中科院数据挖掘hw1

(b) Use the results in part (a) to compute the confidence for the association rules {a, b} {c} and {c}{a, b}. Is confidence a symmetric measure? {a, b}=> {c}, confidence=3/4=75% {c}=> {a, b}, confidence=3/3=100% 两个关联规则的置信度不相等，因此置信度不是对称规则。 (c) List all of the strong association rules (with support s and confidence c) matching the following metarule, where X is a variable representing customers, and itemi denotes variables representing items (e.g. “A”, “B”, etc.):
(g)
4．Consider the data set shown in Table 1（min_sup = 60%, min_conf=80%）. Apriori：最小支持度计数值 4*60%=2.4,所以最小支持度计数为 3 A B C D E 4 4 3 2 2 A L1= B C 4 4 3 C2= AB AC BC
Table 1. Example of market basket transactions.
TID T1 T2 T3 T4
Items-bought {A, D, B, C} {D, A, C, E, B} {A, B, E} {A, B, C}
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由(a)中得出的频繁项集 L 可得所有的关联规则如下： 对{AB}有两个子集{A},{B}, 得到的关联规则为： A=>B, confidence=4/4=100% B=>A, confidence=4/4=100% 对{AC}有两个子集{A}, {C},得到的关联规则为： A=>C, confidence=3/4=75% C=>A, confidence=3/3=100% 对{BC}有两个子集{B}, {C},得到的关联规则为： B=>C, confidence=3/4=75% C=>B, confidence=3/3=100% 对{ABC}有 6 个子集{AB}, {BC},{AC}, {C},{A}, {B},得到的关联规则为： {AB}=>{C}, confidence=3/4=75% {C}=>{AB}, confidence=3/3=100% {BC}=>{A}, confidence=3/3=100% {A}=>{BC}, confidence=3/4=75% {AC}=>{B}, confidence=3/3=100% {B}=>{AC}, confidence=3/4=75% 因为 min_conf=80%，得出所有强关联规则为： buys(X, A)=>buys(X, B) [s=100%, c=100%] buys(X, B)=>buys(X, A) [s=100%, c=100%] buys(X,C)=>buys(X, A) [s=75%, c=100%] buys(X, C)=>buys(X, B) [s=75%, c=100%] buys(X, C)=>buys(X, A)^buys(X, B) [s=75%, c=100%] buys(X, B)^buys(X, C)=>buys(X, A) [s=75%, c=100%] buys(X, A)^buys(X, C)=>buys(X, B) [s=75%, c=100%]
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(c)
Five-number in summary of age: 23,39,51,57,61 Five-number in summary of %fat: 7.8,26.5,30.7,34.1,42.5 Boxplot 如图 3.(b)-(c)所示： Draw a scatter plot based on these two variables. Scatter plot 如图 3.(b)-(c)所示：
(d)
图 3.(b)-(c) Normalize the two variables based on min-max normalization. Suppose new_min=0,new_max=1 Normalized data:
0.11 0.000 0.11 0.288 0.42 0.680 0.47 0.522 0.63 0.565 0.68 0.559 0.71 0.647 0.76 0.772 0.82 1.000 0.82 0.605 0.87 0.738 0.89 0.646 0.92 0.758 0.92 0.723 0.97 0.963 1.00 0.804
25763.2 18 51 28.78 ( aibi ) n A B rA , B 0.3344 n 1 A B 17 12.846 8.994 rA , B <0,negatively correlated
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(f)
age %fat
0.00 0.049
0.00 0.539
(e)
Calculate the correlation coefficient (Pearson’s product moment coefficient). Are these two variables positively or negatively correlated?
(a)
Calculate the mean, median, and standard deviation of age and %fat. mean of age: (23+23+27+27+39+41+47+49+50+52+54+54+56+57+58+58+60+61)/18=46.4 median of age: (50+52)/2=51 standard deviation of age: Ó=12.846
age %fat 23 9.5 23 26.5 27 7.8 27 17.8 39 31.4 41 25.9 47 27.4 49 27.2 50 31.2 52 34.6 54 42.5 54 28.8 56 33.4 57 30.2 58 34.1 58 32.9 60 41.2 61 35.7
HW1
Due Date: Oct. 26 Submission requirements: Please submit your solutions to our class website. Part I: written part：
1. Suppose that a data warehouse consists of four dimensions, date, spectator, location, and game, and two measures, count and charge, where charge is the fare that a spectator pays when watching a game on a given date. Spectators may be students, adults, or seniors, with each category having its own charge rate.
Smooth the fat data by bin means, using a bin depth of 6. Bin 1: 19.1,19.1,19.1,19.1,19.1,19.1 Bin 2: 30.3,30.3,30.3,30.3,30.3,30.3 Bin 3: 36.9,36.9,36.9,36.9,36.9,36.9 Smooth the fat data by bin boundaries, using a bin depth of 6. Bin 1: 7.8,7.8,27.2,27.2,27.2,27.2 Bin 2: 27.4,27.4,32.9,32.9,32.9,32.9 Bin 3: 33.4,33.4,33.4,33.4,42.5,42.5
mean of %fat: (7.8+9.5+17.8+25.9+26.5+27.2+27.4+28.8+30.2+31.2+31.4+32.9+33.4+34.1+34.6+35.7+41.2+4 2.5)/18=28.78 median of %fat: (30.2+31.2)/2=30.7 standard deviation of %fat: Ó=8.994 (b) Draw the boxplots for age and %fat.
(a) Draw a star schema diagram for the data warehouse. star schema 如下图所示：
(b) Starting with the base cuboid [date, spectator, location, game] ， what specific OLAP operations should one perform in order to list the total charge paid by student spectators in Los Angeles? Slice for Spectator=student Slice for Location=LosAngeles Roll-up on Game (total games) Roll-up on Date from day to year (c) Bitmap indexing is a very useful optimization technique. Please present the pros and cons of using bitmap indexing in this given data warehouse. 该立方体一共有四个维（或属性），只需要为这四个为分别维护一张位图索引表，当属性的域 基数较小时，因为比较、连接和聚集操作都变成了位运算，大大减少了处理时间。由于用来表示具体事 务的字符串可以用单个二进位表示，位图索引显著降低了空间和 I/O 开销。但是如果属性的域的基数很 大时，可能会浪费存储空间来存储大量的数据。