Point-of-interest(POI)recommendations in location-based social networks(LBSNs)have developed rapidly by incorporating feature information and deep learning methods.However,most studies have failed to accurately reflec...Point-of-interest(POI)recommendations in location-based social networks(LBSNs)have developed rapidly by incorporating feature information and deep learning methods.However,most studies have failed to accurately reflect different users’preferences,in particular,the short-term preferences of inactive users.To better learn user preferences,in this study,we propose a long-short-term-preference-based adaptive successive POI recommendation(LSTP-ASR)method by combining trajectory sequence processing,long short-term preference learning,and spatiotemporal context.First,the check-in trajectory sequences are adaptively divided into recent and historical sequences according to a dynamic time window.Subsequently,an adaptive filling strategy is used to expand the recent check-in sequences of users with inactive check-in behavior using those of similar active users.We further propose an adaptive learning model to accurately extract long short-term preferences of users to establish an efficient successive POI recommendation system.A spatiotemporal-context-based recurrent neural network and temporal-context-based long short-term memory network are used to model the users’recent and historical checkin trajectory sequences,respectively.Extensive experiments on the Foursquare and Gowalla datasets reveal that the proposed method outperforms several other baseline methods in terms of three evaluation metrics.More specifically,LSTP-ASR outperforms the previously best baseline method(RTPM)with a 17.15%and 20.62%average improvement on the Foursquare and Gowalla datasets in terms of the Fβmetric,respectively.展开更多
We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the...We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the game can be solved neither by applying the Isaacs MinMax principle nor using the Bellman–Isaacs equation approach,i.e.this game is singular.Aprevious paper of one of the authors analysed such a game in the case where the cost functional does not contain the minimiser’s control cost at all,i.e.the weight matrix of this cost equals zero.In this case,all coordinates of the minimiser’s control are singular.In the present paper,we study the general case where the weight matrix of the minimiser’s control cost,being singular,is not,in general,zero.This means that only a part of the coordinates of the minimiser’s control is singular,while others are regular.The considered game is treated by a regularisation,i.e.by its approximate conversion to an auxiliary regular game.The latter has the same equation of dynamics and a similar cost functional augmented by an integral of the squares of the singular control coordinates with a small positive weight.Thus,the auxiliary game is a partial cheap control differential game.Based on a singular perturbation’s asymptotic analysis of this auxiliary game,the existence of the value of the original(singular)game is established,and its expression is obtained.The maximiser’s optimal state feedback strategy and the minimising control sequence in the original game are designed.It is shown that the coordinates of the minimising control sequence,corresponding to the regular coordinates of the minimiser’s control,are point-wise convergent in the class of regular functions.The optimal trajectory sequence and the optimal trajectory in the considered singular game also are obtained.An illustrative example is presented.展开更多
基金the National Natural Science Foundation of China(Grant Nos.62102347,62376041,62172352)Guangdong Ocean University Research Fund Project(Grant No.060302102304).
文摘Point-of-interest(POI)recommendations in location-based social networks(LBSNs)have developed rapidly by incorporating feature information and deep learning methods.However,most studies have failed to accurately reflect different users’preferences,in particular,the short-term preferences of inactive users.To better learn user preferences,in this study,we propose a long-short-term-preference-based adaptive successive POI recommendation(LSTP-ASR)method by combining trajectory sequence processing,long short-term preference learning,and spatiotemporal context.First,the check-in trajectory sequences are adaptively divided into recent and historical sequences according to a dynamic time window.Subsequently,an adaptive filling strategy is used to expand the recent check-in sequences of users with inactive check-in behavior using those of similar active users.We further propose an adaptive learning model to accurately extract long short-term preferences of users to establish an efficient successive POI recommendation system.A spatiotemporal-context-based recurrent neural network and temporal-context-based long short-term memory network are used to model the users’recent and historical checkin trajectory sequences,respectively.Extensive experiments on the Foursquare and Gowalla datasets reveal that the proposed method outperforms several other baseline methods in terms of three evaluation metrics.More specifically,LSTP-ASR outperforms the previously best baseline method(RTPM)with a 17.15%and 20.62%average improvement on the Foursquare and Gowalla datasets in terms of the Fβmetric,respectively.
文摘We consider a finite horizon,zero-sum linear quadratic differential game.The feature of this game is that a weight matrix of the minimiser’s control cost in the cost functional is singular.Due to this singularity,the game can be solved neither by applying the Isaacs MinMax principle nor using the Bellman–Isaacs equation approach,i.e.this game is singular.Aprevious paper of one of the authors analysed such a game in the case where the cost functional does not contain the minimiser’s control cost at all,i.e.the weight matrix of this cost equals zero.In this case,all coordinates of the minimiser’s control are singular.In the present paper,we study the general case where the weight matrix of the minimiser’s control cost,being singular,is not,in general,zero.This means that only a part of the coordinates of the minimiser’s control is singular,while others are regular.The considered game is treated by a regularisation,i.e.by its approximate conversion to an auxiliary regular game.The latter has the same equation of dynamics and a similar cost functional augmented by an integral of the squares of the singular control coordinates with a small positive weight.Thus,the auxiliary game is a partial cheap control differential game.Based on a singular perturbation’s asymptotic analysis of this auxiliary game,the existence of the value of the original(singular)game is established,and its expression is obtained.The maximiser’s optimal state feedback strategy and the minimising control sequence in the original game are designed.It is shown that the coordinates of the minimising control sequence,corresponding to the regular coordinates of the minimiser’s control,are point-wise convergent in the class of regular functions.The optimal trajectory sequence and the optimal trajectory in the considered singular game also are obtained.An illustrative example is presented.
