Question

COURSE: Data Mining and Data Warehousing

Briefly explain the following:

1. Multiway Array Aggregation
2. Iceberg Cube

Answer 1

The Multiway Array Aggregation (or simply MultiWay) method computes a full data cube by using a multidimensional array as its basic data structure. It is a typical MOLAP approach that uses direct arrayaddressing, where dimension values are accessed via the position or index of their corresponding array locations.

Iceberg cube computation by top down multi way approach is an array aggregation which utilises shared computation and performs well on dense data.

MILTIWAY ARRAY AGGREGATION OF ICEBERG CUBE

• Array-based “bottom-up” algorithm
• Using multi-dimensional chunks
• No direct tuple comparisons
• Simultaneous aggregation on multiple dimensions
• Intermediate aggregate values are re-used for computing ancestor cuboids
• Cannot do Apriori pruning: No iceberg optimization

Multi-way Array Aggregation for Cube Computation (MOLAP)

●Partition arrays into chunks (a small subcube which fits in memory).

●Compressed sparse array addressing: (chunk_id, offset)

●Compute aggregates in “multiway” by visiting cube cells in the order which minimizes the # of times to visit each cell, and reduces memory access and storage cost.

Method: the planes should be sorted and computed according to their size in ascending order

●Idea: keep the smallest plane in the main memory, fetch and compute only one chunk at a time for the largest plane

●Limitation of the method: computing well only for a small number of dimensions

●If there are a large number of dimensions, “top-down” computation and iceberg cube computation methods can be explored