數(shù)據(jù)挖掘復(fù)習(xí)題和答案.

1、一、 考慮表中二元分類問題的訓(xùn)練樣本集1. 整個(gè)訓(xùn)練樣本集關(guān)于類屬性的熵是多少？2. 關(guān)于這些訓(xùn)練集中a1,a2的信息增益是多少？3. 對于連續(xù)屬性a3,計(jì)算所有可能的劃分的信息增益。4. 根據(jù)信息增益，a1,a2,a3哪個(gè)是最佳劃分?5. 根據(jù)分類錯(cuò)誤率，a1,a2哪具最佳？6. 根據(jù)gini指標(biāo)，a1,a2哪個(gè)最佳？答1.P(+) = 4/9 and P() = 5/94/9 log2(4/9) 5/9 log2(5/9) = 0.9911.答2：（估計(jì)不考）答3：答4: According to information gain, a1 produces the best split.答

2、5：For attribute a1: error rate = 2/9.For attribute a2: error rate = 4/9.Therefore, according to error rate, a1 produces the best split.答6：二、 考慮如下二元分類問題的數(shù)據(jù)集 1. 計(jì)算a.b信息增益，決策樹歸納算法會選用哪個(gè)屬性2. 計(jì)算a.b gini指標(biāo)，決策樹歸納會用哪個(gè)屬性？這個(gè)答案沒問題3. 從圖4-13可以看出熵和gini指標(biāo)在0,0.5都是單調(diào)遞增，而0.5,1之間單調(diào)遞減。有沒有可能信息增益和gini指標(biāo)增益支持不同的屬性？解釋你的理由Yes

3、, even though these measures have similar range and monotonousbehavior, their respective gains, , which are scaled differences of themeasures, do not necessarily behave in the same way, as illustrated bythe results in parts (a) and (b).貝葉斯分類1. P(A = 1|) = 2/5 = 0.4, P(B = 1|) = 2/5 = 0.4,P(C = 1|) =

4、 1, P(A = 0|) = 3/5 = 0.6,P(B = 0|) = 3/5 = 0.6, P(C = 0|) = 0; P(A = 1|+) = 3/5 = 0.6,P(B = 1|+) = 1/5 = 0.2, P(C = 1|+) = 2/5 = 0.4,P(A = 0|+) = 2/5 = 0.4, P(B = 0|+) = 4/5 = 0.8,P(C = 0|+) = 3/5 = . P(A = 0|+) = (2 + 2)/(5 + 4) = 4/9,P(A = 0|) = (3+2)/(5 + 4) = 5/9,P(B = 1|+) = (1 + 2)/(5

5、+ 4) = 3/9,P(B = 1|) = (2+2)/(5 + 4) = 4/9,P(C = 0|+) = (3 + 2)/(5 + 4) = 5/9,P(C = 0|) = (0+2)/(5 + 4) = 2/9.4. Let P(A = 0,B = 1, C = 0) = K5. 當(dāng)?shù)臈l件概率之一是零，則估計(jì)為使用m-估計(jì)概率的方法的條件概率是更好的，因?yàn)槲覀儾幌Ｍ麄€(gè)表達(dá)式變?yōu)榱恪?. P(A = 1|+) = 0.6, P(B = 1|+) = 0.4, P(C = 1|+) = 0.8, P(A =1|) = 0.4, P(B = 1|) = 0.4, and P(C = 1|)

6、 = 0.22.Let R : (A = 1,B = 1, C = 1) be the test record. To determine itsclass, we need to compute P(+|R) and P(|R). Using Bayes theorem, P(+|R) = P(R|+)P(+)/P(R) and P(|R) = P(R|)P()/P(R).Since P(+) = P() = 0.5 and P(R) is constant, R can be classified bycomparing P(+|R) and P(|R).For this question

7、,P(R|+) = P(A = 1|+) × P(B = 1|+) × P(C = 1|+) = 0.192P(R|) = P(A = 1|) × P(B = 1|) × P(C = 1|) = 0.032Since P(R|+) is larger, the record is assigned to (+) class.3.P(A = 1) = 0.5, P(B = 1) = 0.4 and P(A = 1,B = 1) = P(A) ×P(B) = 0.2. Therefore, A and B are independent.4.P(A

8、 = 1) = 0.5, P(B = 0) = 0.6, and P(A = 1,B = 0) = P(A =1)× P(B = 0) = 0.3. A and B are still independent.5.Compare P(A = 1,B = 1|+) = 0.2 against P(A = 1|+) = 0.6 andP(B = 1|Class = +) = 0.4. Since the product between P(A = 1|+)and P(A = 1|) are not the same as P(A = 1,B = 1|+), A and B arenot conditionally independent given the class.三、 使用下表中的相似度矩陣進(jìn)行單鏈和全鏈層次聚類。繪制樹狀況顯示結(jié)果，樹狀圖應(yīng)該清楚地顯示合并的次序。 There are no apparent relationships between s1, s2, c1, and c2.A2: Percentage of frequent itemsets = 16/32 = 50.0% (including the nullset).A4:False ala