Notes on:

    Roddick, J.F. and Spiliopoulou, M. (2002). 
    A Survey of Temporal Knowledge Discovery Paradigms and Methods.
    IEEE Transactions on Knowledge and Data Engineering 14(4):
    750-767.

The authors define different types of temporal data: Static,
Sequences, Time Stamped, and Fully Temporal. 

Static can be thought of as regular transactional data. There is
no temporal aspect to this data although it may have a transaction
time associated with it.

Sequences are ordered lists of events. They are not time stamped
collections of events. More expressive temporal relationships such as
meets, overlaps, etc. is allowed in this temporal data type.

Time Stamped data are sets of static data taken at regular intervals,
more or less, from the same set of metrics measured again and again.

Fully temporal data has each tuple (attribute-value pair, item),
associated with one or more dimensions of time. This can include
transaction time, an interval of validity, etc. Most of the work
covered in this survey address a single dimension, transaction time.

The input data set for ASAS can include any of these temporal data
types. 

ASAS handles regular transactional data although without some
manipulation of the data set it cannot make use of temporal
information. A simple transformation of regular transaction data which
takes the transaction times along a time line and the purchase of a
particular item, maybe by a particular customer if that data is
present, as an event, can produce a single instance in an ASAS data
set. Instances could be split further into any granularity of time,
depending on what the user wishes to accomplish. If left alone,
regular association rules will be produced.

ASAS handles plain sequences as defined in this survey. It also
handles time stamped data and fully temporal data. ASAS only addresses
one temporal dimension at one time. It is not restricted to any single
temporal dimension though, as long as it can be represented along a
time line. ASAS does not consider temporal relationships between
separate instances of the data set.

The authors say "Temporal association rules are particularly
appropriate as candidates for causal rules' analysis in temporally
adorned medical data..." The main motivation behind ASAS was causal
analysis in the computer system performance domain.

Although unrelated to my own work, a reference to T.D. Wade,
P.J. Byrns, J.F. Steiner, and J. Bondy, "Finding Temporal Patterns - A
Set Based Approach," Artificial Intelligence in Medicine, no. 6,
pp. 263-271, 1994. sounded like it might relate to Shoemaker's Apriori
Sets work.

In the section "Incorporating Temporal Concepts to Conventional
Classification Algorithms" the authors list some temporal semantics
that can be modeled. One of these, "Relative Time" deals with
incorporating more expressive temporal relationships as characterized
by Allen such as during, overlaps, etc. The authors say this is an
open problem. This survey was published in July/August 2002. Are there
any systems that do this besides ASAS? Considering ASAS has been
operational and in use since before this publish date it is a shame I
haven't managed to write a paper worth submitting for publication yet
(2003-11-17). Note: the authors do not mention Rainsford's and
Roddick's paper "Adding Temporal Semantics to Association Rules"
published in 1999 in which they propose an algorithm for mining such
rules. This is odd. Maybe they didn't have a working system?

Also in this section the authors define Multidimensional
Semantics. They say that research to date has assumed all recorded
events relate to a single time line, or dimension and with the same
clock. This is not the case for ASAS. The same time line is shared
only for the events occurring in a single instance of the data set.

This makes two temporal concepts identified by the authors that are
not addressed by work they summarize but that ASAS does.

In the section "Classification of Sequences of Events" the system
FeatureMine is mentioned. One heuristic "feature sets should not
contain redundant features" gives rise to two pruning rules. 1) no
feature showing an accuracy of 100% is specialized further. 2) two
features are correlated so that one always implies the other, then the
latter is removed. This made me think it might be possible to apply
similar logic to the rules produced by ASAS. Often simple, previously
known relationships appear frequently in rules and are of no
interest. After further thought, it seems best to not restrict the
associations to be found unless the user specifies such
restrictions. Mechanisms such as requiring attributes in the
consequence or antecedent and restricting the number of items
appearing in each is sufficient.

A very interesting point: "Moreover, it is pointed out that the
property of interestingness is not monotone since a pattern may be
interesting, even if its sub-patterns are not. Hence, all algorithms
building frequent episodes incrementally are inappropriate for the
discovery of interesting patterns." This is from the work of Berger
and Tuzhilin, "Discovering Unexpected Patterns in Temporal Data Using
Temporal Logic," Temporal Databases - Research and Practice, 1998.
In regards to ASAS which extends Apriori, this statement renders the
Apriori Principle impotent. 

Concluding, the authors mention again that extensions "to take the
temporal dimension into account" of algorithms for mining static data
is an open issue and should be addressed. Measures of interestingness
should also incorporate the temporal dimension. ASAS does both.

Some of these notes might be good to use in our motivation and
contribution sections.