Disclosed are MNAR data analysis methods and apparatuses for analyzing user preference data on products. Also, a product recommendation system using the same is disclosed. A data analysis method based on a binomial mixture model comprises defining a binomial mixture model based data generation model for analyzing user preference data on products; defining a missing data mechanism model for explaining observation and missing of user preference data on the products; learning the data generation model and the missing data mechanism model based on observed user preference data on the products; and determining final preferences on products whose preferences are missing based on the learned data generation model and the learned missing data mechanism model.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A missing not at random (MNAR) data analysis method based on a binomial mixture model, the method comprising: defining a binomial mixture model based data generation model for analyzing user preference data on products; defining a missing data mechanism model for explaining observation and missing of user preference data on the products; learning the data generation model and the missing data mechanism model based on observed user preference data on the products; and determining final preferences on products whose preferences are missing based on the learned data generation model and the learned missing data mechanism model. 2. The method according to claim 1, wherein the binomial mixture model based data generation model is defined based on assumption that users are grouped into a plurality of groups having similar preferences, assumption that user preferences on products follow a binomial distribution model, and assumption that users belonging to a same group share parameters of the binomial distribution model. 3. The method according to claim 1, wherein the missing data mechanism model is based on three factors including user activities, popularities of products, and rating value based selection effects, and the three factors are represented as binary variables, and wherein whether a specific user's preference on a specific product is observed or missing is determined through a Boolean OR operation on the three factors. 4. The method according to claim 1, wherein the learning the data generation model and the missing data mechanism model comprises: representing a posterior distribution of random variables constituting probability models of the data generation model and the missing data mechanism model as multiplication of parametric functions respectively defined for the random variables through mean field approximation based on variational inference; extracting a lower-bound function of marginalized log likelihood for observed variables based on the parametric functions; and learning parameters of the parametric functions maximizing the extracted lower-bound function. 5. The method according to claim 4, wherein, in the learning parameters of the parametric functions, a plurality of parameters included in the parametric functions are sequentially updated until a change amount of the lower-bound function of marginalized log likelihood becomes less than a threshold. 6. The method according to claim 1, further comprising analyzing a trend of the observed user preference data based on the learned data generation model and missing data mechanism model. 7. A missing not at random (MNAR) data analysis method based on a binomial mixture model, the method comprising: defining probability models for analyzing the MNAR data and defining an analysis model by assigning a posteriori distribution to variables constituting the probability models; learning the analysis model through a variational inference for respective variables constituting the analysis model; and predicting missing data based on the learned analysis model, wherein the probability models include a binomial mixture model based data generation model and a missing data mechanism explaining observation and missing of user preference data on products. 8. The method according to claim 7, further comprising determining final preferences on products whose preferences are missing based on the predicted missing data. 9. The method according to claim 7, further comprising analyzing a trend of observed user preference data based on the predicted missing data. 10. The method according to claim 7, further comprising transmitting product recommendation information including final preferences determined for products whose preferences are missing based on the predicted missing data or product recommendation information including a trend of observed user preference data analyzed based on the predicted missing data. 11. A data analysis apparatus for analyzing missing not at random (MNAR) data based on a binomial mixture model, the apparatus comprising: a memory unit storing a program code; and a processor which is connected to the memory unit and executes the program code, wherein the program code includes a step of defining probability models for analyzing the MNAR data and defining an analysis model by assigning a posteriori distribution to variables constituting the probability models; a step of learning the analysis model through a variational inference for respective variables constituting the analysis model; and a step of predicting missing data based on the learned analysis model, wherein the probability models include a binomial mixture model based data generation model and a missing data mechanism explaining observation and missing of user preference data on products. 12. The apparatus according to claim 11, wherein the program code further comprises a step of determining final preferences on products whose preferences are missing based on the predicted missing data. 13. The apparatus according to claim 11, wherein the program code further comprises a step of analyzing a trend of observed user preference data based on the predicted missing data. 14. The apparatus according to claim 11, wherein the program code further comprise a step of transmitting product recommendation information including final preferences determined for products whose preferences are missing based on the predicted missing data or product recommendation information including a trend of observed user preference data analyzed based on the predicted missing data. 15. A product recommendation system including a service apparatus for analyzing missing not at random (MNAR) data based on a binomial mixture model, wherein the service apparatus defines probability models for analyzing the MNAR data and defining an analysis model by assigning a posteriori distribution to variables constituting the probability models, learns the analysis model through a variational inference for respective variables constituting the analysis model, and predicts missing data based on the learned analysis model, and wherein the probability models include a binomial mixture model based data generation model and a missing data mechanism explaining observation and missing of user preference data on products. 16. The product recommendation system according to claim 15, wherein the service apparatus transmits, to a terminal in a network, product recommendation information including final preferences determined for products whose preferences are missing based on the predicted missing data or product recommendation information including a trend of observed user preference data analyzed based on the predicted missing data. 17. The product recommendation system according to claim 15, wherein the service apparatus defines the binomial mixture model based data generation model based on assumption that users are grouped into a plurality of groups having similar preferences, assumption that user preferences on products follow a binomial distribution model, and assumption that users belonging to a same group share parameters of the binomial distribution model. 18. The product recommendation system according to claim 17, wherein the service apparatus defines the missing data mechanism model based on three factors including user activities, popularities of products, and rating value based selection effects, and the three factors are represented as binary variables, and wherein whether a specific user's preference on a specific product is observed or missing is determined through a Boolean OR operation on the three factors. 19. The product recommendation system according to claim 15, wherein the service apparatus represents a posterior distribution of random variables constituting probability models of the data generation model and the missing data mechanism model as multiplication of parametric functions respectively defined for the random variables through mean field approximation based on variational inference, extracts a lower-bound function of marginalized log likelihood for observed variables based on the parametric functions, and learns parameters of the parametric functions maximizing the extracted lower-bound function.