Outline on “AGGREGATION AND RANKING METHOD”
The profusion of information which we notice today in all fields can lead to misinterpretation of
results. So, the need of advanced mathematical and statistical tools proves essential in order to extract
relevant information. In this way, we find in all fields some complex phenomena which can be traced
only by a multitude of variables, each illustrating just one feature and only all together can be
accounted for. Also, often these variables retroact by feedback phenomena which is specific to each
case. For a better appreciation, comprehension, decision or arbitration and deliberation, analysts have
a great need for classification and arrangement of their data through the construction of an aggregate
synthetic variable granting a total mark for each individual (Firm, bank, financial assets, country, area,
patient, site,…) without loss of data. The traditional data analysis methods employed in this field
(ACP, AFC, AFM…) reach their limits and leave behind them many insufficiencies.
Hence, comes the interest of our method which is based on a neuronal approach and which provides
immense advantages compared to the preceding ones as regards to its faculties. We have succeeded in
developing a new technique allowing the construction of an aggregate indicator starting from a data
base of several variables and with the assistance of the Self-organizing Maps.
Our method proceeds in three stages:
- First, CFAR-m realizes self-organization of items into homogeneous subsets (clustering), through a
learning process that takes into account the positive and negative interactions.
- Second, an appropriate weights vector is determined for each item.
- Finally, the weighting vectors are applied to original data to calculate the composite indicator and
make the overall ranking. The weighting system can be characterized as objective since it emanates
from the informational content of the variables themselves and their internal dynamics.
This last feature of the CFAR method represents an invaluable step forward and a real surpassing of
what has been done so far in terms of classification - aggregation, especially that it does not lose any
information (the traditional methods provide an estimate by smoothing data) and it can be especially
adapted to very broad data bases (of qualitative and/or quantitative nature). The CFAR method solves
a major concern of the problems of aggregation in which the question of the importance of each
variable always arises. It breaks with the usual procedures of aggregation based on too simplified
assumptions and resulting in considering, for each variable, an identical weighting for all the
individuals in the sample. Then, the weighting released by the CFAR method emanates from the
informational contents of the same variables and of their internal dynamics. It thus avoids the
adoption either of an equiponderation or of weightings established on hexogen criteria (dispersions of
the variables at the entry, for example) or subjective estimates (which result from the opinion of a
certain number of experts in the field concerned).
There are so many application fields covering all aspects: Economic, Social, Financial, Medical,
Geo-strategic, Aerospatiale, Ecological, etc.