|Title:||Using the Real Dimension of the Data|
|Series:||Linköping Electronic Articles
in Computer and Information Science
|Issue:||Vol. 5 (2000), No. 004|
|Abstract:|| This paper presents a method for extracting the real dimension
of a large data set in a high-dimensional data cube and indicates its use
for visual data mining. A similarity measure structures a data set in a
general, but weak sense. If the elements are part of a high-dimensional
host space (primary space), for instance a data warehouse cube, the resulting
structure doesn't necessarily reflect the real dimension of the embedded
(secondary) space. We show that a metric-structured set has, in general,
a fractal dimension. This means that the data set is a finite subset of
a fractal secondary space of lower dimension.
Mapping the set into the secondary space of lower dimension will not result in loss of information with regard to the semantics defined by the measure. However, it helps to reduce storage and computing efforts. Additionally, the secondary space itself reveals much about the set's structure and can facilitate data mining.
The main problem with the secondary space is that it is unknown, and
if it is not a linear sub-space of
|In ETAI area "Concept Based Knowledge Representation"|
| Original publication
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