Desktop Survival Guide
by Graham Williams
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DATA MINING
Desktop Survival Guide by Graham Williams |
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For this example we will use the survey dataset (see
See Section ![[*]](http://www.togaware.com/datamining/survivor/crossref.png)
). This dataset is a reasonable size and
has some common real world issues. The vignette for
arules, by the authors of the package
hahsler.gruen.etal:2005:arules, also use a similar dataset,
available within the package through data(Survey). We borrow
some of their data transformations here.
We first review the dataset: there are 32,561 entities and 15
variables.
> load("survey.RData")
> dim(survey)
[1] 32561 15
> summary(survey)
Age Workclass fnlwgt
Min. :17.00 Private :22696 Min. : 12285
1st Qu.:28.00 Self-emp-not-inc: 2541 1st Qu.: 117827
Median :37.00 Local-gov : 2093 Median : 178356
Mean :38.58 State-gov : 1298 Mean : 189778
3rd Qu.:48.00 Self-emp-inc : 1116 3rd Qu.: 237051
Max. :90.00 (Other) : 981 Max. :1484705
NA's : 1836
Education Education.Num Marital.Status
HS-grad :10501 Min. : 1.00 Divorced : 4443
Some-college: 7291 1st Qu.: 9.00 Married-AF-spouse : 23
Bachelors : 5355 Median :10.00 Married-civ-spouse :14976
Masters : 1723 Mean :10.08 Married-spouse-absent: 418
Assoc-voc : 1382 3rd Qu.:12.00 Never-married :10683
11th : 1175 Max. :16.00 Separated : 1025
(Other) : 5134 Widowed : 993
Occupation Relationship
Prof-specialty : 4140 Husband :13193 Amer-Indian-Eskimo: 311
Craft-repair : 4099 Not-in-family : 8305 Asian-Pac-Islander: 1039
Exec-managerial: 4066 Other-relative: 981 Black : 3124
Adm-clerical : 3770 Own-child : 5068 Other : 271
Sales : 3650 Unmarried : 3446 White :27816
(Other) :10993 Wife : 1568
NA's : 1843
Sex Capital.Gain Capital.Loss Hours.Per.Week
Female:10771 Min. : 0 Min. : 0.0 Min. : 1.00
Male :21790 1st Qu.: 0 1st Qu.: 0.0 1st Qu.:40.00
Median : 0 Median : 0.0 Median :40.00
Mean : 1078 Mean : 87.3 Mean :40.44
3rd Qu.: 0 3rd Qu.: 0.0 3rd Qu.:45.00
Max. : 99999 Max. :4356.0 Max. :99.00
Native.Country Salary.Group
United-States:29170 <=50K:24720
Mexico : 643 >50K : 7841
Philippines : 198
Germany : 137
Canada : 121
(Other) : 1709
NA's : 583
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The first 5 rows of the dataset give some idea of the type of data:
> survey[1:5,]
Age Workclass fnlwgt Education Education.Num Marital.Status
1 39 State-gov 77516 Bachelors 13 Never-married
2 50 Self-emp-not-inc 83311 Bachelors 13 Married-civ-spouse
3 38 Private 215646 HS-grad 9 Divorced
4 53 Private 234721 11th 7 Married-civ-spouse
5 28 Private 338409 Bachelors 13 Married-civ-spouse
Occupation Relationship Race Sex Capital.Gain Capital.Loss
1 Adm-clerical Not-in-family White Male 2174 0
2 Exec-managerial Husband White Male 0 0
3 Handlers-cleaners Not-in-family White Male 0 0
4 Handlers-cleaners Husband Black Male 0 0
5 Prof-specialty Wife Black Female 0 0
Hours.Per.Week Native.Country Salary.Group
1 40 United-States <=50K
2 13 United-States <=50K
3 40 United-States <=50K
4 40 United-States <=50K
5 40 Cuba <=50K
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The dataset contains a mixture of categorical and numeric variables
while the apriori algorithm works just with categorical variables (or
factors). We note that the variable fnlwgt is a calculated
value and not of interest to us so we can remove it from the dataset.
The variable Education.Num is redundant since is it simply a
numeric mapping of Education. We can remove these from the
data frame simply by assigning NULL to them:
> survey$fnlwgt <- NULL > survey$Education.Num <- NULL |
This still leaves Age, Capital.Gain, Capital.Loss, and Hours.Per.Week. Following hahsler.gruen.etal:2005:arules, we will partition Age and Hours.Per.Week into fours segments each:
> survey$Age <- ordered(cut(survey$Age, c(15, 25, 45, 65, 100)),
labels = c("Young", "Middle-aged", "Senior", "Old"))
> survey$Hours.Per.Week <- ordered(cut(survey$Hours.Per.Week,
c(0, 25, 40, 60, 168)),
labels = c("Part-time", "Full-time", "Over-time", "Workaholic"))
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Again following hahsler.gruen.etal:2005:arules we map Capital.Gain and Capital.Loss to None, and Low and High according to the median:
> survey$Capital.Gain <- ordered(cut(survey$Capital.Gain,
c(-Inf, 0, median(survey$Capital.Gain[survey$Capital.Gain >0]), 1e+06)),
labels = c("None", "Low", "High"))
> survey$Capital.Loss <- ordered(cut(survey$Capital.Loss,
c(-Inf, 0, median(survey$Capital.Loss[survey$Capital.Loss >0]), 1e+06)),
labels = c("None", "Low", "High"))
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That is pretty much it in terms of preparing the data for apriori:
> survey[1:5,]
Age Workclass Education Marital.Status Occupation
1 Middle-aged State-gov Bachelors Never-married Adm-clerical
2 Senior Self-emp-not-inc Bachelors Married-civ-spouse Exec-managerial
3 Middle-aged Private HS-grad Divorced Handlers-cleaners
4 Senior Private 11th Married-civ-spouse Handlers-cleaners
5 Middle-aged Private Bachelors Married-civ-spouse Prof-specialty
Relationship Race Sex Capital.Gain Capital.Loss Hours.Per.Week
1 Not-in-family White Male Low None Full-time
2 Husband White Male None None Part-time
3 Not-in-family White Male None None Full-time
4 Husband Black Male None None Full-time
5 Wife Black Female None None Full-time
Native.Country Salary.Group
1 United-States <=50K
2 United-States <=50K
3 United-States <=50K
4 United-States <=50K
5 Cuba <=50K
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The apriori function will coerce the data into the transactions data type, and this can also be done prior to calling apriori using the as function to view the data as a transaction dataset:
> library(arules) > survey.transactions <- as(survey, "transactions") > survey.transactions transactions in sparse format with 32561 transactions (rows) and 115 items (columns) |
This illustrates how the transactions data type represents variables in a binary form, one binary variable for each level of each categorical variable. There are 115 distinct levels (values for the categorical variables) across all 13 of the categorical variables.
The summary function provides more details:
> summary(survey.transactions)
transactions as itemMatrix in sparse format with
32561 rows (elements/itemsets/transactions) and
115 columns (items)
most frequent items:
Capital.Loss = None Capital.Gain = None
31042 29849
Native.Country = United-States Race = White
29170 27816
Salary.Group = <=50K (Other)
24720 276434
element (itemset/transaction) length distribution:
10 11 12 13
27 1809 563 30162
Min. 1st Qu. Median Mean 3rd Qu. Max.
10.00 13.00 13.00 12.87 13.00 13.00
includes extended item information - examples:
labels variables levels
1 Age = Young Age Young
2 Age = Middle-aged Age Middle-aged
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The summary begins with a description of the dataset sizes. This is followed by a list of the most frequent items occurring in the dataset. A Capital.Loss of None is the single most frequent item, occurring 31,042 times (i.e., pretty much no transaction has any capital loss recorded). The length distribution of the transactions is then given, indicating that some transactions have NA's for some of the variables. Looking at the summary of the original dataset you'll see that the variables Workclass, Occupation, and Native.Country have NA's, and so the distribution ranges from 10 to 13 items in a transaction.
The final piece of information in the summary output indicates the mapping that has been used to map the categorical variables to the binary variables, so that Age = Young is one binary variable, and Age = Middle-aged is another.
Now it is time to find all association rules using
apriori. After a little experimenting we have chosen a
support of 0.05 and a confidence of 0.95. This gives us 4,236 rules.
> survey.rules <- apriori(survey.transactions,
parameter = list(support=0.05, confidence=0.95))
parameter specification:
confidence minval smax arem aval originalSupport support minlen maxlen target
0.95 0.1 1 none FALSE TRUE 0.05 1 5 rules
ext
FALSE
algorithmic control:
filter tree heap memopt load sort verbose
0.1 TRUE TRUE FALSE TRUE 2 TRUE
apriori - find association rules with the apriori algorithm
version 4.21 (2004.05.09) (c) 1996-2004 Christian Borgelt
set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[115 item(s), 32561 transaction(s)] done [0.07s].
sorting and recoding items ... [36 item(s)] done [0.01s].
creating transaction tree ... done [0.08s].
checking subsets of size 1 2 3 4 5 done [0.23s].
writing ... [4236 rule(s)] done [0.00s].
creating S4 object ... done [0.04s].
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> survey.rules set of 4236 rules |
> summary(survey.rules)
set of 4236 rules
rule length distribution (lhs + rhs):
1 2 3 4 5
1 34 328 1282 2591
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.000 4.000 5.000 4.517 5.000 5.000
summary of quality measures:
support confidence lift
Min. :0.05003 Min. :0.9500 Min. :0.9965
1st Qu.:0.06469 1st Qu.:0.9617 1st Qu.:1.0186
Median :0.08435 Median :0.9715 Median :1.0505
Mean :0.11418 Mean :0.9745 Mean :1.2701
3rd Qu.:0.13267 3rd Qu.:0.9883 3rd Qu.:1.3098
Max. :0.95335 Max. :1.0000 Max. :2.9725
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We can inspect the first 5 rules (slightly edited to suit publication):
> inspect(survey.rules[1:5])
lhs rhs support conf lift
1 {} => {Capital.Loss = None} 0.953 0.953 1.00
2 {Occupation = Machine-op-inspct} => {Workclass = Private} 0.058 0.955 1.37
3 {Occupation = Machine-op-inspct} => {Capital.Loss = None} 0.059 0.966 1.01
4 {Race = Black} => {Capital.Loss = None} 0.093 0.967 1.01
5 {Occupation = Other-service} => {Salary.Group = <=50K} 0.097 0.958 1.26
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Or we can list the first 5 rules which have a lift greater that 2.5
> subset(survey.rules, subset=lift>2.5)
set of 40 rules
> inspect(subset(survey.rules, subset=lift>2.5)[1:5])
lhs rhs support conf lift
1 {Age = Young,
Hours.Per.Week = Part-time} => {Marital.Status = Never-married} 0.06 0.95 2.9
2 {Age = Young,
Relationship = Own-child} => {Marital.Status = Never-married} 0.10 0.97 2.9
3 {Age = Young,
Hours.Per.Week = Part-time,
Salary.Group = <=50K} => {Marital.Status = Never-married} 0.06 0.96 2.9
4 {Age = Young,
Hours.Per.Week = Part-time,
Native.Country = United-States}=>{Marital.Status=Never-married} 0.05 0.95 2.9
5 {Age = Young,
Capital.Gain = None,
Hours.Per.Week = Part-time} => {Marital.Status = Never-married} 0.05 0.96 2.9
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Here we build quite a few more rules and then view the rule with highest lift:
> survey.rules <- apriori(survey.transactions,
parameter = list(support = 0.05, confidence = 0.8))
parameter specification:
confidence minval smax arem aval originalSupport support minlen maxlen target
0.8 0.1 1 none FALSE TRUE 0.05 1 5 rules
ext
FALSE
algorithmic control:
filter tree heap memopt load sort verbose
0.1 TRUE TRUE FALSE TRUE 2 TRUE
apriori - find association rules with the apriori algorithm
version 4.21 (2004.05.09) (c) 1996-2004 Christian Borgelt
set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[115 item(s), 32561 transaction(s)] done [0.09s].
sorting and recoding items ... [36 item(s)] done [0.02s].
creating transaction tree ... done [0.10s].
checking subsets of size 1 2 3 4 5 done [0.35s].
writing ... [13344 rule(s)] done [0.00s].
creating S4 object ... done [0.08s].
> inspect(SORT(subset(survey.rules, subset=rhs %in% "Salary.Group"),
by="lift")[1:3])
lhs rhs support conf lift
1 {Occupation = Exec-managerial,
Relationship = Husband,
Capital.Gain = High} => {Salary.Group = >50K} 0.007 1 4.15
2 {Age = Middle-aged,
Occupation = Exec-managerial,
Capital.Gain = High} => {Salary.Group = >50K} 0.005 1 4.15
3 {Age = Middle-aged,
Education = Bachelors,
Capital.Gain = High} => {Salary.Group = >50K} 0.006 1 4.15
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