CN108269172B - Collaborative filtering method based on comprehensive similarity transfer - Google Patents

Abstract

The present invention discloses a collaborative filtering method based on comprehensive similarity migration. Compared with the prior art, the present invention utilizes both user rating information and user attribute information in similarity calculation, and considers the difference between users. For the differences in the scoring standards of satisfaction, the method of measuring the similarity of user scores is adopted to measure the similarity of user scores, which improves the accuracy of similarity calculation and thus improves the quality of data migration. The experimental results show that this model can alleviate the data sparsity problem more effectively than other methods. In the future, joint item similarity or other knowledge, such as text information, can be considered to transfer the data in the auxiliary field. In this way, the quality of the transferred data can be improved, thereby improving the recommendation accuracy.

Description

Collaborative filtering method based on comprehensive similarity transfer

technical field

The invention relates to the field of network information computing, in particular to a collaborative filtering method based on comprehensive similarity migration.

Background technique

At present, the amount of network information is increasing exponentially. On the one hand, network users can obtain rich information, but on the other hand, they are faced with the problem of information overload, and it is difficult to mine useful information from the massive information. The recommendation system can filter out the parts that users are interested in from the massive data according to the user's interests. At present, recommender systems have been widely used, such as Amazon, eBay, MovieLens, GroupLens and other e-commerce platforms.

Collaborative filtering technology is one of the most widely used technologies in recommender systems. Its basic idea is to use the user's historical rating data to predict the user's interest in unrated items, and select the items with the highest interest as the recommendation result. For the traditional collaborative filtering algorithm, the most critical step is to calculate the similarity between users or items, but as the data grows, the user rating data will be extremely sparse, and the recommendation quality will also decrease.

Currently, for the data sparsity problem [1], there are the following solutions: one is to reduce the sparsity of the dataset by filling unrated items [2-4], this algorithm is suitable for items that are not updated frequently and the number of items is much smaller than In the scenario of the number of users, there is a cold start problem depending on the user behavior; the second is to reduce the sparsity of the dataset through matrix decomposition [5]. This algorithm uses the potential relationship between users and items to perform singular value decomposition on the rating matrix. , the training cost of this method is high, and it does not adapt to the change of user interests; the third is to use the idea of transfer learning to promote the learning of the target domain through the intersection between domains [6-7]. The latent relationship achieves the purpose of assisting the training of the target domain. Therefore, it depends on the reliability of the latent relationship. If it is not reliable, it will lead to negative transfer. At present, some scholars have proposed to use multi-domain data to alleviate the problem of data sparseness in the target domain. For example, Jamali [8-9] et al. proposed a context-based matrix factorization modulo HeteroMF,

Its main idea is to use common entities between multiple domains and share the eigenfactors of entities to jointly decompose multiple matrices at the same time. The algorithm needs to train more parameters and consumes a lot of time to calculate gradients; LiBin [10] et al. A rating matrix generation model RMGM (RatingMatrixGenerativeModel), the main idea of which is to find a shared implicit cluster-level rating matrix, and then use this matrix to fill the null values of the original matrix in the target domain. There is no theoretical support; Li Chao [10] and others proposed a transfer model based on user similarity TSUCF (TransferSimilarity

User-basedCollaborativeFiltering), whose main idea is to establish the connection between the auxiliary field and the target field with cross-domain data to achieve the purpose of assisting the target field. This method only uses user rating information, and when measuring the similarity of ratings, only the number of common items is used to measure, without taking into account user preferences.

Although the above algorithms all use auxiliary domain knowledge to improve the recommendation accuracy, there are still some shortcomings: first, the model based on matrix transformation has many model training parameters; Third, when calculating the similarity of user scores, the differences in the scoring standards of users' satisfaction are ignored.

The problem of data sparsity is one of the main bottlenecks of traditional collaborative filtering algorithms. Transfer learning usually uses the potential relationship between the target domain and the auxiliary domain to transfer knowledge to the auxiliary domain, so as to improve the recommendation quality of the target domain. Existing similarity-based transfer models generally only utilize user rating information, and ignore differences in user rating standards in the calculation of rating similarity. In view of the above problems, the present invention proposes a recommendation method based on comprehensive similarity migration.

references:

[1] PanW. Asurveyoftransferlearningforcollaborativerecommendationwithauxiliarydata[J]. Neurocomputing, 2016, 177(C):447-453.

[2] Lemire D, Maclachlan A. Slopeonepredictorsforonlinerating-basedcollaborativefiltering[C]//Proceedingsofthe2005SIAMInternationalConferenceonDataMining. Society for Industry and Applied Mathematics, 2005: 471-475.

[3] Wang P, Ye HW. Apersonalizedrecommendationalgorithmcombiningslopeoneschemeanduserbasedcollaborativefiltering[C]//IndustrialandInformationSystems, 2009. IIS'09. InternationalConferenceon. IEEE, 2009:152-154.

[4] Sun Z, Luo N, Kuang W. Onereal-timepersonalizedrecommendationsystemsbasedonSlopeOnealgorithm[C]//FuzzySystemsandKnowledgeDiscovery(FSKD), 2011EighthInternationalConferenceon. IEEE, 2011, 3:1826-1830.

[5] Sarwar B, Karypis G, Konstan J, et al. Applicationofdimensionalityreductioninrecommendersystem-acasestudy[R]. MinnesotaUnivMinneapolisDeptofComputerScience, 2000.

[6] LiB, YangQ, XueX. Transferlearningforcollaborativefilteringviaarating-matrixgenerativemodel[C]//InternationalConferenceonMachineLearning, ICML2009, Montreal, Quebec, Canada, June. DBLP, 2009: 617-624.

[7] PanW, XiangEW, LiuNN, et al. TransferLearninginCollaborativeFilteringforSparsityReduction[C]//AAAI. 2010, 10:230-235.

[8] Jamali M, Lakshmanan L. Heteromf:recommendationinheterogeneousinformationnetworksusingcontextdependentfactormodels[C]//Proceedingsofthe22ndinternationalconferenceonWorldWideWeb. ACM, 2013: 643-654.

[9] WuS, LiuQ, WangL, et al. Contextualoperationforrecommendersystems[J]. IEEE Transactionsson Knowledge and Data Engineering, 2016, 28(8): 2000-2012.

[10] Li B, Yang Q, Xue X. Transferlearningforcollaborativefilteringviaarating-matrixgenerativemodel[C]//Proceedingsofthe26thannualinternationalconferenceonmachinelearning. ACM, 2009: 617-624.

[11] Li Chao, Zhou Tao, Huang Junming, et al. Cross-platform cross-recommendation algorithm based on user similarity transfer[J]. Chinese Journal of Information, 2016, 30(2): 90-98.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a collaborative filtering method based on comprehensive similarity migration in order to solve the above problems.

The present invention realizes above-mentioned purpose through following technical scheme:

The present invention includes the following steps:

(1) Recommendation method based on comprehensive similarity migration: there are two platforms e ₁ and e ₂ , U ₁ represents users with historical behavior information only in platform e ₁ , and U ₂ represents users with historical behavior information only in platform e ₂ Users with behavioral information, U _c represents users who have historical behavioral information in both platforms e ₁ and e ₂ , and are defined as cross-users; in actual situations, the number of cross-users is much smaller than the number of non-cross-users; User, establishes a similarity relationship for non-intersecting users U ₁ and U ₂ , so as to help the target domain to recommend;

(2) Similarity migration: the similarity between the non-cross user U ₁ and the user U ₂ cannot be calculated directly, but the similarity between the user U ₁ and the user U ₂ and the cross user U _c can be calculated, so the cross user U c can be calculated. User U _c is used as a link to establish the similarity between user U ₁ and user U ₂ ;

U₂与U_c的相似性，记为最后计算

与

的内积，即为U₁和U₂的传递相似度Similarity migration step: first find out the common user set U _c with platform 1 and platform 2; then calculate the similarity between U ₁ and U _c respectively, denoted as a vector

The similarity between U ₂ and U _c , denoted as final calculation

and

The inner product of , which is the transitive similarity of U ₁ and U ₂

综上，则U₁和U₂之间的相似度计算可形式化为：Among them, U ₁₁ represents non-intersecting user 1 in platform 1, U ₂₁ and U ₂₂ represent non-intersecting user 1 in platform 2, U _c1 , U _c2 , etc. represent cross-users, and S ₁ , S ₂ , etc. represent similarity; if To calculate the similarity between U ₁₁ and U ₂₁ , it can be calculated indirectly through U _c1 , U _c2 , U _c3 transitions

To sum up, the similarity calculation between U ₁ and U ₂ can be formalized as:

(3) Similarity calculation: Before calculating the similarity between the non-intersecting users U ₁ and U ₂ , it is necessary to calculate the similarity between the non-intersecting users U ₁ and U ₂ and the intersecting users respectively. The similarity calculation is as follows:

1) User rating similarity

This paper measures the similarity of user ratings through the consistency of rating distribution and credibility;

如果1,2,...,n与x₁,x₂,...,x_n的匹配度越大，则表明两者的一致性越高；计算公式如下所示；The consistency of the score distribution is determined by the score distribution of the same items evaluated by two users; the more consistent the score distribution, the more similar the interests of the two users; let {ur ₁ ,ur ₂ ,...,ur _n }, {ur ₁ ,ur ₂ ,...,ur _n } are the rating sets of user u and user v for common items, respectively, and the two sets of data are sorted in ascending order, namely {ur ₁ ,ur ₂ ,...,ur _n },

If 1,2,...,n and x ₁ ,x ₂ ,...,x _n match more closely, it indicates that the two are more consistent; the calculation formula is as follows;

The credibility is determined according to the number of the same items evaluated by two users. If the number is small, even if the score distribution is the same, it does not mean that the two are necessarily similar; the calculation formula is as follows;

Among them, I _u represents the set of items evaluated by user u;

The user rating similarity calculation formula is as follows;

sim ₁ (u,v)=dist(u,v)conf(u,v) (1-4)

2) User attribute similarity

User attribute similarity is measured according to user attributes; it is generally believed that users with the same attributes have similar interests to a certain extent; the calculation formula is as follows;

Among them, n represents the number of attributes, sim(u, v, i) represents whether the two users are the same on the ith attribute, if they are the same, it is 1, otherwise it is 0, and d _i represents the degree of discrimination of the ith attribute, If users with a certain attribute have rated all items, it means that the attribute has no discrimination, and its value is determined by different data sets;

3) Final similarity

Under normal circumstances, when the user rates an item, the user's rating information should be used as much as possible. When the user does not rate an item, the user's attribute information should be used as much as possible. When the number of items rated by the user increases, the method transitions smoothly. To use the rating information for recommendation, this paper uses the sigmoid function for smoothing, and the end-user similarity is defined as follows:

sim(u,v)=αsim ₁ (u,v)+(1-α)sim ₂ (u,v) (1-6)

Among them, C _uv represents the set of items jointly evaluated by user u and user v; expressed by the above formula, the user similarity calculation will smoothly transition to the use of rating information as the number of items evaluated by the user increases. Prediction accuracy in cold start state;

(4) Method description:

A) Method for calculating user similarity: the first step is to calculate the similarity of user attributes according to the user attribute information; the second step is to calculate the similarity of user scores according to the information of user scores; the third step: the similarity of user attributes and user scores are calculated according to the similarity of user attributes , calculate the end-user similarity;

第二步计算U₂与U_c之间的相似度

第三步计算迁移相似度第四步利用迁移相似度

结合UCF方法进行推荐。B) Recommendation method based on transfer learning: the first step calculates the similarity between U ₁ and U _c

The second step calculates the similarity between U ₂ and U _c

The third step calculates the migration similarity The fourth step utilizes the transfer similarity

Combined with UCF method for recommendation.

The beneficial effects of the present invention are:

The present invention is a collaborative filtering method based on comprehensive similarity migration. Compared with the prior art, the present invention utilizes both user rating information and user attribute information in similarity calculation, and considers the relationship between users. The differences in the scoring standards of satisfaction, the method of measuring the similarity of user scores by the consistency of user score distribution, improves the accuracy of similarity calculation, and thus improves the quality of data migration. The experimental results show that the model can alleviate the data sparsity problem more effectively than other methods. In the future, joint item similarity or other knowledge, such as text information, can be considered to transfer the data in the auxiliary field. In this way, the quality of the transferred data can be improved, thereby improving the recommendation accuracy.

Description of drawings

Fig. 1 is a user rating matrix diagram of the present invention;

Fig. 2 is the similarity migration schematic diagram of the present invention;

Fig. 3 is the RMSE value contrast figure of different methods under the A group of the present invention;

Fig. 4 is the B group different method RMSE value contrast figure of the present invention;

Fig. 5 is the C group different method RMSE value contrast figure of the present invention;

Fig. 6 is the D group different method RMSE value comparison diagram of the present invention;

Fig. 7 is E group different method RMSE value comparison diagram of the present invention;

Fig. 8 is the RMSE value contrast figure of different methods under N=5 of the present invention;

Fig. 9 is N=10 different methods RMSE value comparison diagram of the present invention;

Fig. 10 is N=20 different methods RMSE value comparison diagram of the present invention;

Fig. 11 is N=30 different methods RMSE value comparison diagram of the present invention;

Fig. 12 is a comparison diagram of RMSE values of different methods of N=40 of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings:

Recommended method based on comprehensive similarity transfer:

The invention proposes a recommendation method based on comprehensive similarity migration, which utilizes auxiliary domain information to alleviate the problem of data sparsity in the target domain.

The method of the present invention will be described below by taking two movie platforms as examples. Suppose there are two platforms e ₁ and e ₂ , U ₁ represents a user with historical behavior information only on platform e ₁ , U ₂ represents a user with historical behavior information only on platform e ₂ , U _c represents a user on platform e ₁ Users who have historical behavior information in both and e ₂ are defined as cross-users. The user behavior matrix is shown in Figure 1.

In practice, the number of cross-users is much smaller than the number of non-cross-users.

The traditional recommendation method is to use a small proportion of cross-users to recommend a large proportion of non-cross-users, which will cause cold start problems and data sparse problems, resulting in low recommendation quality.

The method of the present invention establishes a similarity relationship for the non-intersecting users U ₁ and U ₂ through cross-users, thereby helping the target field to recommend.

Similarity transfer:

As shown in Figure 1, the similarity between the non-intersecting user U ₁ and the user U ₂ cannot be calculated directly, but the similarity between the user U ₁ and the user U ₂ and the intersecting user U _c can be calculated, so the intersecting user U _c is used as a link to establish the similarity between user U ₁ and user U ₂ .

U₂与U_c的相似性，记为

最后计算

与

的内积，即为U₁和U₂的传递相似度Similarity migration step: first find out the common user set U _c with platform 1 and platform 2; then calculate the similarity between U ₁ and U _c respectively, denoted as a vector

The similarity between U ₂ and U _c , denoted as

final calculation

and

The inner product of , which is the transitive similarity of U ₁ and U ₂

Similarity migration is shown in Figure 2;

综上，则U₁和U₂之间的相似度计算可形式化为：Wherein, U ₁₁ represents non-intersecting user 1 in platform 1, U ₂₁ and U ₂₂ represent non-intersecting user 1 in platform 2, U _c1 , U _c2 etc. represent cross-users, S ₁ , S ₂ etc. represent similarity. If you want to calculate the similarity between U ₁₁ and U ₂₁ , you can indirectly calculate through U _c1 , U _c2 , U _c3 transitions

To sum up, the similarity calculation between U ₁ and U ₂ can be formalized as:

Similarity calculation:

Based on the above analysis, before calculating the similarity between the non-intersecting users U ₁ and U ₂ , it is necessary to calculate the similarity between the non-intersecting users U ₁ and U ₂ and the intersecting users respectively. The similarity calculation is as follows:

1) User rating similarity

The invention measures the similarity of user scores through two aspects of score distribution consistency and reliability.

如果1,2,...,n与x₁,x₂,...,x_n的匹配度越大，则表明两者的一致性越高。计算公式如下所示。The consistency of the rating distribution is determined by the rating distribution of the same item evaluated by two users. The more consistent the score distribution is, the more similar the interests of the two users are. Let {ur ₁ ,ur ₂ ,...,ur _n },{ur ₁ ,ur ₂ ,...,ur _n } be the rating sets of user u and user v for common items, respectively. ascending sort, ie {ur ₁ ,ur ₂ ,...,ur _n },

If 1,2,...,n and x ₁ ,x ₂ ,...,x _n match more closely, it indicates that the two are more consistent. The calculation formula is shown below.

The credibility is determined according to the number of the same items that two users have evaluated. If the number is small, even if the score distribution is consistent, it does not mean that the two are necessarily similar. The calculation formula is shown below.

Among them, I _u represents the set of items evaluated by user u.

The user rating similarity calculation formula is as follows.

sim ₁ (u,v)=dist(u,v)conf(u,v) (1-4)

2) User attribute similarity

User attribute similarity is measured according to user attributes. It is generally believed that users with the same attributes have similar interests to a certain extent. The calculation formula is shown below.

Among them, n represents the number of attributes, sim(u, v, i) represents whether the two users are the same on the ith attribute, if they are the same, it is 1, otherwise it is 0, and d _i represents the degree of discrimination of the ith attribute, If users with a certain attribute have rated all items, it means that the attribute has no discrimination, and its value is determined by different data sets.

3) Final similarity

In general, when a user rates an item, the user's rating information for the item should be used as much as possible, and when the user does not rate an item, the user's attribute information should be used as much as possible. When the number of items rated by the user increases, the method should smoothly transition to using the rating information for recommendation. The present invention uses the sigmoid function for smoothing, and the final user similarity is defined as follows:

sim(u,v)=αsim ₁ (u,v)+(1-α)sim ₂ (u,v) (1-6)

Among them, C _uv represents the set of items jointly evaluated by user u and user v. According to the above formula, the user similarity calculation will smoothly transition to the use of rating information as the number of items evaluated by the user increases, and this smooth transition can improve the prediction accuracy in the cold start state.

Method description:

1) Calculate the user similarity method: the first step is to calculate the user attribute similarity according to the user attribute information; the second step is to calculate the user rating similarity according to the user rating information; the third step: according to the user attribute similarity and the user rating similarity , calculate the end-user similarity.

第二步计算U₂与U_c之间的相似度第三步计算迁移相似度

第四步利用迁移相似度

结合UCF方法进行推荐。2) Recommendation method based on transfer learning: the first step is to calculate the similarity between U ₁ and U _c

The second step calculates the similarity between U ₂ and U _c The third step calculates the migration similarity

The fourth step utilizes the transfer similarity

Combined with UCF method for recommendation.

experiment:

Experimental data:

The experiment adopts the dataset of MovieLen movie website. The dataset description is shown below.

Table 1 Movielens data description

The experimental dataset is divided as follows.

Table 5 Data set division

Evaluation indicators:

In order to measure the prediction accuracy of the method, the root mean square error RMSE (Root Mean Squared Error, RMSE) is used in this experiment to verify the difference between the prediction result obtained by the method of the present invention and the user's real score.

The RMSE calculation method is as follows:

Among them, r _ui represents the actual rating of item i by user u, pre _ui represents the predicted rating of item i by user u, T is the test set, and |T| represents the size of the test set. The smaller the RMSE, the closer the predicted value is to the actual value, and the higher the accuracy of the predicted result.

Comparison method:

1) UCF method: Only cross-users can be used for recommendation.

2) Recommendation method based on user similarity transfer (TSUCF): Using the score information of cross-users with a small proportion as a link, establish a connection between users of two different e-commerce companies to achieve the effect of recommendation.

3) The method of the present invention: The method of the present invention makes improvements on the TSUCF method. One is to make full use of the user attribute information, and the other is to consider the differences in the user's scoring standards, and use the score distribution consistency of common items to measure the similarity of user scores. sex.

Experimental results:

Considering that the size of the number of nearest neighbors N will affect the results, the experiments are carried out on the premise that the number of nearest neighbors is 5, 10, 20, 30, and 40.

It can be clearly seen from the above Figures 2 to 7 that the method of the present invention can achieve better recommendation results under different numbers of nearest neighbors.

Considering the influence of the number of cross-users on the experimental results, the experiments were carried out to compare the methods under the number of cross-users of 95, 189, 283, 377, and 471 respectively.

It can be clearly seen from the above Figures 8 to 12 that the method of the present invention can achieve the best recommendation effect under different cross-user numbers.

The method of the present invention uses the similarity of user attributes and the similarity of user ratings to migrate the data in the auxiliary field to solve the problem of data sparsity in the target field. In this way, the quality of the migrated data can be improved, thereby improving the recommendation accuracy.

The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments, and the descriptions in the above-mentioned embodiments and the description are only to illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have Various changes and modifications fall within the scope of the claimed invention. The claimed scope of the present invention is defined by the appended claims and their equivalents.

Claims (1)

1. A collaborative filtering method based on comprehensive similarity migration is characterized by comprising the following steps:

(1) the recommendation method based on the comprehensive similarity migration comprises the following steps: is provided with two platforms e₁And e₂，U₁Shown only on platform e₁Users in whom historical behavior information exists, U₂Shown only on platform e₂Users in whom historical behavior information exists, U_cIs shown on a platform e₁And e₂Users who have historical behavior information in the user group are defined as cross users; in practical cases, the number of cross users is much smaller than the number of non-cross users; by cross-user, as non-cross-user U₁And U₂Establishing similarity relation to help the target field to recommend;

(2) and (3) similarity migration: non-cross user U₁And user U₂Similarity cannot be directly calculated, however, user U₁And user U₂Respectively with cross users U_cCan be calculated, so that the cross users U can be crossed_cCreating user U as a link₁And user U₂The similarity of (2);

and (3) similarity migration step: first, find and platform e₁And a platform e₂Public user set U_c(ii) a Then calculate U separately₁And U_cSimilarity of (2) is expressed as a vector

U₂And U_cIs recorded as

Final calculation

And

is the inner product of (1), namely U₁And U₂The transfer similarity of (2);

wherein, U₁₁Presentation platform e₁Non-intersecting users 1, U in₂₁、U₂₂Presentation platform e₂Non-intersecting users 1, U in_c1、U_c2Equal for cross-users, S₁、S₂Etc. represent similarity; if U is to be calculated₁₁And U₂₁The similarity between the two can pass through U_c1、U_c2、U_c3Transitional, indirect calculation

To sum up, then U₁And U₂The similarity calculation between them can be formalized as:

(3) and (3) similarity calculation: calculating non-cross user U₁And U₂Before the similarity, non-cross user U needs to be calculated₁、U₂The similarity with the cross users respectively is calculated as follows:

1) similarity of user scores

Measuring the similarity of user scores through two aspects of score distribution consistency and credibility;

the consistency of the score distribution isThe score distribution of the same items evaluated by two users; the more consistent the score distribution, the more similar the interests of the two users are; let { ur₁,ur₂,...,ur_n}，

Respectively carrying out increasing ordering on two groups of data for the scoring sets of the common items of the user u and the user v, namely { ur₁,ur₂,...,ur_n}，

If 1,2, n and x₁,x₂,...,x_nThe greater the matching degree of (A) is, the higher the consistency of the two is; the calculation formula is as follows:

the credibility is determined according to the quantity of the same articles evaluated by two users, and if the quantity is small, the two items are not similar to each other even if the grading distribution is consistent; the calculation formula is as follows:

wherein, I_uAn item set representing a user u's rating;

the user score similarity calculation formula is as follows:

sim₁(u,v)＝dist(u,v)conf(u,v) (1-4)

2) user attribute similarity

The user attribute similarity is measured according to the user attribute; users with the same attributes have similar interests to some extent; the calculation formula is as follows:

wherein n represents the number of attributes, sim (u, v, i) represents whether two users are the same on the ith attribute, if so, the number is 1, otherwise, the number is 0, and d_iThe discrimination degree of the ith attribute is represented, if all the articles are scored by a user with a certain attribute, the attribute is not distinguished, and the value of the discrimination degree is determined by different data sets;

3) final degree of similarity

After the user scores a certain article, the user is used for scoring the article, and when the user does not score the certain article, the user attribute information is used; when the number of the items scored by the user is increased, the method is smoothly transited to the step of recommending by using scoring information, the step of smoothing is performed by using a sigmoid function, and finally the similarity of the user is defined as follows:

sim(u,v)＝αsim₁(u,v)+(1-α)sim₂(u,v) (1-6)

wherein, C_uvA set of items representing a common evaluation of user u and user v; the user similarity calculation is smoothly transited to the use scoring information along with the increase of the number of the goods evaluated by the user, and the smooth transition can improve the prediction accuracy rate in the cold start state.

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