Applied Data Analysis and Visualization II (ECB3ADAVE2)
Institution
Universiteit Utrecht (UU)
A detailed summary of all the relevant unsupervised learning methods.
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,Week 1
Key Words
▪ Supervised / unsupervised learning
▪ Antecedent and consequent
▪ Support, confidence and lift
▪ Apriori algorithm and Apriori principle
Supervised vs. unsupervised learning
▪ Supervised learning
Building a statistical model for predicting / estimating an output (y) based on one or
more inputs (x).
o Classification: predict to which category an observation belongs (qualitative
outcomes).
o Regression: predict a quantitative outcome.
▪ Unsupervised learning
Inputs (x) but no outputs (y). Try to learn structure and relationships from data, like …
… discovering associations among variable values → association rule analysis
… discovering unknown subgroups of observations → clustering
… dimension reduction → principal components analysis
Association rule analysis
Goal: to find joint values of the variables x1, …, xp that appear together most frequently in the
data base.
In the case of binary valued data, association rule analysis is called ‘market basket’ analysis.
Transactions are represented in a binary incidence matrix:
1, if the jth item is purchased as part of transaction i.
xij {
0, if the jth item is not purchased as part of transaction i.
This matrix can now be used to find association rules.
An association rule is the implication
A⇒B antecedent ⇒ consequent
In market basket analysis, it can be seen as an if-then statement:
If you buy A, there is a chance that you buy B as well.
3
, Properties of association rules
The support (or prevalence) of association rule A ⇒ B is the relative frequency of the rule.
It’s the probability of simultaneously observing A and B in a randomly selected market basket,
so Pr(A,B).
number of transactions containing A and B
supp(A ⇒ B) =
total number of transactions
Note that this is the support of an association rule. The support of just an item (set) A is defined as:
number of transactions containing A / total number of transactions.
The confidence of association rule A ⇒ B is the conditional probability of B given A, so
Pr(B|A). It is the likelihood of item B being purchased when item A is purchased.
number of transactions containing A and B
conf(A ⇒ B) =
number of transactions containing A
▪ If conf = 1 : B is always purchased when A is purchased.
▪ If conf = 0 : B is never purchases when A is purchased.
Drawback: The confidence for an association rule having a very frequent consequent (B) will
always be high, even if the antecedent (A) is not frequent. Because of this, a rule containing
two items that actually have a weak association may still have a high confidence value.
To overcome this challenge, lift is introduced.
The lift of association rule A ⇒ B calculates the conditional probability of item B given A,
while controlling for the support (frequency) of B.
number of transactions containing A and B / number of transactions containing A
lift(A ⇒ B) =
number of transactions containing B
In other words:
the rise in the probability of having B in the transaction because of the knowledge that A is present
lift(A ⇒ B) = the probability of having B in the transaction without any knowledge about the presence of A
▪ If lift = 1 A and B are independent.
▪ If lift > 1 A and B often occur together.
▪ If lift < 1 A and B are substitutes to each other. The presence of one item has a
negative effect on the presences of the other item.
Lift can be seen as the “strength” of the rule.
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