Recognition of the Purchasing Intentions of WeChat Users Based on Forgetting Curve

To recognize the purchasing intentions of WeChat users, the key is to determine users’ intentions through analysis on the chat data. There is little report on the recognition of the purchasing intentions among WeChat users, because the research on WeChat data mining is still in its infancy. Nevertheless, the economic benefits of WeChat-based intention recognition have attracted wide attention from the industry and academia [3]. For instance, the intention recognition helps the sellers understand the users’ demand and make accurate recommendations to the users.

Through its research on major industries in the US, Double Click Inc. Doub leC lick Search found that most consumers tend to search for and discuss about the items they want to buy on the Internet before purchasing these items (Doub leC lick Search before the Purchase-Understanding Buyer Search Activity as it Builds to Online Purchase: http//www.doubleclick.com/insight/pdfs/searchpurchase_0502.pdf). Goldberg et al. [4] proposed the concept of “buy wish”, a.k.a. the purchase intention, and acquired the purchase intentions of users from their shopping lists and comments on the items. Zhang and Nasraoui [5] combined the query flow graph and the text into a new query recommendation algorithm. Kooti et al. [6] suggested that people’s consumption behaviour is affected by age, gender and other factors.

With the boom of social networking and chat apps in recent years, WeChat, Weibo and Twitter have become the main tools for young people to release and exchange information. Yang and Li [7] collected the product information of people’s daily necessities and their hashtags in Twitter, and recognized users’ purchasing intentions through template matching. Considering the huge amount of data and the lack of tags, Liu et al. [8] designed a sorting algorithm based on weakly supervised graphs for intention recognition.

Unlike the traditional ways to recognize purchasing intentions, this paper conducted recognition of the chat data of WeChat in view of the popularity of new media among the masses. Meanwhile, the forgetting curve was adopted to recognize the purchasing intentions revealed in the chats between WeChat users, considering the impacts of interest drift [9].

4.1 Forgetting curve model

The German psychologist Ebbinghaus was the first to study human forgetting law through scientific experiments. The natural forgetting curve of human beings is named as the Ebbinghaus forgetting curve after him. The forgetting law is shown in Table 1 below.

Table 1. The forgetting law

Zeng et al. [11] mathematically analysed the forgetting law, and fitted the law of human forgetting curve with a negative exponential curve. The resulting function expression is:

$\text{p}\left( t,k \right)={{p}_{0}}{{e}^{-kt}}\left( t>0 \right)$ (1)

where, k is the attenuation rate; p₀ is the initial memory value.

When users chat frequently in a short time, their purchasing intention of an item is considered as attenuating at a constant rate, i.e. the attenuation of the intention conforms to the attenuation law of a single memory curve. Hence, the strength of user a’s purchasing intention of item p_i at time t_n can be expressed as:

$S_{\text{a}}^{{}}({{t}_{n}},{{p}_{i}})={{S}_{\text{a}}}({{t}_{0}},{{p}_{i}})*{{e}^{-{{k}_{a}}{{t}_{n}}}}+\overset{\to }{\mathop{{{K}_{{{\text{t}}_{n}}}}}}\,\overset{{}}{\mathop{\cdot \overset{\to }{\mathop{{{P}_{{{t}_{n}}}}}}\,}}\,\cdot {{e}^{-n}}({{t}_{n}}>{{t}_{0}})$  (2)

${{S}_{\text{a}}}({{t}_{0}},{{p}_{i}})=\overset{\to }{\mathop{{{K}_{\text{t}{}_{0}}}}}\,\cdot \overset{\to }{\mathop{{{P}_{{{\text{t}}_{0}}}}}}\,$  (3)

Equation (3) shows the user a’s purchasing intention of item p_i at time t_o, i.e. in the initial phase. Let K be the set of the user’s keywords extracted at time t_o and P be the set of items the user is interested in. Then, the user’s purchasing strength at time t_o can be obtained based on K and P. The user’s purchasing strength at time t_n can be determined through the same steps. In addition, let k_a be the forgetting rate of user a. The forgetting rate differs from user to user, because of the user difference in repeated learning. A user may be interested in an item at some point due to a stimulant, but the interest level will decline over time. If the same stimulant occurs, user a’s interest in the item will gradually decrease and approach a constant value. Here, the incremental stimulation of a keyword to the purchasing intention of an item is adjusted via e^-n  under the stimulant of $\overrightarrow{K}·\overrightarrow{P}$. Note that n∈(0,1,2,3...)=N-1, with N being the number of cumulative time points.

4.2 Multi-stage quantification of intention strength

The forgetting curve can reflect the change of human memory value, but only that in a single time period. It cannot be directly applied to describe users’ purchasing intentions revealed in chats. If a user is desirous of purchasing an item, he/she will talk about many topics on the items continuously. In this case, the chat is frequent in the short term and continuous in the long term. In another case, an item is not mentioned throughout the chat because it does not attract the user’s interest. However, the item might be mentioned suddenly on another day. Thus, a multi-stage quantification method was proposed for intention strength by adding these situations into the forgetting curve [12].

The user’s chat on the same topic at different times is equivalent to the repeated learning of an interest. Thus, the moment of repeated learning is the time when the keyword is mentioned again. Let t₁, t₂ and t₃ be the moments of repeated learning. Then, the change of user intention can be illustrated as Figure 1 below.

As shown in Figure 1, the repeated learning can be divided into multiple stages. Each stage represents a new process of natural forgetting, and has a unique forgetting rate and initial memory value. To measure the real-time purchasing intention, it is necessary to determine the initial memory value S(a,n) and forgetting rate k(a,n) of each stage.

figure_1.jpg

Figure 1. The change of user intention

It can be seen that the initial memory value S(a,n) of stage n+1 is higher than the final memory value of stage n-1. The difference between the two values is referred to the repeated learning increment. The initial memory value of stage n+1 can be expressed as:

$\text{S(a,n)}=\text{S(a,n-1)*}{{\text{e}}^{\text{-}{{\text{k}}_{\text{(a,n-1)}}}({{t}_{n}}-{{t}_{n-1}})}}+\overset{\to }{\mathop{{{K}_{{{\text{t}}_{n}}}}}}\,\cdot \overset{\to }{\mathop{{{P}_{{{t}_{n}}}}}}\,\cdot {{e}^{-n}}$ (4)

It can be seen from Figure 1 that the curve of forgetting rate k(a,n) can be overlapped with the curve of forgetting rate k(a,n-1)  after moving to the lower left. Therefore, the relationship between the two curves can be obtained from that between k(a,n) and k(a,n-1) . The height difference β between the two curves can be determined by moving the initial point of the curve for stage n+1 to that of the curve for stage n in Figure 1. The value of β can be calculated as:

$\beta =S(a,n-1)\left[ {{e}^{-{{k}_{(a,n)}}({{t}_{n}}-{{t}_{n-1}})}}-{{e}^{-{{k}_{(a,n-1)}}({{t}_{n}}-{{t}_{n-1}})}} \right]$  (5)

From the nature of the exponential function, the maximum value of β can be determined as $β=S(a,n-1)[1-e^{-k_{a,n-1}t_n-t_{n-1}}]$. Assuming that $η=t_n-t_{n-1}$, we have:

$\text{k}(a,n)=\frac{\ln \left( \frac{\beta }{{{S}_{(a,n-1)}}}+{{e}^{-{{k}_{(a,n-1)}}\eta }} \right)}{-\eta }$ (6)

The above equation shows that the value of k(a,n) can be determined based on the value of β. In addition, the adjustment degree of the forgetting rate in each repeated learning, denoted as $\theta$, should also be known. The value of $\theta$ is positively correlated with the time gap between two adjacent repeated learning processes, i.e. the interval between a user’s mentioning of the same item. Here, $\theta$ is called the inertia factor, because its value reflects how lazy a user is to mention an item. Then, the maximum value of β can be divided into $\theta$ segments:

$\beta =\frac{S(a,n-1)\left[ 1-{{e}^{-{{k}_{(a,n-1)}}({{t}_{n}}-{{t}_{n-1}})}} \right]}{\theta }$  (7)

Substituting equation (7) into equation (6), we have the expression for k(a,n) :

$\text{k}(a,n)=\frac{\ln \left[ 1+(\theta -1){{e}^{-{{k}_{(a,n-1)}}\eta }} \right]-\ln \theta }{-\eta }$ (8)

The value of k(a,n) can be determined when the following parameters are known, including the forgetting rate k(a,n-1) , the time segment η and the inertia factor $\theta$. Then, the strength of the purchasing intention of each stage can be obtained.