with values in the interval [0,1] describe two ways

to transform this similarity value into a dissimilarity value in the interval

[0,∞].

d =

1- s

and d = - log s.

24. Proximity is typically de?ned between a pair of objects.

(a) De?ne two ways in which you might de?ne the proximity among a group

of objects.

Two examples are the following: (i) based on pairwise proximity, i.e.,

minimum pairwise similarity or maximum pairwise dissimilarity, or (ii)

for points in Euclidean space compute a centroid (the mean of all the

points —seeSection 8.2) and then compute the sum or average of the

distances of the points to the centroid.

(b) How might you de?ne the distance between two sets of points in Eu-

clidean space?

One approach is to compute the distance between the centroids of the

two sets of points.

(Make no assumption about the data objects, except that a proximity

measure is de?ned between any pair of objects.)

One approach is to compute the average pairwise proximity of objects

in one group of objects with those objects in the other group. Other

approaches are to take the minimum or maximum proximity.

Note that the cohesion of a cluster is related to the notion of the proximity

of a group of objects among themselves and that the separation of clusters

is related to concept of the proximity of two groups of objects. (See Section

8.4.) Furthermore, the proximity of two clusters is an important concept in

agglomerative hierarchical clustering. (See Section 8.2.)

25. You are given a set of points S in Euclidean space, as well as the distance of

each point in S to a point x. (It does not matter if x ∈S.)

(a) If the goal is to ?nd all points within a speci?ed distance εof point y ,

y = x , explain how you could use the triangle inequality and the al-

ready calculated distances to x to potentially reduce the number of dis-

tance calculations necessary? Hint: The triangle inequality, d( x , z) ≤

d( x, y ) + d(y , x ), can be rewritten as d( x , y ) ≥d(x , z) - d( y , z).

Unfortunately, there is a typo and a lack of clarity in the hint. The

hint should be phrased as follows:

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