Providing Case-Based Retrieval as a Decision Support Strategy in Time Dependent Medical Domains - Computational Intelligence in Healthcare: Advanced Methodologies - page 203

in section 2, which will also describe some CBR contributions in the medical
field relying on these techniques.
On the other hand, our research group has recently proposed [32,31] to exploit
a different technique for dimensionality reduction, namely Temp ora l Abs t rac -
tions (TA) [46,6,40,30]. TA is an Artificial Intelligence (AI) methodology, which,
among the other things, has been employed for:
- supporting a flexible description of phenomena at different levels of time
granularity (e.g. hours, minutes, seconds);
- providing a knowledge-based interpretation of temporal data.
On the other hand, rather interestingly, TA have been scarcely explored for re-
ducing time series dimensionality, especially in the CBR literature. Instead we
have observed that, through TA, huge amounts of temporal information, like the
one embedded in a time series, can be effectively mapped to a compact repre-
sentation, that not only summarizes the original longitudinal data, but also ab-
stracts meaningful behaviours in the data themselves, which can be interpreted
by end users as well (in an easier way if compared to mathematical methods
outputs). TA-based dimensionality reduction appears to be well suited for sev-
eral application domains, and in particular for medical ones. TA for time series
dimensionality reduction and retrieval in a CBR context will be presented in
section 3. The section will also introduce a framework we are developing, which
relies on TA both for dimensionality reduction and for supporting multi-level
abstraction and retrieval, as well as flexible query answering. The approach will
be illustrated by means of a case study in haemodialysis.
Finally, section 4 will address conclusions and future work.
2 Mathematical Methods for Dimensionality Reduction
in Time Dependent Medical Domains
In this section, we will provide details of mathematical methods employed for
time series dimensionality reduction, and will describe a set of significant appli-
cations of these techniques in a CBR context.
2.1 Theoretical Background
A wide literature exists about similarity-based retrieval of time series. Several
different approaches have been proposed (see the survey in [17]), typically based
on the common premise of dimensionality reduction. As a matter of fact, a (dis-
cretized) time series can always be seen as vector in an n -dimensional space (with
n typically extremely large). Simple algorithms for retrieving similar time series
take polynomial time in n . Multidimensional spatial indexing (e.g. resorting to
R-trees [16]) is a promising technique, that allows sub-linear retrieval; neverthe-
less, these tree structures are not adequate for indexing high-dimensional data
sets [7].