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Homework 3 (Advanced) Data Mining: Algorithms and Applications

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Homework 3
(Advanced) Data Mining: Algorithms and Applications
1. Suppose that we have age data including the following numbers in sorted order. Then answer the questions below. (5
points each)
age: 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70
(a) Use smoothing by bin means to smooth the above data, using a bin depth of 3. Illustrate your steps. Comment
on the effect of this technique for the given data.
(b) Use IQR measure to determine if there are any outliers in this data.
(c) Use min-max normalization to transform the value 35 for age onto the range [0.0, 1.0].
(d) Use z-score normalization to transform the value 35 for age? (you need to compute mean and standard deviation
first)
(e) Use normalization by decimal scaling to transform the value 35 for age.
2. Write a function in your preferred languagewhich can take a data vector and do min-max normalization by transforming
data onto a desired range. For example, it should be able get the age data above and map it between any two numbers.
(foo (a, min_new, max_new) where a is an one-dimensional array) (25 points)
department age salary status count
sales 31_35 46K_50K senior 30
sales 26_30 26K_30K junior 40
sales 31_35 31K_35K junior 40
systems 21_25 46K_50K junior 20
systems 31_35 66K_70K senior 5
systems 26_30 46K_50K junior 3
systems 41_45 66K_70K senior 3
marketing 36_40 46K_50K senior 10
marketing 31_35 41K_45K junior 4
secretary 46_50 36K_40K senior 4
secretary 26_30 26K_30K junior 6
Table 1: Data shows the count of each feature combination. For instance, There are 30 senior sales staff who are 31…35 years
old and have 46…50K salary. Since each combination is unique, their corresponding groups are mutually exclusive which
implies counts are not double counts for any of the cases. Notice that the status column is the class label to indicate whether
someone is junior or senior.
3. Using information gain on the data in Table 1, do calculations for two levels of a decision tree which decides whether
a person is senior or junior. Please show your calculations and clearly write down your junior and senior counts not
to confuse yourself. Note that you need to calculate the information gain for all attributes (department, age, salary)
and pick the one to start your tree. In your subsets of your data, you’ll perform the same operation for the attributes
available. (You can use a computing environment to write the mathematical expressions. i.e., p∗logp,(1/2)∗log2(1/2)
) (25pts)
4. Using the decision tree you generate if-then rules. (25pts)
1

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