CN112199589B - Strong time-sequence item recommendation method and system based on weighted Bayes personalized sorting - Google Patents

Strong time-sequence item recommendation method and system based on weighted Bayes personalized sorting Download PDF

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CN112199589B
CN112199589B CN202011072547.4A CN202011072547A CN112199589B CN 112199589 B CN112199589 B CN 112199589B CN 202011072547 A CN202011072547 A CN 202011072547A CN 112199589 B CN112199589 B CN 112199589B
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陈建海
荣大中
沈睿
何钦铭
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Zhejiang University ZJU
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Abstract

The invention discloses a strong time-sequence item recommendation method and system based on weighted Bayes personalized ranking on the basis of a traditional recommendation method based on Bayes personalized ranking, and belongs to the field of recommendation systems. According to the method, all triples representing the preference degree partial order relation of the same user to two different items are extracted based on the implicit feedback data set, and by introducing the credibility of the partial order relation triples as the weight coefficient of the corresponding item of each partial order relation triplet, the method can enable the training effect generated by the more credible partial order relation triples to be stronger and the training effect generated by the more unreliable partial order relation triples to be weaker. The credibility of the triple of the partial order relationship is calculated by the time sequence information of the related items, so that the final trained model includes the consideration of the time sequence information of the recommended items, and a better effect can be obtained when the recommended items with stronger time sequence are processed.

Description

Strong time-sequence item recommendation method and system based on weighted Bayes personalized sorting
Technical Field
The invention relates to the field of recommendation systems, in particular to a strong-timeliness project recommendation method and system based on weighted Bayesian personalized sorting.
Background
The development of recommendation systems has been in history for many years and has been applied in many scenarios. The conventional recommendation system considers the like degree of the user to the item as a matrix, which is called a user item matrix, wherein the ith row and the jth column of the matrix represent the like degree of the ith user to the jth item. Some values in the user item matrix are known, and the conventional recommendation system needs to predict the values of the rest of the matrix according to the known values. After the whole user item matrix is completed, the traditional recommendation system finally recommends items to the user according to the values in the matrix.
User preference information for items can generally be divided into two categories:
(1) feedback (explicit feedback) is displayed. The preference degree information of the user to the item is explicit, for example, the rating of the online film watching platform user to the movie is given, and the high or low energy of the rating directly reflects the preference degree of the user to the item.
(2) Implicit feedback (implicit feedback). The preference degree information of the user to the item is implicit, for example, the film watching record of the user on the online film watching platform can only indirectly reflect the preference degree of the user to the item. The user has a high probability of being liked to a movie that the user has selected to watch, and the user does not necessarily dislike a movie that the user has not selected to watch. Summarizing the characteristics of implicit feedback, implicit feedback contains noise and has only positive and no negative examples.
At present, some conventional recommendation systems exist in the prior art, such as an Adaptive k-nearest neighbor recommendation model (Adaptive KNN) based on traditional bayesian personalized ranking, and the like, and known values in a user item matrix are used for training parameters of the model, and finally unknown values in the user item matrix are predicted through the model after parameter training is completed. The method has good effect on general commodity recommendation and the like, for example, the first commodity and the second commodity are commodities worth recommending to the user, if the user purchases the first commodity, the second commodity can be recommended to the user, and if the user purchases the second commodity, the first commodity can be recommended to the user.
But for some items with strong timing sequence, such as titles, music, books, movies, the user's preference for the items in these fields is gradually changing. Taking the theme as an example, the user likes simpler themes initially, and as the user learns and promotes continuously, the themes preferred by the user become harder and more complex. Users often do not have interest in more difficult topics than simpler topics. If the first topic and the second topic are both topics worth recommending to the user, the two topics are similar in knowledge point, but different in difficulty, and the second topic is more difficult than the first topic. If the user has made a topic, a topic B may be recommended to the user. However, if the user has made a topic B, then recommending the topic A to the user may not be an intelligent choice.
Therefore, for these items with strong timing, it is necessary to research a suitable recommendation method and recommendation system.
Disclosure of Invention
Aiming at the defects of the traditional recommendation method in processing the recommended items with stronger time sequence, the invention provides a strong time sequence item recommendation method and system based on weighted Bayesian personalized sorting. By introducing the credibility of the partial order relation triples as the weight coefficient of the corresponding item of each partial order relation triplet, the method can enable the training effect generated by the more credible partial order relation triples to be stronger and the training effect generated by the less credible partial order relation triples to be weaker. The reliability of the triple of the partial order relationship is calculated by the time sequence information of the related items, so that the model which is finally trained contains the consideration of the time sequence information of the recommended items, and a better effect can be achieved when the recommended items with stronger time sequence are processed.
The invention provides the following technical scheme:
a strong time-sequence item recommendation method based on weighted Bayesian personalized sorting comprises the following steps:
s1: aiming at a certain strong time sequence project, acquiring user, interacted project and interaction time data, preprocessing the acquired data, and generating an implicit feedback data set; the implicit feedback data set comprises all the user preference degree partial order relation triples of two different items;
s2: obtaining relative time sequence information of two items in each partial order relation triple according to interaction records of users and the items, and determining the credibility of each partial order relation triple according to the relative time sequence information; the credibility of each partial order relation triple is in direct proportion to the difference value of the relative time sequence information of two items in the triple;
s3: training a preset recommendation model according to the implicit feedback data set generated in the step S2, introducing the credibility of each partial ordering relation triple into an objective function by adopting a weighted Bayes personalized sorting method in the training process, and completing the training of the recommendation model;
s4: and after the training is finished, obtaining a predicted user item matrix, and recommending items to the user according to the preference degree of the user to the non-interactive items in the user item matrix from high to low.
Further, the step S2 specifically includes:
acquiring user, interacted projects and interaction time data aiming at a certain strong time sequence project;
traversing the interacted projects and the non-interacted projects of the user, and generating a partial order relation triple (u, i, j) representing the preference degree of the same user to two different projects as a training set; in the partial order relationship triple (u, i, j), it indicates that the user u has interacted with the item i but not with the item j, i.e. the preference degree of the user u for the item i is likely to be greater than that of the item j.
Further, the recommendation model minimizes an objective function in a training process, where the objective function is:
Figure GDA0002753238270000031
wherein, (u, i, j) represents a partial order relationship triple, and a user u interacts with the item i and does not interact with the item j; dsRepresenting a training set consisting of partially ordered relational triplets, cijRepresenting the confidence of the triplet (u, i, j), σ being the sigmoid function, λθIs a coefficient of the regularization that,
Figure GDA0002753238270000032
represents the predicted value of the preference degree of the user u for the item i,
Figure GDA0002753238270000033
representing a predicted value of the user's u like degree to the item j, theta is a model parameter of the recommendation model, | · |2Is a norm.
Further, the recommendation model adopts a matrix decomposition model, and the user matrix W and the item matrix H in the matrix decomposition model are trained to minimize:
Figure GDA0002753238270000034
wherein, WuLatent feature vector, H, representing user uiLatent feature vector, H, representing item ijA latent feature vector representing item j;
the matrix decomposition model adopts a gradient descent method in the training process, and the formula is as follows:
Figure GDA0002753238270000035
Figure GDA0002753238270000036
Figure GDA0002753238270000037
wherein the content of the first and second substances,
Figure GDA0002753238270000038
a difference value representing the predicted values of the preference degrees of the user u to the item i and the item j;
η is the learning rate, and ← represents a parameter update symbol.
Further, the calculation formula of the reliability is as follows:
Figure GDA0002753238270000041
wherein, tiIs the relative timing information of item i, tjIs the relative timing information of the item j,
Figure GDA0002753238270000042
is (t)j-ti) The average value of (a) of (b),
Figure GDA0002753238270000043
is (t)j-ti) Is the standard deviation of (a), mu is the hyperparameter, cijIs the confidence level of the partially ordered relationship triplet (u, i, j).
Further, the relative timing information of a certain item is the number of users who have interacted with the item.
Further, the item with strong time sequence is a title, music, book or movie.
Another object of the present invention is to provide a strong-chronology item recommendation system based on improved weighted bayesian personalized ranking, for implementing the recommendation method described above, the recommendation system includes:
the data acquisition module is used for acquiring user data in the platform, wherein the user data comprises a user name, an interacted item and interaction time;
the data preprocessing module is used for generating a partial order relation triple representing the preference degree of the same user to two different items as an implicit feedback data set;
the credibility generating module is used for obtaining the relative time sequence information of two items in each partial order relation triple according to the number of the interacted users of the items, and then obtaining the credibility of each partial order relation triple according to the relative time sequence information;
a model storage module which stores a recommended model to be selected;
the model training module is used for reading the implicit feedback data set generated by the data preprocessing module and training the selected recommended model, the reliability of each partial ordering relation triple is introduced into a target function by adopting a weighted Bayes personalized sorting method in the training process, and a predicted user item matrix is generated after the training is finished;
and the recommendation query module is used for sequencing the predicted preference degrees of the non-interactive items in the user item matrix and recommending items to the user from high preference degrees to low preference degrees.
Preferably, the recommendation model comprises a matrix decomposition model and an adaptive k-nearest neighbor model.
Preferably, the reliability is that the difference value of the relative time sequence information of the two items is adjusted to mean value 1 and standard deviation as 1 through linear transformation
Figure GDA0002753238270000044
Mu is a hyperparameter as a result of a normal distribution of (1).
The recommendation method based on the Bayesian personalized ranking adds the concept of the credibility of the partial order relationship triples on the basis of the traditional recommendation method based on the Bayesian personalized ranking, can adjust the influence on model parameters during training according to the credibility of the partial order relationship triples, and can better process recommendation items with stronger time sequence compared with the traditional method.
For example, when the user does not do the title a but does not do the title a, the user's preference degree for the title a is not high more than the reliability of the title a, and because the user may be only that the current learning progress does not yet touch the title a, the preference degree partial order relationship has a small influence on the model parameters during training. When the user does the title C but does not do the title A, the user has higher credibility that the preference degree of the user for the title C is larger than that of the title A, and because the user already does the more difficult title C, the possibility that the user still is interested in the simpler title A is not high, so the preference degree bias-order relation has larger influence on the model parameters during training. Because the preference degrees of the two partial order relations have different influence on the model parameters, the positions of the title A and the title C are not equal to each other for the user who only makes the title B. Theoretically, the predicted preference degree of the user for the title C should be greater than that of the title A, which is quite consistent with the idea of the recommendation method of the invention.
The test result shows that in the movie recommendation data set, compared with the traditional method, the method of the invention can reduce the error rate by 2.39%, and can reduce the error rate by 14.32% in title recommendation, and therefore, the method of the invention can greatly improve the recommendation effect of the items with strong time sequence.
Drawings
FIG. 1 is a block diagram illustrating the structure and process of the overall module of the present invention;
FIG. 2 is a schematic diagram of a matrix decomposition recommendation model employed in the present invention;
FIG. 3 is a detailed work flow diagram of the data module of the present invention;
FIG. 4 is a relationship diagram of training round number, batch and partial order relationship triplets;
FIG. 5 is a graph of the effect of the test on the MovieLens dataset;
fig. 6 is a graph of the test effect on the PTA data set.
Detailed Description
The invention will be described in further detail below with reference to the drawings and examples, which are intended to facilitate the understanding of the invention without limiting it in any way.
The invention is described in further detail below with reference to the figures and examples.
The integral module diagram of the invention is shown in fig. 1, and the emphasis is on a data module and a model module, and the integral process mainly comprises the following steps:
step 1: acquiring user, interacted projects and interaction time data aiming at a certain strong time sequence project, preprocessing the acquired data and generating an implicit feedback data set; the implicit feedback data set comprises all the user preference degree partial order relation triples of two different items;
step 2: obtaining relative time sequence information of two items in each partial order relation triple according to interaction records of users and the items, and determining the credibility of each partial order relation triple according to the relative time sequence information; the reliability of each partial order relation triple is in direct proportion to the difference value of the relative time sequence information of two items in the triple;
and step 3: training a preset recommendation model according to the implicit feedback data set generated in the step S2, introducing the credibility of each partial ordering relation triple into an objective function by adopting a weighted Bayes personalized sorting method in the training process, and completing the training of the recommendation model;
and 4, step 4: and after the training is finished, obtaining a predicted user item matrix, and recommending items to the user according to the preference degree of the user to the non-interactive items in the user item matrix from high to low.
Workflow of data Module referring to FIG. 3, as follows:
(1) removing the last implicit feedback data in time sequence of each user, and generating the same expression by using the remaining implicit feedback dataAnd (4) selecting the triple of the preference degrees of the user to two different items in a partial order relation as a training set. For example, user u has watched movie i1Movie i3And movie i4Without seeing movie i2And the last movie viewed by the user is movie i3Then a partially ordered relationship triplet (u, i) may be generated1，i2)、 (u，i1，i3)、(u，i4，i2) And (u, i)4，i3)。
(2) And counting the relative time sequence information of each item. The invention employs tiRepresenting relative timing information of item i, wherein t is definediT can be set to the number of users interacting with item i in the implicit feedback dataiAs the relative timing information of item i. If tiIf the number of the users is larger, the known number of the users interested in the item i is larger, the item i accords with the taste of the public, the threshold of the interest in the item i is lower, and the users are more likely to be interested in the item i at a relatively earlier time; otherwise, if tiAnd if the number of the users is smaller, the user knows that the number of the users interested in the item i is smaller, the threshold of the interest in the item i is higher, and the user is more likely to interest the item i at a relatively later time. If ti＞tjThen, there are: under a general condition, a user is interested in the item i and then interested in the item j; in rare cases, the user is interested in item j first and then item i.
For example for a recommended item of a movie: if the number of viewers of a certain movie is small, the appreciation threshold is high, and the movie is relatively more likely to be interested by the user at a later time; if the number of viewers of a certain movie is large, the movie is more popular and has a lower appreciation threshold, and the movie is more likely to be interested by the user at an earlier time. Therefore, the number of implicit feedback records related to each recommended item can be directly taken as the relative timing information of the recommended item.
(3) And calculating the credibility of each partial order relation triple in the training set according to the relative time sequence information of the items. For theTriple (u, i, j) of partial order relationship, the invention uses cijIndicates its degree of confidence, wherein cijAnd (t)j-ti) And (4) positively correlating. When the user is known to be interested in the item i and whether the user is interested in the item j is unknown, the later the item i is generally interested in the user, and the earlier the item j is generally interested in the user, the greater the degree of preference of the user for the item i is than the degree of confidence that the item j is. Conversely, due to the characteristic that the implicit feedback contains noise, the less the user has a greater degree of preference for item i than item j.
In one embodiment of the invention, the confidence level c of the partially ordered relationship triplesijAnd (t)j-ti) Is a linear relationship between the first and second components,
Figure GDA0002753238270000071
wherein
Figure GDA0002753238270000072
Is (t)j-ti) The average value of (a) of (b),
Figure GDA0002753238270000073
is (t)j-ti) And μ is a hyperparameter, and is generally 4. The present invention approximately considers (t)j-ti) Reliability c of triple satisfying normal distribution and partial order relationijIn fact, it is (t)j-ti) Adjusted to mean 1 and standard deviation by linear transformation
Figure GDA0002753238270000074
The result after normal distribution.
(4) And (4) reconsidering the last piece of implicit feedback data in the time sequence of each user which is removed before, and taking the partial order relation triple generated newly as a test set. For example, user u has watched movie i1Movie i3And movie i4Without seeing movie i2And the last movie viewed by the user is movie i3Then only one of the newly generated partial ordering relationship triples in this step is (u, i)3，i2)。
The invention adopts a matrix decomposition model as a recommendation model, and the schematic diagram of the matrix decomposition model is shown in figure 2. The parameters θ of the matrix decomposition model are actually the user matrix W and the item matrix H. WuLatent feature vector, H, representing user uiRepresenting the latent feature vector for item i. In the matrix-decomposition model,
Figure GDA0002753238270000075
||θuij||2＝|Wu|2+|Hi|2+|Hj|2。
in the model module, the recommended model is trained according to the training set provided by the data module, and the training is finished after the loss function value gradually converges. After the model training is completed, in the model module, the current recommendation effect of the recommendation model can be tested according to the test set provided by the data module.
The model module adopts the recommendation method based on weighted Bayes personalized ranking for the training process of the model. Unlike the traditional recommendation method based on bayesian personalized ranking, this method tries to train the parameter θ of the model to minimize:
Figure GDA0002753238270000076
wherein, (u, i, j) represents a partial order relationship triple, and a user u interacts with the item i and does not interact with the item j; dsRepresenting a training set, cijDenotes the confidence of (u, i, j), σ is sigmoid function, λθIs a coefficient of the regularization that,
Figure GDA0002753238270000077
representing the difference value of the predicted values of the preference degrees of the user u to the item i and the item j, theta is a model parameter of the recommendation model, | · u2Is a norm.
Here the weight coefficient cijIs the calculated partial order relation ternary in the data moduleConfidence of group (u, i, j). For the matrix decomposition model, i.e., the parametric user matrix W and the item matrix H of the model are trained to minimize:
Figure GDA0002753238270000081
by using
Figure GDA0002753238270000082
To represent
Figure GDA0002753238270000083
In the case where the training parameters W and H attempt to minimize the value of the above equation, a gradient descent method is employed, namely:
Figure GDA0002753238270000084
Figure GDA0002753238270000085
Figure GDA0002753238270000086
where η is the learning rate. Credibility c of partial order relation tripleijThe higher the gradient is, the larger the coefficient is, and the larger the influence on the model parameter value is.
In the implementation of the present invention, each round of training of the model module includes 5000 batches, each batch includes 128 total triple of partial order relationship selected randomly, and the 128 triple of partial order relationship is D of each batch during trainings. The relationship of the training round number, the batch and the triple of the partial order relationship is shown in fig. 4.
The model module calculates AUC indexes according to the test set provided by the data module, the test of the model recommendation effect is realized through the AUC indexes, and the higher the AUC indexes of the model are, the better the recommendation effect is. The specific process for calculating the AUC index is as follows:
(1) and for each user, counting the proportion of the partial order relation triple related to the user in the test set in the recommendation model, and taking the proportion as the AUC value of the user.
(2) And (5) counting the average value of the AUC values of all the users, namely obtaining the AUC index of the recommendation model.
In the field of recommendation system research, the MovieLens data set is a data set related to movie scores, and is famous, and the data set contains records of scores of movies by users. The user's rating of the movie is removed from the data set, and the data set can be considered as an implicit feedback data set.
The 'spelling problem A' is an open teaching auxiliary platform for automatic program evaluation and automatic program evaluation for colleges and universities, which is developed in 2015 9 months by cooperation of a Zhejiang university national program design series course teaching team with the Internet and Yi company and Hangzhou Baiteng education and science and technology limited company. The PTA data set is derived from the user's question making records on the platform.
Based on the two data sets and by using a matrix decomposition model, the invention tests and compares the proposed recommendation method based on the weighted Bayes personalized ranking and the traditional recommendation method based on the Bayes personalized ranking, and the result is shown in FIG. 5 and FIG. 6.
The experimental results can be used to conclude that: due to the fact that time sequence information of recommended items is considered, compared with the traditional method, the AUC index which can be finally achieved by the recommendation method based on weighted Bayesian personalized ranking is greatly improved.
As shown in fig. 5, on the MovieLens dataset, the AUC index value of the recommendation method based on weighted bayes personalized ranking of the present invention can reach 89.80%, and the AUC index value of the conventional method can reach 89.55%, which is equivalent to reducing (0.8980-0.8955)/(1-0.8955) ═ 0.0239, i.e. 2.39% error rate.
As shown in fig. 6, on the PTA data set, the AUC index value of the recommendation method based on weighted bayesian personalized ranking can reach 90.13%, and the AUC index value of the conventional method can reach 88.48%, which is equivalent to reducing the error rate of (0.9013-0.8848)/(1-0.8848) ═ 0.1432, i.e. 14.32%.
The reason that the recommendation method based on weighted Bayes personalized ranking is superior to the MovieLens data set in the performance of the PTA data set is that the time sequence of the title recommendation is stronger than that of the movie recommendation.
The above-mentioned embodiments are intended to illustrate the technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only specific embodiments of the present invention, and are not intended to limit the present invention, and any modifications, additions, equivalents, etc. made within the scope of the principles of the present invention should be included in the scope of the present invention.

Claims (8)

1. A strong time-sequence item recommendation method based on weighted Bayes personalized sorting is characterized by comprising the following steps:
s1: acquiring user, interacted projects and interaction time data aiming at a certain strong time sequence project, preprocessing the acquired data and generating an implicit feedback data set; the implicit feedback data set comprises all the user preference degree partial order relation triples of two different items;
s2: obtaining relative time sequence information of two items in each partial order relation triple according to interaction records of users and the items, and determining the credibility of each partial order relation triple according to the relative time sequence information; the reliability of each partial order relation triple is in direct proportion to the difference value of the relative time sequence information of two items in the triple;
s3: training a preset recommendation model according to the implicit feedback data set generated in the step S2, introducing the credibility of each partial ordering relation triple into an objective function by adopting a weighted Bayes personalized sorting method in the training process, and completing the training of the recommendation model;
the recommendation model minimizes an objective function in a training process, wherein the objective function is as follows:
Figure FDA0003502197550000011
wherein, (u, i, j) represents a partial order relationship triple, and a user u interacts with the item i and does not interact with the item j; dsRepresenting a training set consisting of partially ordered relational triplets, cijRepresenting the confidence of the triplet (u, i, j), σ being the sigmoid function, λθIs a coefficient of the regularization that,
Figure FDA0003502197550000012
represents the predicted value of the preference degree of the user u for the item i,
Figure FDA0003502197550000013
representing a predicted value of the user's u like degree to the item j, theta is a model parameter of the recommendation model, | · |2Is a norm;
the recommendation model adopts a matrix decomposition model, and the user matrix W and the item matrix H in the matrix decomposition model are trained to minimize:
Figure FDA0003502197550000014
wherein, WuLatent feature vector, H, representing user uiLatent feature vector, H, representing item ijA latent feature vector representing item j;
the matrix decomposition model adopts a gradient descent method in the training process, and the formula is as follows:
Figure FDA0003502197550000015
Figure FDA0003502197550000016
Figure FDA0003502197550000021
wherein the content of the first and second substances,
Figure FDA0003502197550000022
a difference value representing the predicted values of the preference degrees of the user u to the item i and the item j; η is the learning rate, and ← represents a parameter update symbol;
s4: and after the training is finished, obtaining a predicted user item matrix, and recommending items to the user according to the preference degree of the user to the non-interactive items in the user item matrix from high to low.
2. The strong temporal item recommendation method based on weighted Bayesian personalized ranking according to claim 1, wherein the step S2 specifically comprises:
acquiring user, interacted projects and interaction time data aiming at a certain strong time sequence project;
traversing the interacted projects and the non-interacted projects of the user, and generating a partial order relation triple (u, i, h) representing the preference degree of the same user to two different projects as a training set; in the partially ordered relationship triple (u, i, h), it represents that the user u has interacted with the item i and not with the item j.
3. The strong temporal item recommendation method based on weighted Bayesian personalized ranking according to claim 1, wherein the calculation formula of the credibility is as follows:
Figure FDA0003502197550000023
wherein, tiIs the relative timing information of item i, tjIs the relative timing information of the item j,
Figure FDA0003502197550000024
is (t)j-ti) The average value of (a) of (b),
Figure FDA0003502197550000025
is (t)j-ti) Is the standard deviation of (a), mu is the hyperparameter, cijIs the confidence level of the partially ordered relationship triplet (u, i, j).
4. The strong temporal item recommendation method according to claim 1, wherein the relative temporal information of a certain item is the number of users who have interacted with the item.
5. The method according to claim 1, wherein the strongly-ordered items are titles, music, books or movies.
6. A strong-temporal-sequence item recommendation system based on weighted bayesian personalized ranking, for implementing the recommendation method of claim 1, the recommendation system comprising:
the data acquisition module is used for acquiring user data in the platform, wherein the user data comprises a user name, an interacted item and interaction time;
the data preprocessing module is used for generating a partial order relation triple representing the preference degree of the same user to two different items as an implicit feedback data set;
the credibility generating module is used for obtaining the relative time sequence information of two items in each partial order relation triple according to the number of the interacted users of the items, and then obtaining the credibility of each partial order relation triple according to the relative time sequence information;
a model storage module which stores a recommended model to be selected;
the model training module is used for reading the implicit feedback data set generated by the data preprocessing module and training the selected recommended model, the reliability of each partial ordering relation triple is introduced into a target function by adopting a weighted Bayes personalized sorting method in the training process, and a predicted user item matrix is generated after the training is finished;
and the recommendation query module is used for sequencing the predicted preference degrees of the non-interactive items in the user item matrix and recommending items to the user from high preference degrees to low preference degrees.
7. The system according to claim 6, wherein the recommendation model comprises a matrix decomposition model and an adaptive k-nearest neighbor model.
8. The system as claimed in claim 6, wherein the confidence level is obtained by adjusting the difference between the relative timing information of the two items to mean 1 and standard deviation as follows through linear transformation
Figure FDA0003502197550000031
Mu is a hyperparameter as a result of a normal distribution of (1).
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