CS 6604 Assignment #2
Assigned: Sep 25, 2007
Date Due: Oct 3, 2007, in class, before class starts
1. (5 points) Present the Venn diagram showing inter-relationships between the following classes
of constraints: monotonic, anti-monotonic, succinct, convertible anti-monotone, convertible
monotone, loosely anti-monotonic, loosely monotonic, and others.
2. (10 points) Assume that you are given a 2-class dataset where instances of each class cor-
respond to strings of length 2. The first character of the string is binary and the second
character of the string has six possible values, from ‘A’ through ‘F.’ The instances of the
first class are: ‘1A’, ‘0E’, ‘0B’, ‘1B’, ‘1F’, ‘0D’. The instances of the second class are: ‘0A’,
‘0C’, ‘1C’, ‘0F’, ‘0B’, and ‘1D’. Using the two characters of the instances as ‘features’ for
classification, construct decision trees in at least two ways, using different choices of impurity
measures. You must choose the impurity measures such that one decision tree branches on the
first character at the root node, and the other decision tree branches on the second character
at the root node. In light of your answer to the above, present general guidelines on which
impurity measure is better in which types of datasets.
3. (10 points) In class we presented three different impurity measures. Verify whether each of
them is a concave function. If so, prove it. If not, provide a counter example. Why is it
important that impurity be a concave measure?
4. (20 points) Typically frequent itemset mining algorithms are run with a minimum support
constraint. However, it is difficult for a data miner to ‘guess’ what a reasonable minimum
support constraint might be for a dataset. Hence there is growing interest in mining ‘top-k’
patterns which refer to, in this case, finding the kitemsets that have the highest support.
Can you think of an anti-monotonicity or monotonicity guiding principle for mining such
patterns? You are free to make any additional assumptions to the formulation if it helps in
identifying an efficient constraint and suggests a suitable algorithm.
5. (25 points) In class we discussed how to mine itemsets with constraints on their average value
over some attribute or variance over the attribute. Explain how you will mine itemsets X
that have the following constraints with respect to a numeric attribute a(e.g., price): (i)
Median (X.a) ≤or ≥θ, (ii) Mode(X.a) ≤or ≥θ.
6. (30 points) Read the paper ‘How to quickly find a witness’ which presents an algorithm for
finding itemsets with constraints on the variance. Compare the ideas in this paper to the one
by Bonchi and Lucchese presented in class ‘Pushing Tougher Constraints in Frequent Pattern
Mining’ which gives an alternate algorithm for finding such itemsets. Determine whether the
notions of ‘witness’ presented in the former and the ‘loose anti-monotonicity’ presented in the
latter are compatible and if so, identify the relationships between them.
Turnin a typed (not handwritten) paper copy giving answers to the questions, plots, including a
brief description of how you solved each question. Write enough to convince us that you completed
the assignment independently.