Optimization method and system for supervised learning under tensor mode is provided; wherein the method includes: receiving an input training tensor data set; introducing a within class scatter matrix into an objective function such that between class distance is maximized, at the same time, within class distance is minimized by the objective function; constructing an optimal frame of the objective function of an optimal projection tensor machine OPSTM subproblem; constructing an optimal frame of an objective function of an OPSTM problem; solving the revised dual problem and outputting alagrangian optimal combination and an offset scalar b; calculating a projection tensor W*; calculating a optimal projection tensor W; by the W together with the b, constructing a decision function; inputting to-be-predicted tensor data which has been rank-one decomposed into the decision function for prediction. This overcomes issues such as curse of dimensionality, over learning and small sample occurred when vector mode algorithms process the tensor data, and effectively avoids a time-consuming alternative projection iterative process of the tensor mode algorithms of the prior art.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. An optimization method for supervised learning under tensor mode, wherein the method comprise: receiving an input training tensor data set; introducing a within class scatter matrix into an objective function such that between class distance is maximized, at the same time, within class distance is minimized by the objective function; constructing an optimal frame of the objective function of an optimal projection tensor machine OPSTM subproblem; transforming N vector modes of quadratic programming subproblems into a multiple quadratic programming problem under a single tensor mode, and constructing an optimal frame of an objective function of an OPSTM problem; according to lagrangian multiplier method, obtaining a dual problem of the optimal frame of the objective function, introducing a tensor rank one decomposition into calculation of tensor transvection, and obtaining a revised dual problem; utilizing sequential minimal optimization SMO algorithm to solve the revised dual problem and output an alagrangian optimal combination and an offset scalar b; calculating a projection tensor W*; performing the rank one decomposition to the projection tensor W*; performing a back projection to a component obtained after performing the rank one decomposition to the projection tensor W*; performing rank one decomposition inverse operation to the component obtained after performing the back projection to obtain an optimal projection tensor W which is corresponded to the training tensor data set; decision function construction phase: by the optimal projection tensor W which has been rank-one decomposed together with the offset scalar b, constructing a decision function; application prediction phase: inputting to-be-predicted tensor data which has been rank-one decomposed into the decision function for prediction. 2. The method of claim 1, wherein after introducing the within class scatter matrix into an objective function of an STM subproblem, through an eta coefficient η, the objection function of the quadratic programming problem of an n-th subproblem is changed into: min w ( n ) , b ( n ) , ξ ( n )  1 2  [ (  w ( n )  F 2 + η  ( ( w ( n ) ) T  S w ( n )  w ( n ) ) )  ∏ 1 < i < N i ≠ n  (  w ( i )  F 2 + η  ( ( w ( i ) ) T  S w ( n )  w ( i ) ) ) ] + C  ∑ m = 1 M  ξ m ( n ) wherein, Sw(n) is an n-th order within class scatter matrix estimated after the training tensor data set is expanded along the n-th order; w(n) is an n-th order optimal projection vector of the training tensor data, n=1, 2, . . . N; C is a penalty factor; ξm(n) is a slack variable; eta coefficient η is configured to measure the importance of the within class scatter matrix. 3. The method of claim 2, wherein the optimal frame of an objective function of an OPSTM problem is a combination of N vector modes of quadratic programming problems, which respectively corresponds to a subproblem; wherein, a quadratic programming problem of an n-th subproblem is: min w * ( n ) , b ( n ) , ξ ( n )  1 2   w * ( n )  F 2  ∏ 1 ≤ i ≤ N i ≠ n   w * ( i )  F 2 + C  ∑ m = 1 M  ξ m ( n ) S . t .  y m  ( ( w * ( n ) ) T  ( V m  ∏ 1 ≤ i ≤ N i ≠ n  × i  w * ( i ) ) + b ( n ) ) ≥ 1 - ξ m ( n )   ξ m ( n ) ≥ 0   m = 1 , 2 , …   M wherein, w*(n) is the n-th order projection vector of the training tensor data set; w*(n)=Λ(n)1/2P(n)Tw(n), wherein Λ(n) and P(n) meet that P(n)T(E+ηSw(n))P(n)=Λ(n); E is an identity matrix; V m = X m  ∏ i = 1 N  × i  [ ( P ( i )  Λ ( i )  1 / 2 ) - 1 ] T is tensor input data obtained after tensor input data Xm in the training tensor data set is projected along each order; Xi is an i-mode multiplication operator; b(n) is the n-th order offset scalar of the training tensor data set. 4. The method of claim 3, wherein according to a formula  W *  F 2 = ∏ n = 1 N   w * ( n )  F 2 , and a formula (w*(n))T(Vm Π1<i<Ni≠n×iw*(n))=<W*, Vm<, transforming the N vector modes of quadratic programming subproblems into the multiple quadratic programming subproblem under a single tensor mode; a constructed optimal frame of the objective function of the OPSTM problem meets that: min W * , b , ξ  1 2   W *  F 2 + C  ∑ m = 1 M  ξ m S . t .  y m  ( 〈 W * , V m 〉 + b ) ≥ 1 - ξ m ξ m ≥ 0   m = 1 , 2 , …   M wherein, < > is a transvection operator, and ξ m = max n = 1 , 2 , …   N  { ξ m ( n ) } . 5. The method of claim 4, wherein according to lagrangian multiplier method, an obtained dual problem of the optimal frame of the objective function is: max α  ∑ m = 1 M  α m - 1 2  ∑ i , j = 1 M  α i  α j  y i  y j  〈 V i , V j 〉 S . t .  ∑ m = 1 M  ( α m  y m ) = 0   0 < α m < C   m = 1 , 2 , …   M ; introducing the tensor rank one decomposition into the calculation of the tensor transvection; an obtained revised dual problem is: max α  ∑ m = 1 M  α m - 1 2  ∑ i , j = 1 M  ∑ p = 1 R  ∑ q = 1 R  α i  α j  y i  y j  ∏ n = 1 N  〈 V ip ( n ) , V jp ( n ) 〉 S . t .  ∑ m = 1 M  ( α m  y m ) = 0 0 < α m < C   m = 1 , 2 , …   M . 6. The method of claim 5, wherein calculating the projection tensor W* according to a formula, W * = ∑ m = 1 M  α m  y m  V m . 7. An optimization system for supervised learning under tensor mode is provided, wherein the system comprises: a data receiving unit configured to receive an input training tensor data set; a within class scatter introducing unit configured to introduce a within class scatter matrix into an objective function such that between class distance is maximized, at the same time, within class distance is minimized by the objective function; a subproblem optimal frame constructing unit configured to construct an optimal frame of an objective function of an optimal projection tensor machine OPSTM subproblem; a problem optimal frame constructing unit configured to transform N vector modes of quadratic programming subproblems into a multiple quadratic programming problem under a single tensor mode, and construct an optimal frame of an objective function of an OPSTM problem; a dual problem obtaining unit configured to obtain a dual problem of the optimal frame of the objective function, introduce a tensor rank one decomposition into calculation of tensor transvection, and obtain a revised dual problem according to lagrangian multiplier method; a dual problem solving unit configured to utilize sequential minimal optimization SMO algorithm to solve the revised dual problem and output an alagrangian optimal combination and an offset scalar b; a projection tensor calculating unit configured to calculate a projection tensor W*; a projection tensor decomposition unit configured to perform the rank one decomposition to the projection tensor W*; a back projection unit configured to perform a back projection to a component obtained after performing the rank one decomposition to the projection tensor W*; an optimal projection tensor calculating unit configured to perform rank one decomposition inverse operation to the component obtained after performing the back projection to obtain an optimal projection tensor W which is corresponded to the training tensor data set; a decision function constructing unit configured to construct a decision function construction phase and construct a decision function by the optimal projection tensor W which has been rank-one decomposed together with the offset scalar b, a predicting unit configured to input to-be-predicted tensor data which has been rank-one decomposed into the decision function for prediction in the application prediction phase. 8. The system of claim 7, wherein after the within class scatter introducing unit introduces the within class scatter matrix into an objective function of an STM subproblem, through an eta coefficient η, the objection function of the quadratic programming problem of the n-th subproblem is changed into: min w ( n ) , b ( n ) , ξ ( n )  1 2  [ (  w ( n )  F 2 + η  ( ( w ( n ) ) T  S w ( n )  w ( n ) ) )  ∏ 1 < i < N i ≠ n  (  w ( i )  F 2 + η  ( ( w ( i ) ) T  S w ( n )  w ( i ) ) ) ] + C  ∑ m = 1 M  ξ m ( n ) wherein, Sw(n) is an n-order within class scatter matrix estimated after the training tensor data set is expanded along the n-th order; w(n) is the n-th order optimal projection vector of the training tensor data, n=1, 2, . . . N; C is a penalty factor; ξm(n) is a slack variable; eta coefficient η is configured to measure the importance of the within class scatter matrix. 9. The system of claim 8, wherein in the subproblem optimal frame constructing unit, the optimal frame of the objective function of the OPSTM problem is a combination of N vector modes of quadratic programming problems, which respectively corresponds to a subproblem; wherein, a quadratic programming problem of the n-th subproblem is: min w * ( n ) , b ( n ) , ξ ( n )  1 2   w * ( n )  F 2  ∏ 1 ≤ i ≤ N i ≠ n   w * ( i )  F 2 + C  ∑ m = 1 M  ξ m ( n ) S . t .  y m  ( ( w * ( n ) ) T  ( V m  ∏ 1 ≤ i ≤ N i ≠ n  × i  w * ( i ) )  b ( n ) ) ≥ 1 - ξ m ( n ) ξ m ( n ) ≥ 0   m = 1 , 2 , …   M wherein, w*(n) is the n-th order projection vector of the training tensor data set; w*(n)=Λ(n)1/2P(n)Tw(n), wherein Λ(n) and P(n) meet that P(n)T(E+ηSw(n))P(n)=Λ(n); E is an identity matrix; V m = X m = ∏ i = 1 N  × i  [ ( P ( i )  Λ ( i )  1 / 2 ) - 1 ] T is tensor input data obtained after tensor input data Xm in the training tensor data set is projected along each order; Xi is an i-mode multiplication operator; b(n) is the n-th order offset scalar of the training tensor data set. 10. The system of claim 9, wherein according to a formula  w *  F 2 = ∏ n = 1 N   w * ( n )  F 2 , and a formula (w*(n))T(Vm Π1<i<Ni≠n×iw*(n))=<W*, Vm<, the problem optimal frame constructing unit transforms the N vector modes of quadratic programming subproblems into the multiple quadratic programming subproblem under a single tensor mode; a constructed optimal frame of the objective function of the OPSTM problem meets that: min W * , b , ξ  1 2   W *  F 2 + C  ∑ m = 1 M  ξ m S . t .  y m  ( 〈 W * , V m 〉 + b ) ≥ 1 - ξ m ξ m ≥ 0   m = 1 , 2 , …   M wherein, < > is a transvection operator, and ξ m = max n = 1 , 2 , …   N  { ξ m ( n ) } . 11. The system of claim 10, wherein according to lagrangian multiplier method, the dual problem solving unit obtains the dual problem of the optimal frame of the objective function, which is: max α  ∑ m = 1 M  α m - 1 2  ∑ i , j = 1 M  α i  α j  y i  y j  〈 V i , V j 〉 S . t .  ∑ m = 1 M  ( α m  y m ) = 0   0 < α m < C   m = 1 , 2 , …   M ; the dual problem solving unit introduces the tensor rank one decomposition into the calculation of the tensor transvection; an obtained revised dual problem is: max α  ∑ m = 1 M  α m - 1 2  ∑ i , j = 1 M  ∑ p = 1 R  ∑ q = 1 R  α i  α j  y i  y j  ∏ n = 1 N  〈 V ip ( n ) , V jp ( n ) 〉 S . t .  ∑ m = 1 M  ( α m  y m ) = 0 0 < α m < C   m = 1 , 2 , …   M . 12. The system of claim 11, wherein the projection tensor calculating unit calculates the projection tensor W* according to a formula, W * = ∑ m = 1 M  α m  y m  V m .