FIRE: a two-level interactive visualization for deep exploration of association rules

Abstract

While rule mining is critical for decision-making applications, rule mining systems still lack support for interactive exploration of multitude of generated rules and understanding of relationships among rule results produced with various parameter settings. Based on a novel parameter space-driven approach, our proposed Framework forInteractiveRuleExploration [FIRE (PARAS/FIRE homepage: http://paras.cs.wpi.edu/)] addresses this usability shortcoming. FIRE features innovative visual displays and interactions to enable interactive rule exploration. We propose two linked interactive displays, namely the parameter space view (PSpace) and the rule space view (RSpace) that together enable enhanced sense-making of rule relationships. The PSpace view visualizes the distribution of rules produced for diverse parameter settings. This not only facilitates user parameter selection for rule mining but also enhances an analyst’s understanding of rule relationships in the parameter space context. The RSpace view provides a detailed display of the rules using a novel rule glyph visualization to facilitate interactive visual rule comparisons. We evaluate the usability and effectiveness of our FIRE framework with two studies. First, in a case study a researcher explored a dataset of interest using the FIRE paradigm as well as the state-of-the-art rule visualization techniques from the ARulsViz R package. Further, our user study with 22 subjects establishes the usability and effectiveness of the proposed visual displays and interactions of FIRE using several benchmark datasets. Overall, this research encompasses significant contributions at the intersection of data mining and visual analytics.

Appendix

1.1 Preprocessing of the bike sharing dataset

The Bike Sharing dataset [29] was preprocessed before loading into FIRE [11] and R ARulesViz [14], as described below.

Fig. 45

Original casual user count

Fig. 46

Original Registered User Count

Fig. 47

Adjusted casual user count

Fig. 48

Adjusted registered user count

Table 3 Discretized attributes: bike sharing dataset

Fig. 49

Adjacency lattice example

• 1. Data corresponding to three of the attributes was eliminated. The attributes are instant (unique identifier), dteday (date) and yr (contains 2 values: year 1 and year 2).

• 2. The casual and registered users increased over time. In particular, the casual users increase at 0.895 users per day, whereas the registered users increase at a rate of 4.874 users per day. To cancel the effect of the overall growth, the data was rotated to negate the slope of the trend lines. In Figs. 45 and 46, we show the original user counts, and in Figs. 47 and 48 we show the adjusted user counts for the casual and registered users categories. This processing is similar in flavor to season trend decomposition in [8].

• 3. Further, the attributes were discretized as shown in Table 3.

1.2 Association rules and redundancy

An adjacency lattice (Fig. 49) denotes items such as X, Y and Z. The support value of each item (say, X) or itemset (say, XY) indicates the total instances of the item or itemset in the dataset. For example, in a set of 100 records, X occurs in 80 and Y in 60 records. Itemset XY has a support of 40 records. For a rule $R = (X \longrightarrow Y$), its confidence can be represented as confidence $(R) = \frac{\hbox {support}(X \cup Y)}{\hbox {support}(X)}$.

Table 4 Redundancy in generated association rules

Aggarwal et al. [1] define rule redundancy relationships, such that redundant rules may be filtered out to present succinct results to the user. The redundant rules could always be derived on demand, if so desired. We examine how these redundancy relationships can be identified in the parameter space model. In particular, redundancy can be of two types [1], as defined below.

Definition 1

Simple redundancy Let $A \Rightarrow B$ and C$\Rightarrow D$ be two rules such that the itemsets A, B, C and D satisfy the condition $A \cup B = C \cup D$. The rule $C \Rightarrow D$ is simply redundant with respect to the rule $A \Rightarrow B$, if $C \supset A$.

Definition 2

Strict redundancy We consider two rules generated from itemsets $X_{i}$ and $X_{j}$, respectively, such that $X_{i} \supset X_{j}$. Let $A \Rightarrow B$ and $C \Rightarrow D$ be rules satisfying $A \cup B = X_{i}$, $C \cup D = X_{j}$, and $C \supseteq A$. Then the rule $C \Rightarrow D$ is strictly redundant with respect to the rule $A \Rightarrow B$.

The concept of redundancy can be illustrated using the rules generated from the lattice (Fig. 49) as listed in Table 4. Based on Definitions 1 and 2, if a rule $\mathcal {R}_{1}$ is simple or strict redundant with respect to another rule $\mathcal {R}_{2}$, then $\mathcal {R}_{2}$ is said to simple or strict dominate$\mathcal {R}_{1}$, respectively. In Table 4, the rule ($X \Rightarrow YZ$) simple dominates the rules ($XY \Rightarrow Z$) and ($XZ \Rightarrow Y$) (Def. 1). In Table 4, the rule ($X \Rightarrow YZ$) strict dominates rules ($X \Rightarrow Y$) and ($X \Rightarrow Z$) (Def. 2). In general, a rule may be dominated by several dominating rules and may in turn dominate several other dominated rules.