CN106779941B - The automobile recommended method and system decomposed based on matrix and tensor joint - Google Patents
The automobile recommended method and system decomposed based on matrix and tensor joint Download PDFInfo
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Abstract
The invention discloses the automobile recommended methods and system decomposed based on matrix and tensor joint；The tensor the following steps are included: construction automobile is given a mark, construct automaker and relationship with customer matrix, automobile product structure tree is constructed, automaker and relationship with customer matrix and automobile product structure tree are completely, for assisting the occurrence lacked in prediction tensor；According to automobile product structure tree, introduces tree group lasso trick model to carry out specification to final loss function, obtain weight；Loss function is established, loss function is iterated with alternating least-squares method；To loss function derivation zero setting, the iteration function of matrix is then found out；Restore tensor, the i.e. missing values of completion tensor；For different users, according to the element in the tensor X of completion, the vehicle successively liked to user recommended user according to the order from high to low of marking.
Description
Technical field
The present invention relates to a kind of automobile recommended methods and system decomposed based on matrix and tensor joint.
Background technique
Recommendation problem origin, i.e., according to information existing between user and product come to user recommend new product or
The product being likely to purchase.Common method is often contacting according to user and product, such as the purchaser record of user or user
Marking record, come predict user may favorite product recommend user.It, then can be according to a user to certain in automotive field
Vehicle is given a mark to predict the marking situation of other vehicles.And such marking record is often extremely sparse.
Tensor resolution completion technology consider it is various between user and vehicle contact, for example user-vehicle-evaluation refers to
Target marking, can preferably analyze the potential connection between three.Its cardinal principle is to construct a tensor, the value of the inside
It is specific marking (1 to 5 points), missing values 0 are decomposed using CP common in tensor to carry out completion to tensor, to predict
The true marking of missing values.However, there is no in view of other auxiliary letters during common tensor resolution completion
Breath.
Summary of the invention
The purpose of the present invention is to solve the above-mentioned problems, provides a kind of automobile decomposed based on matrix and tensor joint
Recommended method and system, it is using the relation of the supply between automaker and automobile component part supply quotient and according to automobile institute
The vehicle system of category and manufacturer are formed by tree-like hierarchy relationship to carry out constraint loss function, to reach better prediction result.
To achieve the goals above, the present invention adopts the following technical scheme:
A kind of automobile recommended method decomposed based on matrix and tensor joint, comprising the following steps:
S1, construction automobile marking tensor X, construction automaker and relationship with customer matrix E, construct automobile product structure
T is set, automaker and relationship with customer matrix E and automobile product structure tree T are completely, for assisting prediction tensor X
The occurrence of middle missing；
S2, come according to automobile product structure tree T, introducing tree group lasso trick model Tree-guided Group Lasso to most
Whole loss function carries out specification, obtains weight W (v)；
What S3, the automobile obtained according to S1 marking tensor X, automaker and relationship with customer matrix E and S2 were obtained
Weight W (v) establishes loss function, is iterated with alternating least-squares method ALS to loss function；To loss function derivation
Then zero setting finds out the iteration function of matrix A, B, C, S and M；
After S4, matrix A, B and C are by the iteration in S3, pass through matrix A, the apposition of B, CIt is opened to restore
Measure X, the i.e. missing values of completion tensor X；Calculate the RMSE and MAE of iteration, the numerical value of RMSE and MAE are smaller to illustrate prediction result
Better, the numerical value of RMSE and MAE are smaller to be illustrated to predict that numerical value differs smaller with actual numerical value；
S5, judge whether the RMSE acquired in S4 meets the condition of convergence of setting or judge whether the number of iterations meets setting
The condition of convergence, recycle and terminate if meeting, otherwise return to S3；
S6, for different users, according to the element in the tensor X of completion, according to marking order from high to low according to
The secondary vehicle liked to user recommended user.
The step of S1 are as follows:
Automobile marking tensor X is constructed, automobile gives a mark tensor dimension as I × J × K, and I is user's number, and J is vehicle quantity, K
For standards of grading number；
Construct automaker and relationship with customer matrix E；Two dimensions of matrix E are manufacturer and supplier respectively.
The dimension of matrix E is U × V, and wherein U indicates manufacturer's number, and V indicates supplier's number；Value E in matrixuvWhat is indicated is system
Make quotient u whether with supplier v there are relations of the supply；If being equal to 1, then it represents that there is supply between manufacturer u and supplier v and close
System.On the contrary, relation of the supply is not present if being equal to 0；
Construct automobile product structure tree T；According to the subordinate relation building in automotive field, between vehicle-vehicle system-manufacturer
One tree out；Each leaf node is each vehicle, and intermediate node is is constituted according to vehicle system or manufacturer belonging to vehicle
Set, root node be all vehicles composed by big collection；Only one father node of each child node, and same node layer
It is not overlapped.
In S1, the automobile element representation in tensor X of giving a mark is marking of the user i to the standards of grading k of vehicle j；Automobile
The missing values needs of marking tensor X are predicted；Standards of grading include: space, power, comfort, oil consumption, manipulation, appearance, interior
Decorations and cost performance.
The tree group lasso trick model Tree-guided Group Lasso:
Wherein, a represent be automobile product structure tree T intermediate node weight, b represent be automobile product structure tree
The weight of T leaf node；gvIt is the number of the included vehicle of intermediate node, the marking situation of vehicle system and manufacturer grading three
Then product is normalized product, normalize between 0-1, and sv=1-gv；GVWhat is represented is any one in tree
Node (may be leaf node, it is also possible to intermediate node or root node), is the set of vehicle；In homography B (square
Battle array B be tensor X by CP decomposite come second factor matrix, dimension is J × R, J representative vehicle quantity, and R represents tensor
Order) several rows, vehicle corresponding to several rows belongs to the node G in treeV, | | * | | expression is Euclid norm；
| * | representative is L1 norm；C is the child node of structure tree T interior joint v.
The loss function is as follows:
F (A, B, C, M, S)=Tensor (A, B, C)+Enterp (M, S)+Weight (B)+Manu (M, B)
Wherein, Tensor (A, B, C), Enterp (M, S), Manu (M, B), Weight (B) are respectively as follows:
Wherein, involved A, B and C be tensor X by CP decomposite come factor matrix, dimension is respectively I × R, J
× R, K × R, wherein R is the order of tensor；The full name in English of CP is: CANDECOMP/PARAFAC decomposition；
M and S is the factor matrix that matrix E is come out by matrix decomposition, and dimension is respectively U × R, V × R, BkThe square of representative
The row k of battle array B, wherein 0≤k < J；λTIt is the regularization parameter of function Tensor (A, B, C), λEIt is function Enterp (M, S)
Regularization parameter, λMIt is regularization parameter, the λ of function Manu (M, B)WIt is the regularization parameter of function Weight (B).A||F、
||B||F、||C||FRespectively correspond matrix A, the F- norm of B, C.MjWhat is indicated is the jth column of matrix M, wherein 0≤j < U, i.e.,
The feature vector of manufacturer j.What is represented is j-th of node of first layer, i.e. j leaf node；
What is represented is i-th layer of j-th of set of automobile product structure tree T,It is i-th layer of jth of automobile product structure tree T
The weight of a set, X(2)It is tensor X according to the expansion mode-2 expansion of 2 ranks, λ is regularization parameter, and ⊙ indicates that Khatri-Rao multiplies
Product.
Joint decomposition is carried out to matrix E and tensor X, and makes MjWithDifference is minimum, i.e., corresponding constraint letter
Number Manu (M, B)；Tensor X is decomposed and is decomposed using CP, basic matrix decomposition E=M × S is used to matrix decompositionT。
The iteration function of matrix A, B, C, S and M:
C=(X(3)(B⊙A))(BTB*ATA+λTIR)-1
S=ETM(MTM+λEIR)-1
X(1)Tensor X is represented according to the expansion mode-1 expansion of 1 rank；X(2)Tensor X is represented to be unfolded according to mode-2；X(3)It represents
Tensor X is unfolded according to mode-3；IRWhat is represented is the unit matrix of R × R；AT、BT、CT、ET、MT、STRepresenting matrix A, B, C, E,
M, the transposition of S.
The RMSE and MAE for calculating iteration:
It is the prediction result of the original missing values of tensor, and yiIt is the legitimate reading of the original missing values of tensor, what n was represented is
The sum of missing values.
The S5 setting the number of iterations is 50 times, and it is 0.7 that RMSE, which is arranged, when the number of iterations is more than that 50 or RMSE is lower than
When 0.7, then stop recycling.
A kind of automobile recommender system decomposed based on matrix and tensor joint, comprising:
Structural unit: for constructing automobile marking tensor X, construction automaker and relationship with customer matrix E, vapour is constructed
Vehicle product tree T, automaker and relationship with customer matrix E and automobile product structure tree T are completely, for assisting
The occurrence lacked in prediction tensor X；
Specification unit: for introducing tree group lasso trick model Tree-guided Group according to automobile product structure tree T
Lasso to carry out specification to final loss function, obtains weight W (v)；
Loss function establishes unit: for according to automobile give a mark tensor X, automaker and relationship with customer matrix E with
And weight W (v), loss function is established, loss function is iterated with alternating least-squares method ALS；Loss function is asked
Zero setting is led, the iteration function of matrix A, B, C, S and M is then found out；
Tensor reduction unit: after matrix A, B and C pass through iteration, pass through matrix A, the apposition of B, CTo go back
Former tensor X, the i.e. missing values of completion tensor X；Calculate the RMSE and MAE of iteration, the numerical value of RMSE and MAE are smaller to be illustrated to predict
As a result better, the numerical value of RMSE and MAE are smaller to be illustrated to predict that numerical value differs smaller with actual numerical value；
Judging unit: for judging whether the RMSE acquired meets the condition of convergence of setting or judges whether the number of iterations is full
The condition of convergence set enough, recycling if meeting terminates, and otherwise returns to loss function and establishes unit；
Recommendation unit: for being directed to different users, according to the element in the tensor X of completion, according to marking slave height to
The vehicle that low order is successively liked to user recommended user.
Structural unit includes:
Automobile marking tensor constructing module, for constructing automobile marking tensor X, automobile marking tensor dimension is I × J × K,
I is user's number, and J is vehicle quantity, and K is standards of grading number；
Relational matrix constructing module, for constructing automaker and relationship with customer matrix E；Two dimensions of matrix E
It is manufacturer and supplier respectively；The dimension of matrix E is U × V, and wherein U indicates manufacturer's number, and V indicates supplier's number；Square
Value E in battle arrayuvIndicate be manufacturer u whether with supplier v there are relations of the supply；If being equal to 1, then it represents that manufacturer u and confession
Answer between quotient v that there are relations of the supply.On the contrary, relation of the supply is not present if being equal to 0；
Automobile product structure tree constructing module, for constructing automobile product structure tree T；According in automotive field, vehicle-vehicle
Subordinate relation between system-manufacturer constructs one tree；Each leaf node is each vehicle, and intermediate node is according to vehicle
The set that vehicle system or manufacturer are constituted belonging to type, root node are big collection composed by all vehicles；Each child node is only
There is a father node, and same node layer is not overlapped.
Tree group lasso trick model is a kind of to can be achieved at the same time sparse features variables choice and model based on regularization method
The method of parameter Estimation.Sometimes there is group structure between multiple characteristic variables of sample, the group structure between input variable is made
For prior information, a group lasso trick model is proposed.Many data not only have a group structure, and there are partial ordering relations between group, i.e.,
Tree construction.When handling this data, needs to make full use of tree construction as prior information, be obtained using above-mentioned prior information
Tree group lasso trick model
Beneficial effects of the present invention:
1 makes full use of between structural relation and manufacturer and supplier between automobile and its affiliated vehicle system, manufacturer
Coupled relation, realize the recommended method chosen of automobile；
2 present invention increase during carrying out marking prediction using tensor completion to the potential structure of product and manufacture
The considerations of relation of the supply between quotient and supplier, more can significantly improve the accuracy of marking prediction.It is missed from root mean square
Can be seen that on poor (RMSE) and mean error (MAE) two indices model provided by the invention compared with other common methods have compared with
It is big to be promoted.
3 in automotive field, we can according between vehicle-vehicle system-manufacturer tree-like hierarchical structure and manufacturer
Relation of the supply between supplier carrys out marking of the aid forecasting user about the Score index of some vehicle, i.e., in tensor
Missing values.
Because often user can consider vehicle belonging to a vehicle when buying automotive type or scoring to automobile
The supplier of system, manufacturer and auto parts and components.Finally according to marking of the user come for vehicle index is predicted, will give a mark
Higher vehicle recommends user.
Detailed description of the invention
Fig. 1 is more relationship tensor resolution model flow figures of tree guidance provided by the invention.
Fig. 2 (a) is tensor X；
Fig. 2 (b) matrix E；
Fig. 2 (c) structure tree T；
Fig. 3 is the Experimental comparison results of RMSE and MAE on automotive field data set.
Fig. 4 be probe into automobile SC for this method automotive field influence.
Fig. 5 is the influence probed by automotive type class relations institute composed structure tree depth for this method.
Specific embodiment
The invention will be further described with embodiment with reference to the accompanying drawing.
The present invention provides a kind of methods decomposed based on matrix and tensor joint, and using between manufacturer and supplier
Relation of the supply and vehicle according to affiliated vehicle system, manufacturer be formed by tree-like hierarchy relationship to be constrained.Such as Fig. 1 institute
Show, comprising the following steps:
Step1, fabric tensor X, matrix E and tree T, as shown in Fig. 2 (a)-Fig. 2 (c)；
Step1.1, fabric tensor X, three dimensions of tensor are user-vehicle-standards of grading.User in tensor X must
It must be all properties for commenting at least one vehicle, likewise, vehicle therein must be beaten excessively by least one user.Scoring
Standard has 8, is respectively as follows: space, power, comfort, oil consumption, manipulation, appearance, interior trim and cost performance.XijkThat indicate is user
I gives a mark to the evaluation index k of vehicle j, and marking section is the marking that 1 to 5. users carry out 1-5 points to these standards of grading.
Measure X ∈ RI×J×K, I is user's number, and J is vehicle quantity, and k is standards of grading, i.e., quantity is 8.
Two dimensions of Step1.2, structural matrix E, matrix E are manufacturer and supplier respectively.Matrix E ∈ RU×V, wherein
U indicates manufacturer's number, and V indicates supplier's number.Value E in matrixuvWhat is indicated is whether manufacturer u exists with supplier v
Relation of the supply.If EuvEqual to 1, then it represents that there are relations of the supply between manufacturer u and supplier v.On the contrary, not deposited if being equal to 0
In relation of the supply.
Step1.3, structural texture tree T, according in automotive field, subordinate relation between vehicle-vehicle system-manufacturer can be with
Construct one tree.Each leaf node is each vehicle, such as 2017 sections of 320Li M sports types.Intermediate node is according to vehicle
The set that vehicle system or manufacturer are constituted belonging to type, such as 2017 sections of 320Li M sports types belong to 3 system of BMW, and 3 system of BMW is
It is manufactured by Bayerische Motorne Werke Aktiengeellschaft.Root node is big collection composed by all vehicles.
In addition, algorithm run before matrix E and structure tree T be all it is complete, it is specific for assisting to lack in prediction tensor
Value.
Step2, the weight W (v) that each vehicle v is calculated according to tree T.
The structure tree T according to caused by product in S1, only one father node of each child node, and same node layer does not have
There is overlapping, because a vehicle has and be pertaining only to a vehicle system, a vehicle system has and is pertaining only to a manufacturer.Based on this different
Structure information we introduce tree-guided group lasso to carry out specification, constraint function to final loss function are as follows:
Here λWIt is the regularization parameter of representative function Weight (B), BkWhat is indicated is the row k of matrix B, is corresponded to
K-th of vehicle,What is represented is i-th layer of j-th of set of structure tree,It is the weight of the corresponding set.
Wherein what (a) was represented is the weighted value for the intermediate node set, and that (b) represent is the weight of leaf node, gvBe by
Number of the node comprising vehicle and the rank value of its affiliated vehicle system and manufacturer are determined, and sv=1-gv。In corresponding square
Several rows of battle array B, vehicle corresponding to these rows belong to the node G in treeV, | * | expression is L1 norm, | | * | | expression
It is Euclid norm.
The loss function of Step3, entire model are as follows:
F (A, B, C, M, S)=Tensor (A, B, C)+Enterp (M, S)+Weight (B)+Manu (M, B)
Here the Tensor (A, B, C) being related to, Enterp (M, S), Manu (M, B), Weight (B) are as follows:
Wherein involved A, B, C are that tensor X decomposites the factor matrix come, and dimension is respectively I × R, J × R, K ×
R, wherein R is the order of tensor.M, S is that matrix E decomposites the factor matrix come, and dimension is respectively U × R, V × R, BkThe square of representative
The row k of battle array B, MjRepresent the jth row of matrix M.X(2)It is that tensor X is unfolded according to mould 2, λ is the regularization ginseng of corresponding different functions
Number, ⊙ indicate Khatri-Rao product.
Step4, loss function is iterated with alternating least-squares method (ALS)
Joint decomposition is carried out to matrix E and tensor X, and makes close as far as possible, i.e. Manu (M, B).We are decomposed to tensor X
It is decomposed using CP, basic matrix decomposition is used to matrix decomposition.Make the loss function in Step3 to matrix A, B, C, M, S are asked
Then local derviation makes local derviation be equal to zero.Can be in the hope of matrix A, B, C, the iteration function of M, S:
C=(X(3)(B⊙A))(BTB*ATA+λTIR)-1
S=ETM(MTM+λEIR)-1
It is wherein X(n)It represents tensor X to be unfolded according to mode-n, IRWhat is represented is the unit matrix of R × R.Represent be
J-th of node of first layer, i.e. j leaf node.Represent other rows in matrix B in addition to k.
Step5, matrix A, B, C pass through after above-mentioned iteration, can pass throughIt restores tensor X, that is, mends
Missing values before complete.The RMSE and MAE of this iteration, the number of RMSE and MAE can be calculated according to calculation method once
Be worth it is smaller illustrate that prediction result is better, predict that numerical value with actual numerical value differs smaller.
Here representative isTo the prediction result of the original missing values of tensor, and yiIt is the true knot of the original missing values of tensor
Fruit.Here the sum for being missing from value that n is represented.
Step6, judge whether the RMSE acquired after each iteration or the number of iterations meet the condition of convergence of setting, if full
Sufficient then circulation terminates, and otherwise continues iteration.
It is 50 times that the number of iterations, which is arranged, and it is 0.7 that RMSE, which is arranged, when the number of iterations is more than 50 or RMSE lower than 0.7
When, then stop recycling.
Step7, for different users, we according to predict it is coming as a result, according to marking order from high to low
User is successively allowed to recommend vehicle.
As shown in Figure 3-Figure 5, the recommended method provided by the invention in automotive field and each algorithm phase in the prior art
Than root-mean-square error (RMSE) and mean error (MAE) are smaller, and the accuracy of prediction is higher, has compared with the prior art larger
Promotion.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (8)
1. a kind of automobile recommended method decomposed based on matrix and tensor joint, characterized in that the following steps are included:
S1, construction automobile marking tensor X, construction automaker and relationship with customer matrix E, construct automobile product structure tree T,
Automaker and relationship with customer matrix E and automobile product structure tree T are completely, for assisting to lack in prediction tensor X
The occurrence of mistake；
S2, come according to automobile product structure tree T, introducing tree group lasso trick model Tree-guided Group Lasso to final
Loss function carries out specification, obtains weight W (v)；
The weight W that S3, the automobile obtained according to S1 marking tensor X, automaker and relationship with customer matrix E and S2 are obtained
(v), loss function is established, loss function is iterated with alternating least-squares method ALS；To loss function derivation zero setting,
Then the iteration function of matrix A, B, C, S and M is found out；
After S4, matrix A, B and C are by the iteration in S3, pass through matrix A, the apposition of B, CRestore tensor X,
That is the missing values of completion tensor X；Calculate the RMSE and MAE of iteration, the numerical value of RMSE and MAE are smaller to be illustrated to predict numerical value and reality
Numerical value difference in border is smaller；
S5, judge whether the RMSE acquired in S4 meets the condition of convergence of setting or judge whether the number of iterations meets the receipts of setting
Condition is held back, recycling if meeting terminates, and otherwise returns to S3；
S6, it is successively given according to the element in the tensor X of completion according to the order from high to low of marking for different users
The vehicle that user recommended user likes；
Wherein the step of S1 are as follows:
Construct automobile give a mark tensor X, automobile give a mark tensor dimension be I × J × K, I be user's number, J be vehicle quantity, K be comment
The quasi- number of minute mark；
Construct automaker and relationship with customer matrix E；Two dimensions of matrix E are manufacturer and supplier respectively；Matrix E
Dimension be U × V, wherein U indicate manufacturer's number, V indicate supplier's number；Value E in matrixuvThat indicate is manufacturer u
Whether there are relations of the supply with supplier v；If being equal to 1, then it represents that there are relations of the supply between manufacturer u and supplier v；Phase
Instead, if being equal to 0, relation of the supply is not present；
Construct automobile product structure tree T；According in automotive field, the subordinate relation between vehicle-vehicle system-manufacturer constructs one
Tree；Each leaf node is each vehicle, and intermediate node is according to the collection that vehicle system or manufacturer are constituted belonging to vehicle
It closes, root node is big collection composed by all vehicles；Only one father node of each child node, and same node layer does not have
Overlapping.
2. a kind of automobile recommended method decomposed based on matrix and tensor joint as described in claim 1, characterized in that S1
In, the automobile element representation in tensor X of giving a mark is marking of the user i to the standards of grading k of vehicle j；Automobile gives a mark tensor X's
Missing values needs are predicted；Standards of grading include: space, power, comfort, oil consumption, manipulation, appearance, interior trim and cost performance.
3. a kind of automobile recommended method decomposed based on matrix and tensor joint as described in claim 1, characterized in that described
Tree group lasso trick model Tree-guided Group Lasso:
Wherein, a represent be automobile product structure tree T intermediate node weight, b represent be automobile product structure tree T leaf
The weight of child node；gvIt is multiplying for the number of the included vehicle of intermediate node, the marking situation of vehicle system and manufacturer grading three
Product, is then normalized product, normalizes between 0-1, and sv=1-gv；GVWhat is represented is any one section in tree
Point, it may be possible to leaf node, it is also possible to which intermediate node or root node are the set of vehicle；In the several of homography B
It goes, vehicle corresponding to several rows belongs to the node G in treeV, | | * | | expression is Euclid norm；| * | representative
It is L1 norm；C is the child node of structure tree T interior joint v；Matrix B be tensor X by CP decomposite come second factor square
Battle array, dimension are J × R, J representative vehicle quantity, and R represents the order of tensor.
4. a kind of automobile recommended method decomposed based on matrix and tensor joint as described in claim 1, characterized in that described
Loss function is as follows:
F (A, B, C, M, S)=Tensor (A, B, C)+Enterp (M, S)+Weight (B)+Manu (M, B)
Wherein, Tensor (A, B, C), Enterp (M, S), Manu (M, B), Weight (B) are respectively as follows:
Wherein, involved A, B and C be tensor X by CP decomposite come factor matrix, dimension is respectively I × R, J × R,
K × R, wherein R is the order of tensor；The full name in English of CP is: CANDECOMP/PARAFAC decomposition；
M and S is the factor matrix that matrix E is come out by matrix decomposition, and dimension is respectively U × R, V × R, BkThe matrix B of representative
Row k, wherein 0≤k < J；λTIt is the regularization parameter of function Tensor (A, B, C), λEIt is the canonical of function Enterp (M, S)
Change parameter, λMIt is regularization parameter, the λ of function Manu (M, B)WIt is the regularization parameter of function Weight (B)；||A||F、||B|
|F、||C||FRespectively correspond matrix A, the F- norm of B, C；MjWhat is indicated is the jth column of matrix M, wherein 0≤j < U, that is, manufacture
The feature vector of quotient j；What is represented is j-th of node of first layer, i.e. j leaf node；
What is represented is i-th layer of j-th of set of automobile product structure tree T,It is i-th layer of j-th of set of automobile product structure tree T
Weight, X(2)It is tensor X according to the expansion mode-2 expansion of 2 ranks, λ is regularization parameter, and ⊙ indicates Khatri-Rao product；
Joint decomposition is carried out to matrix E and tensor X, and makes MjAnd jDifference is minimum, that is, corresponds to constraint function
Manu (M, B)；Tensor X is decomposed and is decomposed using CP, basic matrix decomposition E=M × S is used to matrix decompositionT。
5. a kind of automobile recommended method decomposed based on matrix and tensor joint as described in claim 1, characterized in that matrix
A, the iteration function of B, C, S and M:
A=[X(1)(C⊙B)][CTC*BTB+λTIR]-1
C=(X(3)(B⊙A))(BTB*ATA+λTIR)-1
S=ETM(MTM+λEIR)-1
X(1)Tensor X is represented according to the expansion mode-1 expansion of 1 rank；X(2)Tensor X is represented to be unfolded according to mode-2；X(3)Represent tensor X
It is unfolded according to mode-3；IRWhat is represented is the unit matrix of R × R；AT、BT、CT、ET、MT、STRepresenting matrix A, B, C, E, M, S's
Transposition.
6. a kind of automobile recommended method decomposed based on matrix and tensor joint as described in claim 1, characterized in that described
Calculate the RMSE and MAE of iteration:
It is the prediction result of the original missing values of tensor, and yiIt is the legitimate reading of the original missing values of tensor, what n was represented is missing from
The sum of value.
7. a kind of automobile recommended method decomposed based on matrix and tensor joint as described in claim 1, characterized in that described
It is 50 times that the number of iterations, which is arranged, in S5, and it is 0.7 that RMSE, which is arranged, when the number of iterations is more than that 50 or RMSE is lower than 0.7, then
Stop circulation.
8. a kind of automobile recommender system decomposed based on matrix and tensor joint, characterized in that include:
Structural unit: for constructing automobile marking tensor X, construction automaker and relationship with customer matrix E, construction automobile is produced
Product structure tree T, automaker and relationship with customer matrix E and automobile product structure tree T are completely, for assisting to predict
The occurrence lacked in tensor X；
Specification unit: for introducing tree group lasso trick model Tree-guided Group Lasso according to automobile product structure tree T
To carry out specification to final loss function, obtains weight W (v)；
Loss function establishes unit: for according to automobile marking tensor X, automaker and relationship with customer matrix E and power
Weight W (v), establishes loss function, is iterated with alternating least-squares method ALS to loss function；Loss function derivation is set
Zero, then find out the iteration function of matrix A, B, C, S and M；
Tensor reduction unit: after matrix A, B and C pass through iteration, pass through matrix A, the apposition of B, CIt is opened to restore
Measure X, the i.e. missing values of completion tensor X；Calculate the RMSE and MAE of iteration, the numerical value of RMSE and MAE are smaller to be illustrated to predict numerical value
Differ smaller with actual numerical value；
Judging unit: it is set for judging whether the RMSE acquired meets the condition of convergence of setting or judge whether the number of iterations meets
The fixed condition of convergence, recycling if meeting terminates, and otherwise returns to loss function and establishes unit；
Recommendation unit: for being directed to different users, according to the element in the tensor X of completion, according to marking from high to low
The vehicle that order is successively liked to user recommended user；
Wherein structural unit includes:
Automobile marking tensor constructing module, for constructing automobile marking tensor X, automobile gives a mark tensor dimension as I × J × K, and I is
User's number, J are vehicle quantity, and K is standards of grading number；
Relational matrix constructing module, for constructing automaker and relationship with customer matrix E；Two dimensions of matrix E are distinguished
It is manufacturer and supplier；The dimension of matrix E is U × V, and wherein U indicates manufacturer's number, and V indicates supplier's number；In matrix
Value EuvIndicate be manufacturer u whether with supplier v there are relations of the supply；If being equal to 1, then it represents that manufacturer u and supplier v
Between there are relations of the supply；On the contrary, relation of the supply is not present if being equal to 0；
Automobile product structure tree constructing module, for constructing automobile product structure tree T；According in automotive field, vehicle-vehicle system-
Subordinate relation between manufacturer constructs one tree；Each leaf node is each vehicle, and intermediate node is according to vehicle
The set that affiliated vehicle system or manufacturer are constituted, root node are big collection composed by all vehicles；Each child node only has
One father node, and same node layer is not overlapped.
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