Enhancing Cubes with Models to Describe Multidimensional Data

Abstract

The Intentional Analytics Model (IAM) has been recently envisioned as a new paradigm to couple OLAP and analytics. It relies on two basic ideas: (i) letting the user explore data by expressing her analysis intentions rather than the data she needs, and (ii) returning enhanced cubes, i.e., multidimensional data annotated with knowledge insights in the form of interesting model components (e.g., clusters). In this paper we contribute to give a proof-of-concept for the IAM vision by delivering an end-to-end implementation of describe, one of the five intention operators introduced by IAM. Among the research challenges left open in IAM, those we address are (i) automatically tuning the size of models (e.g., the number of clusters), (ii) devising a measure to estimate the interestingness of model components, (iii) selecting the most effective chart or graph for visualizing each enhanced cube depending on its features, and (iv) devising a visual metaphor to display enhanced cubes and interact with them. We assess the validity of our approach in terms of user effort for formulating intentions, effectiveness, efficiency, and scalability.

Keywords: Data exploration; Models; Multidimensional data; OLAP.

Fig. 1

The IAM approach: the user expresses an intention and receives in return an enhanced cube

Fig. 2

The enhanced cube resulting from the intention in Example 1; the highlight is in red

Fig. 3

Roll-up lattices (left) and an excerpt of the part-of partial order (right) for the SALES cube in Example 2

Fig. 4

An excerpt of the multidimensional lattice for the SALES cube

Fig. 5

Cubes C₁ (left), C₂ (top-right), and C₃ (bottom-right) in Example 6; in red the highlights for the top-1 model, in green some of the proxy inter-cell relationships

Fig. 6

Cubes C₁ (left) and C₂ (right) in Example 9; in red the highlight for the top-1 model, in green some of the proxy inter-cell relationships

Fig. 7

Results on the 30 (left) and 300 (right) samples data for Kneedle (columns 1 and 3) and L-method (columns 2 and 4)

Fig. 8

Chart types: multiple line graph (a), radar chart (b), heat map (c), grouped column chart (d), bubble chart (e), scatter plot (f), and parallel line chart (g); in orange and blue, the different components of the related models

Fig. 9

The visualization obtained for the intention in Example 11

Fig. 10

Average cumulative highlight coverage at different session steps for the 1-facet and 3-facets interestingness measures

Fig. 11

Execution times for increasing cardinalities of the base cube