Data Mining: Concepts and Techniques, 3rd Edition

5.6 Exercises

5.1 Assume that a 10-D base cuboid contains only three base cells: (1) (a₁, d₂, d₃, d₄, …, d₉, d₁₀), (2) (d₁, b₂, d₃, d₄, …, d₉, d₁₀), and (3) (d₁, d₂, c₃, d₄, …, d₉, d₁₀), where a₁ ≠ d₁, b₂ ≠ d₂, and c₃ ≠ d₃. The measure of the cube is count().

(a) How many nonempty cuboids will a full data cube contain?

(b) How many nonempty aggregate (i.e., nonbase) cells will a full cube contain?

(c) How many nonempty aggregate cells will an iceberg cube contain if the condition of the iceberg cube is “count ≥ 2”?

(d) A cell, c, is a closed cell if there exists no cell, d, such that d is a specialization of cell c (i.e., d is obtained by replacing a ∗ in c by a non-∗ value) and d has the same measure value as c. A closed cube is a data cube ...