# Booming Up the Long Tails: Discovering Potentially Contributive Users in Community-Based Question Answering Services

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4 Step 1 Expertise(u 1 ) u 1 Step 2 Step 3 Step 4 Estimated Expertise(u n+1 ) w 1, w 2, w 4, w 6 WordLevel(w 1 ) w 1, w 3, w 4, w 5 u n+1 Expertise(u 2 ) u 2 Vocabulary w 2, w 4, w 6, w 7 WordLevel(w 2 ) w 3, w 4, w 5, w 8 Estimated Expertise(u n+2 ) u n+2. Expertise(u n ) u n w 1, w 3, w 6, w 8 WordLevel(w 3 ). WordLevel(w n ) w 2, w 3, w 6, w 8. Estimated Expertise(u n+k ) u n+k WordLevel(w i ) Heavy Users U H Light Users U L Figure 3: The overall procedure of predicting the expertise of a light user. Measurement of Availability The second component, availability, is simply the number of a user s answers with their importance proportional to their recency. Figure 4 intuitively describes this concept: each bar represents an answer, and the height indicates its importance. Thus, the availability of a light user u l, denoted by Availability(u l ), should have the property in Property 4. Importance Availability(u a ) < Availability(u b ) u b u a Answers Timeline Present Figure 4: An intuitive illustration of availability. Property 4. The availability of a user becomes higher as the user wrote more answers at the time closer to the present. Detailed Methodology In this section, we formalize our methodology informally presented in the previous section. Table 2 lists the measures that will be formally defined in this section. Table 2: The notation used throughout this paper. Notation Description Affordance(u l ) Expertise(u h ) EstimatedExpertise(u l ) W ordlevel(w i) Availability(u l ) the answer affordance of a light user the expertise of a heavy user the estimation of the expertise of a light user the word level of a usable word the availability of a light user Answer Affordance The answer affordance of a light user u l is defined as Eq. (1), reflecting Property 1. Here, w a (0 w a 1) is a balancing factor, and its suitable value depends on the context and data set. EstimatedExpertise(u l ) is defined in the subsection Expertise, and Availability(u l ) in the subsection Availability. Affordance(u l ) =w a EstimatedExpertise(u l )+ (1 w a) Availability(u l ) Expertise As shown in Figure 3, EstimatedExpertise(u l ) is obtained through four steps. All measures defined here will be made to have the range [0, 1] by min-max normalization unless a measure inherently has that range. Step 1: The expertise of a heavy user u h is defined through Eqs. (2) (4), reflecting Property 2. Here, w e (0 w e 1) is a balancing factor. Expertise(u h ) = w e Entropy(u h ) + (1 w e) Rating(u h ) (2) First, Entropy(u h ) is Eq. (3), which is basically the entropy of a user s interests. The more concentrated a user s answers are, the lower the entropy is. Here, we assume that there are only two categories the target category and one including all others since we are not interested in other than the target category. The entropy E(u h ) starts to decrease at P (c u h ) = 0.5. Hence, the entropy curve for P (c u h ) > 0.5 is flipped vertically such that Entropy(u h ) monotonically increases as P (c u h ) increases. (1 + (1 E(u h ))) if P (c target u h ) > 0.5 Entropy(u h ) = 2 E(u h ) otherwise 2 (3) E(u h ) = P (c u h ) log 2P (c u h ) c {c target,c others } (1) 605

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