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Table . . Partition of units into homogeneous groups
partitions into groups
Partition
Partition
Partition
Table . . Stable groups: distribution of units
Stable groups: cardinalities in decreasing order
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-
-
-
-
Total
Table . shows the cardinality of the groups of the successive partitionings.
In fact, this is only the first step to follow in order to pursue stable groups. he three
partitionings are then cross-tabulated, resulting in a subdivision of the objects
into
cells. he individuals in each of these cells are those who have al-
ways been grouped together in the three partitionings. hey constitute the potential
stable groups. In fact, only groups are not empty, and out of these groups
contain less than individuals. he distribution of the individuals is given in Ta-
ble . . In practice the number of stable groups with substantial cardinality is always
much smaller than the number of cells resulting from crossing the basic partitions
(in the example, only cells among have more than individuals, compared to
cells that have less than individuals, while all the others are empty). In its first
phase,the methodpresented belowusesa partitioning technique that is designed for
large data tables. he groups obtained from this phase are then clustered through an
agglomerative algorithm. his method combines the advantages of both approaches,
namely:
. he ability to treat very large matrices;
. A detailed description of the main clusters;
. he ability to make a critical choice with respect to the number of clusters.
=
Mixed Strategy for Very Large Datasets
4.6.2
When a large number of objects are to be classified, the following classification strat-
egy will be used. he idea is to combine the two approaches presented above: find-
ing a partition and then building a classification tree. he first step is to obtain, at
alowcost,apartitionofthen objects into k homogeneous groups, where k is far
greater than the “expected” number of groups in the population (say k
=
when
n
=
, ). he second step is an ascending hierarchical classification, where the
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