## 4 Results
### Evaluation of the ALDA Model
#### 4.2.2 User's Preference Prediction  
We utilize perplexity to compare the accuracy of predicting users' content preference drift estimated by these models. As perplexity in information theory is a measure that is often used to judge probability models or probability distribution prediction samples, we utilize perplexity to evaluate the effect of user's preference inferred by each model. The ability of perplexity is to predict words in new documents, which are not observed. The smaller the value of perplexity, the better the performance of the model in mining user's intention. _Perplexity_ can be calculated as follows:  
\[Perplexity_{portion}(\mathcal{M})=\left(\sum_{d=1}^{D}\sum_{i=P+1}^{N_{d}}p(w_ {i}|\mathcal{M},w_{1:p})\right)^{-\frac{1}{\sum_{d=1}^{D}(N_{d}-p)}}\]  
where \(\mathcal{M}\) is the set of model parameters learned from the training set, \(d\) represents the document, and \(N_{d}\) is the number of words in the document.  
To make the experimental results more reliable, we sample the observed in the AOL dataset at different scales (from 10% to 90%). It can be seen from Figure 4 that the perplexity of each model gradually decreases with the expansion of the percentage of the observed data. This shows that each model gets better at predicting consumer preferences with the growth of the observed data. Compared with the other five models, the perplexity degree of our ALDA model is the smallest, from 1100 to 2500, which indicates that ALDA preforms best among the six models for identifying consumer interests. This is because ALDA models the interactive relationship between queries and webpages. In reality, a consumer's shopping process is actually a process of understanding and evaluating products. First, users may enter inaccurate keywords to express their needs. Then, users enhance their understanding of products through browsing the search results and adjusting the input keywords. Consumers will repeat this learning process until finding the right product.  
Figure 3: PMI score of each model on AOL query log dataset.  
That is to say, the topics of query keywords and the topic of search results are semantically related to each other. Thus, modeling this interaction between queries and webpages helps us to more accurately capture changes in consumer's interests and preferences. This is the fundamental reason our model is better than other models in identifying consumers' purchase intentions.  
As LDA and Twitter-BTM do not model how the topics in search queries relate to the topics in the corresponding search results, they obtain the worst performance on understanding users' preference. Both UCTI and UATM learn the topic distributions in the user's content and followees' content, which enables extensive mining and understanding of user's preference and intention, and the experimental results also confirm that UCIT and UATM significantly perform better than LDA and Twitter-BTM. HDLDA models query the document and the webpage document in two hierarchical LDA processes, and they assume that the query document is semantically related to the webpage document, which contributes to a slight lead over UCIT and UATM in understanding the user's interest. Although HDLDA produces good results, it performs worse than ALDA. This is due to HDLDA failing to capture the interactive relationship between queries and webpages. In summary, our ALDA model always outperforms the other comparison models on predicting consumers' purchase intentions.