106 D. Anand, KK Bharadwaj/ Expert Systems with Applications 38(2011)5101-5109 prix=(1-x)*prik +a*prg (18) RMSE(山) to get the final prediction for the active user, where a can be set to any of the sparsity measures as given belot The rmse over all active users is the average of RMSE of individual Overall sparsity measure(OS)(Eq (8)). active users User-item specific sparsity measures(LGR, UIS1, UIS2)(Eqs. RMSE=N>RMSE(ur) (10)-(12) Unified measure of sparsity(UMS)(Eq (13)). Whereas the MAE weighs the individual differences equally, RMSE 5. Experiments and results gives relatively high weight to large errors. It is useful when large errors are particularly undesirable. It has been demonstrated in a In order to evaluate the performance of the recent study that a small difference in rMSE can lead to a very sig- ferent a estimates, based on various proposed nificant improvement when ordering items by their predicted pref- everal experiments are conducted on the ve lar Movie- erences(Koren, 2008) It is to be noted that for any Given x(x= 10, 15, 20, 25)configura- aim of these experiments is to show the superior performance of tions, only users having more than x ratings contribute to the error the proposed techniqu (Luo et al., 2008). the prediction methodologies under different data settings 5. 1. Experimental setup 5.2. Experiment 1 The MovieLens dataset consists of 100,000 ratings provided by In order to demonstrate the effectiveness of the various 943 users on 1682 movies. The ratings scale is in the range 1-5 sed a-estimation schemes, we conduct experiments using both with 1-"bad"to -excellent". The ratings are discrete. Each user datasets(ML300 and Jester300)to compare the performance of in the dataset has rated at least 20 movies. The jester dataset pro- the proposed schemes with both the fixed-a schemes, under the des 4.1 million ratings by 73, 421 users on 100 jokes. The ratings various aforementioned configurations. The parameter y in all experiments was set to 30. The number of nearest local and global are different from each other, since the overall sparsity of Movie- neighbors used for prediction (k) was restricted to 30 Lens is quite high whereas the jester dataset is quite dense. More- The prediction accuracy of the following schemes are over the number of items in MovieLens is much higher than the compared number of users, whereas in jester the users far exceed the number ixed- schemes of jokes. Testing the various prediction techniques on these two datasets allow for comparison under diverse data environments. Fixed-a scheme 1(Luo et al., 2008). For all the experiments 300 users were randomly selected from Fixed-ox scheme 2(Luo et al, 2008 ) both the MovieLens and jester datasets, the respective datasets being denoted as ML300 and Jester300 respectively The datasets Proposed schemes. were then divided into 200 training users and 100 active users. The ratings from the training users are utilized in order to predict . Overall sparsity (OS). ratings for the test users. The number of ratings provided by the Local global ratio(LGR). active user is varied as 10, 15 20 and 25 giving rise to four different User-item specific sparsity measure(UIS1). configurations Given10, Given15, Given20 and Given25 respec- tively. The training ratings are used as explicit ratings available, User-item specific sparsity measure(UlS2 thus aiding neighborhood construction as well as guiding the User specific sparsity measure(USS). learning process of the GA, whereas the test ratings are considered as ratings which are unavailable and hence need to be predicted. Tables 1 and 2 demonstrate the results of applying the various eighting schemes to ML300 and Jester 300 datasets. The results The ratings from the Jester dataset, were discretized by rounding illustrate the improved prediction quality of the a-estimation To compare the prediction quality of the proposed methods, we schemes based on user and item sparsity measures. All the pro- and Root Mean Squared Error(RMSE). MAE measures the average tions, outperform the fixed-z schemes under all configurations absolute deviation of the predicted rating of an item from the for both datasets, thus highlighting the importance of considering actual rating for the item. sparsity both at the user and item level, in order to weigh the pre- The mae(ui for the active user ui is as follows: dictions from local and global neighbors. For the ML300 dataset, the LGR scheme performs best, with the r owest MAe among all the proposed schemes under all configura tions, whereas UiS2 gives the least RMS g all schemes for the where Si is the cardinality of the test ratings set of same dataset. The measures OS and USs consistently perform The total mae over all the active users n worse than the other proposed schemes, but offer better prediction accuracy than the fixed-a schemes, both in terms of MAE and (20) RMSE. For the Jester300 dataset, the OS scheme performs the best in almost all configurations with the lowest MAE and RMSe, except Asma aller value of MAE signifies better prediction quality. a related for the Given 15 configuration when UiSI performs best, giving aracy metric is the rmse squares the error before sum- the least MAE. The USs measure performs the worst while still ming them. The RMsE(ui)for Iser u can be defined as: being better than the fixed-o schemes.pri;k ¼ ð1 aÞ  prL i;k þ a  prG i;k ð18Þ to get the final prediction for the active user, where a can be set to any of the sparsity measures as given below:  Overall sparsity measure (OS) (Eq. (8)).  User-specific sparsity measure (USS) (Eq. (9)).  User-item specific sparsity measures (LGR, UIS1, UIS2) (Eqs. (10)–(12)).  Unified measure of sparsity (UMS) (Eq. (13)). 5. Experiments and results In order to evaluate the performance of the system utilizing dif￾ferent a estimates, based on various proposed sparsity measures, several experiments are conducted on the vastly popular Movie￾Lens(http://www.MovieLens.umn.edu) and Jester datasets. The aim of these experiments is to show the superior performance of the proposed techniques over the fixed-a schemes presented in (Luo et al., 2008). 5.1. Experimental setup The MovieLens dataset consists of 100,000 ratings provided by 943 users on 1682 movies. The ratings scale is in the range 1–5 with 1-‘‘bad” to 5-‘‘excellent”. The ratings are discrete. Each user in the dataset has rated at least 20 movies. The Jester dataset pro￾vides 4.1 million ratings by 73,421 users on 100 jokes. The ratings are continuous and lie in the range 10 to 10. MovieLens and Jester are different from each other, since the overall sparsity of Movie￾Lens is quite high whereas the Jester dataset is quite dense. More￾over the number of items in MovieLens is much higher than the number of users, whereas in Jester the users far exceed the number of jokes. Testing the various prediction techniques on these two datasets allow for comparison under diverse data environments. For all the experiments 300 users were randomly selected from both the MovieLens and Jester datasets, the respective datasets being denoted as ML300 and Jester300 respectively. The datasets were then divided into 200 training users and 100 active users. The ratings from the training users are utilized in order to predict ratings for the test users. The number of ratings provided by the active user is varied as 10, 15, 20 and 25 giving rise to four different configurations Given10, Given15, Given20 and Given25 respec￾tively. The training ratings are used as explicit ratings available, thus aiding neighborhood construction as well as guiding the learning process of the GA, whereas the test ratings are considered as ratings which are unavailable and hence need to be predicted. The ratings from the Jester dataset, were discretized by rounding the rating value to the nearest integer. To compare the prediction quality of the proposed methods, we employ two accuracy metrics namely Mean Absolute Error(MAE) and Root Mean Squared Error(RMSE). MAE measures the average absolute deviation of the predicted rating of an item from the actual rating for the item. The MAE(ui) for the active user ui is as follows: MAEðuiÞ ¼ 1 jSij X jSij k¼1 jpri;k ri;kj ð19Þ where jSij is the cardinality of the test ratings set of user ui. The total MAE over all the active users, NT can be computed as: MAE ¼ 1 NT XNT i¼1 MAEðuiÞ ð20Þ A smaller value of MAE signifies better prediction quality. A related accuracy metric is the RMSE which squares the error before sum￾ming them. The RMSE(ui) for active user uican be defined as: RMSEðuiÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 jSij X jSij k¼1 ðpri;k ri;kÞ 2 vuut ð21Þ The RMSE over all active users is the average of RMSE of individual active users. RMSE ¼ 1 NT XNT i¼1 RMSEðuiÞ ð22Þ Whereas the MAE weighs the individual differences equally, RMSE gives relatively high weight to large errors. It is useful when large errors are particularly undesirable. It has been demonstrated in a recent study that a small difference in RMSE can lead to a very sig￾nificant improvement when ordering items by their predicted pref￾erences (Koren, 2008). It is to be noted that for any Given x (x = 10, 15,20,25) configura￾tions, only users having more than x ratings contribute to the error (MAE,RMSE) computation.We run three experiments to compare the prediction methodologies under different data settings. 5.2. Experiment 1 In order to demonstrate the effectiveness of the various pro￾posed a-estimation schemes, we conduct experiments using both datasets (ML300 and Jester300) to compare the performance of the proposed schemes with both the fixed-a schemes, under the various aforementioned configurations. The parameter c in all experiments was set to 30. The number of nearest local and global neighbors used for prediction (K) was restricted to 30. The prediction accuracy of the following schemes are compared: Fixed-a schemes.  Fixed-a scheme 1 (Luo et al., 2008).  Fixed-a scheme 2 (Luo et al., 2008). Proposed schemes.  Overall sparsity (OS).  Local global ratio (LGR).  User-item specific sparsity measure (UIS1).  User-item specific sparsity measure (UIS2).  User specific sparsity measure (USS). Tables 1 and 2 demonstrate the results of applying the various weighting schemes to ML300 and Jester 300 datasets.The results illustrate the improved prediction quality of the a-estimation schemes based on user and item sparsity measures. All the pro￾posed schemes when used for weighting local and global predic￾tions, outperform the fixed-a schemes under all configurations for both datasets, thus highlighting the importance of considering sparsity both at the user and item level, in order to weigh the pre￾dictions from local and global neighbors. For the ML300 dataset, the LGR scheme performs best, with the lowest MAE among all the proposed schemes under all configura￾tions, whereas UIS2 gives the least RMSE among all schemes for the same dataset. The measures OS and USS consistently perform worse than the other proposed schemes, but offer better prediction accuracy than the fixed-a schemes, both in terms of MAE and RMSE. For the Jester300 dataset, the OS scheme performs the best in almost all configurations with the lowest MAE and RMSE, except for the Given15 configuration when UIS1 performs best, giving the least MAE. The USS measure performs the worst while still being better than the fixed-a schemes. 5106 D. Anand, K.K. Bharadwaj / Expert Systems with Applications 38 (2011) 5101–5109