Explain discretization and concept hierarchy generation for numeric data.

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 Discretization and Concept Hierarchy Generation for Numeric Data

It is difficult and laborious to specify concept hierarchies for numeric attributes due to the wide diversity of possible data ranges and the frequent updates if data values. The manual specification also could be arbitrary. Concept hierarchies for numeric attributes concept can be constructed automatically based on data distribution analysis. Five methods for hierarchy generation are defined below:

  • Binning
  • Histogram analysis
  • Entropy-based discretization
  • Data segmentation by natural partitioning

a) Binning

Attribute values can be discretized by distributing the values into bins and replacing each bin with the mean bin value or bin median value. These techniques can be applied recursively to the resulting partitions in order to generate concept hierarchies.

b) Histogram Analysis

Histograms can also be used for discretization. Partitioning rules can be applied to define the range of values. The histogram analyses algorithm can be applied recursively to each partition in order to automatically generate a multilevel concept hierarchy, with the procedure terminating once a pre-specified number of concept levels have been reached. A minimum interval size can be used per level to control the recursive procedure. This specifies the minimum width of the partition or the minimum member of partitions at each level.


c) Cluster Analysis

A clustering algorithm can be applied to partition data into clusters or groups. Each cluster forms a node of a concept hierarchy, where all noses are at the same conceptual level. Each cluster may be further decomposed into sub-clusters, forming a lower level in the hierarchy. Clusters may also be grouped together to form a higher-level concept hierarchy.


d)Segmentation by natural partitioning

Breaking up annual salaries in the range of into ranges like (Rs.50,000-Rs.100,000) are often more desirable than ranges like (Rs.51, 263, 89-Rs.60,765.3) arrived at by cluster analysis. The 3 - 4-5 rule can be used to segment numeric data into relatively uniform natural intervals. In general, the rule partitions a given range of data into 3,4,or 5 equality intervals, recursively level by level based on value range at the most significant digit. The rule can be recursively applied to each interval creating a concept hierarchy for the given numeric attribute.

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