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Chapter 3. Data Analysis and Visualization Modules
sample rule can be characterized by the fact that its body contains components or
production conditions, and its head an error state.
• The support of the pattern:
Absolute support S is defined as the total number of entities for which the rule holds.
Support or relative support s is the fraction of all entities for which the rule holds.
Note that this is different from the definition of support of an association pattern,
which is defined in terms of data groups (transactions), not in terms of entities.
• The confidence of the pattern when interpreted as a rule:
Confidence C is defined as
C := s(body →[dt]→ head) / s(body).
• The lift of the pattern:
The Lift L of a pattern Itemset1 →[dt1 ]→ ... →[dtn−1 ] Itemsetn is defined
as
L := s(Itemset1 →[dt1 ]→ ... →[dtn−1 ]→ Itemsetn ) / (s(Itemset1 ) *
... * s(Itemsetn )).
When interpreting the lift value of a sequence, we can not simply formulate in
analogy to what we have done for association patterns: lift > 1 (< 1) means that
the pattern appears more (less) frequently than expected assuming that all involved
items are statistically independent. The problem is that in the enumerator part of
the lift formula given above, we do not count all common occurrences of all involved
items but only the occurrences in the correct time order.Therefore, an interpretation
of lift values is difficult. One can, however, say that a lift value greater than 0.5
always stands for a positive correlation of the involved items in the given time
ordering. Apart from that, lift values should only be used for comparisons (this
sequence is more positively correlated than that sequence’), and these comparisons
should only be drawn between sequences of the same number of items and the same
number of time steps.
• The purity of the sequence pattern:
The purity P of a sequence Itemset1 →[dt1 ]→ ... →[dtn−1 ]→ Itemsetn is
defined as
P := s(Itemset1 →[dt1 ]→ ... →[dtn−1 ]→ Itemsetn ) / maxi=1...n ( s(Itemseti )
).
P = 1 means that the pattern describes a ’perfect sequence’: none of the parts
Itemseti ever occurs on any entity without all the other parts in the time ordering
defined by the sequence.
• The weight (cost,price) of the pattern:
If a weight field has been defined on the input data, we can calculate the weight
of a sequence as the average of summed weights of the entities which support the
sequence.