Topic 4_1

• Data cube


  A lattice of cuboids, where the bottom-most cuboid is the base cuboid and the top-most cuboid (apex) contains only one cell

  
• Materialization of data cube

  1. Materialize every cuboid (full materialization)

  2. Materialize none (no materialization)

  3. Materialize some (partial materialization)
• Formula for calculating the number of cuboids in an n-dimensional cube with L levels

  
• Data Generalization


  A process of abstracting conceptual level knowledge from large set of task-relevant data in a database from a relatively low conceptual level to higher conceptual levels
• Descriptive data mining


  • Describes data in a concise manner, highlighting interesting general properties. Supports interest.
• Predictive data mining


  • Constructs a model and attempts to predict behavior of new data (classification, regression, etc.)
• MOLAP (Multidimensional Online Analytical Processing)


  Fast on-line analytical processing takes minimum time if aggregates for all the cuboids are precomputed
• Data Cube Materialization / Precomputation


  Precomputation of some of the cuboids in advance leads to fast response time and avoids redundant computations during on-line analytical processing
• Types of Data Cube Materialization


  • No materialization: Don't precompute any of the non-base cuboid
  • Full materialization: Precompute all the cubes
  • Partial Materialization: Selectively compute a proper subset of the cuboids

  
• Base cell


  A cell which belongs to a base cuboid
• Aggregate cell


  A cell which belongs to a non-base cuboid
• Ancestor-descendent relationship between cells


  An i-D cell a is an ancestor of a j-D cell b if: 1) i<j and 2) for 1≤m≤n, am=bm whenever am≠"*" and 3) if j=i+1, a is called parent of b or b is a child of a
• Full cube


  All cells and cuboids are materialized. All possible combination of dimensions and values.

  
• Iceberg cube


  Partial materialization. Materializing only the cells in a cuboid whose measure value is above the minimum threshold (Iceberg Condition: count(*) >= min support)
• Closed cube


  No ancestor cell is created if its measure is equal to that of its descendent cell
• Shell cube


  Only cuboids with limited number of dimensions are created
• Formula for calculating the number of cells in a full cube

  
• Iceberg cube


  A subset of a full cube that contains only the most significant data, excluding low-value or insignificant data points
• Closed cube


  Contains data for all possible combinations of dimensions, even if some intersections have no data associated with them
• Shell cube


  Contains only non-empty cells, meaning it stores data only for intersections of dimensions where data actually exists