WO2017092022A1 - 一种张量模式下的有监督学习优化方法及系统 - Google Patents

一种张量模式下的有监督学习优化方法及系统 Download PDF

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WO2017092022A1
WO2017092022A1 PCT/CN2015/096375 CN2015096375W WO2017092022A1 WO 2017092022 A1 WO2017092022 A1 WO 2017092022A1 CN 2015096375 W CN2015096375 W CN 2015096375W WO 2017092022 A1 WO2017092022 A1 WO 2017092022A1
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tensor
projection
objective function
rank
unit
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王书强
曾德威
申妍燕
施昌宏
卢哲
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深圳先进技术研究院
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Priority to US15/310,330 priority patent/US10748080B2/en
Priority to PCT/CN2015/096375 priority patent/WO2017092022A1/zh
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  • the invention belongs to the technical field of pattern recognition, and in particular relates to a supervised learning optimization method and system in a tensor mode.
  • the prior art still uses vector mode algorithms to process tensor data.
  • the original data must be feature extracted (vectorized) in the preprocessing stage.
  • the spatial information and the intrinsic correlation unique to the tensor data are easily destroyed, and the model parameters are too many, which may easily lead to Dimensional disasters, over-learning, small samples, etc.
  • the embodiment of the present invention provides a supervised learning optimization method and system in a tensor mode to solve the dimensional disaster, over-learning, and smallness of the vector mode algorithm provided by the prior art when processing tensor data.
  • the problem of the sample and the like overcomes the existing tensor mode algorithm.
  • the algorithm of the present invention is to solve the limitations of the existing algorithm, such as the problem that the time complexity of the algorithm is high, and the local minimum is often encountered.
  • a supervised learning optimization method in a tensor mode comprising:
  • the quadratic programming sub-problems of N vector patterns are transformed into multiple quadratic programming problems in a single tensor mode, and the optimization framework of the objective function of the OPSTM problem is constructed.
  • the dual problem of the optimization framework of the objective function is obtained, and the tensor rank-one decomposition is introduced into the calculation of the tensor inner product to obtain the modified dual problem.
  • sequence minimum optimization SMO algorithm is used to solve the modified dual problem, and the optimal combination of Lagrangian and the offset scalar b are output;
  • the to-be-predicted tensor data is subjected to rank-one decomposition, and is input to the decision function for prediction.
  • the objective function of the quadratic programming problem of the n-th sub-problem becomes:
  • w (n) is the n-th order optimal projection vector of the training tensor data set
  • n 1, 2, ... N
  • C is a penalty factor
  • It is a slack variable
  • the eta coefficient ⁇ is used to measure the importance of the intra-class scatter matrix.
  • the optimization framework of the objective function of the OPSTM problem is a combination of N vector pattern quadratic programming problems, respectively corresponding to a sub-problem, wherein the quadratic programming problem of the n-th sub-problem is:
  • E is the unit matrix
  • Is the tensor input data obtained by projecting the tensor input data X m in the tensor data set along each order
  • ⁇ i is the i-mode multiplication operator
  • b (n) is the nth order of the training tensor data set.
  • the quadratic programming sub-problems of N vector patterns are transformed into multiple quadratic programming problems in a single tensor mode.
  • the optimization framework of the objective function of the constructed OPSTM problem satisfies:
  • the tensor rank-one decomposition is introduced into the calculation of the tensor inner product, and the modified dual problem is:
  • a supervised learning optimization system in a tensor mode comprising:
  • a data receiving unit configured to receive the input training tensor data set
  • An intra-class scatter introduction unit is used to introduce an intra-class scatter matrix into the objective function, so that the objective function maximizes the distance between the classes while minimizing the intra-class distance;
  • Sub-problem optimization framework building unit for constructing an optimization framework of the objective function of the optimal projection tensor OPSTM sub-problem
  • the problem optimization framework building unit is used to transform the quadratic programming sub-problems of N vector patterns into multiple quadratic programming problems in a single tensor mode, and to construct an optimization framework of the objective function of the OPSTM problem;
  • the dual problem obtaining unit is configured to obtain the dual problem of the optimization framework of the objective function according to the Lagrangian multiplier method, and introduce the tensor rank-one decomposition into the calculation of the tensor inner product to obtain the modified dual problem. ;
  • the dual problem solving unit is used to solve the modified dual problem by using the sequence minimum optimization SMO algorithm, and output the optimal combination of Lagrangian and the offset scalar b;
  • a projection tensor calculation unit for calculating a projection tensor W * ;
  • a projection tensor decomposition unit for performing rank-one decomposition on the projection tensor W * ;
  • a back projection unit configured to perform back projection on a component obtained by rank-decomposing the projection tensor W * ;
  • An optimal projection tensor calculation unit is configured to perform a rank-one decomposition inverse operation on the component after the back projection, and obtain an optimal projection tensor W corresponding to the training tensor data set;
  • a decision function building unit is used to construct a decision function stage, and the optimal projection tensor W is decomposed by the rank one and the offset scalar b together to construct a decision function;
  • a prediction unit configured to input the predicted tensor data into the decision function after the rank-first decomposition in the application prediction stage, and perform prediction.
  • the intra-class scatter introducing unit introduces the intra-class scatter matrix into the objective function of the STM sub-problem by the eta coefficient ⁇
  • the objective function of the quadratic programming problem of the n-th sub-problem becomes:
  • w (n) is the n-th order optimal projection vector of the training tensor data set
  • n 1, 2, ... N
  • C is a penalty factor
  • It is a slack variable
  • the eta coefficient ⁇ is used to measure the importance of the intra-class scatter matrix.
  • the optimization framework of the objective function of the OPSTM problem is a combination of N vector pattern quadratic programming problems, respectively corresponding to a sub-problem, wherein the quadratic programming of the n-th sub-problem
  • the problem is:
  • E is the unit matrix
  • Is the tensor input data obtained by projecting the tensor input data X m in the tensor data set along each order
  • ⁇ i is the i-mode multiplication operator
  • b (n) is the nth order of the training tensor data set.
  • the problem optimization framework building unit is based on a formula And formula
  • the quadratic programming sub-problems of N vector patterns are transformed into multiple quadratic programming problems in a single tensor mode.
  • the optimization framework of the objective function of the constructed OPSTM problem satisfies:
  • the dual problem solving unit obtains the dual problem of the optimization framework of the objective function according to the Lagrangian multiplier method:
  • the dual problem solving unit introduces the tensor rank-one decomposition into the calculation of the tensor inner product, and the modified dual problem is:
  • the projection tensor calculation unit is based on a formula Calculate the projection tensor W * .
  • the quadratic programming problem of the N vector patterns is transformed into the multiple quadratic programming problem under the single tensor mode, and the optimized framework of the transformed objective function is the optimization framework of the objective function of the OPSTM problem.
  • the number of parameters of the model is greatly reduced, which overcomes the problems of dimensional disaster, over-learning, small sample and so on when the traditional vector mode algorithm deals with tensor data, and highlights its excellent classification effect while ensuring efficient processing.
  • the algorithm provided by the embodiment of the present invention can efficiently process tensor data directly in the tensor field, and has the characteristics of optimal classification ability, and has strong practicability and generalization.
  • FIG. 1 is a flow chart showing an implementation of an embodiment of a supervised learning optimization method in a tensor mode of the present invention
  • FIG. 2 is a structural block diagram of an embodiment of a supervised learning optimization system in the tensor mode of the present invention.
  • the input training tensor data set is received; the intra-class scatter matrix is introduced into the objective function, so that the objective function maximizes the inter-class distance while minimizing the intra-class distance; constructing an optimal projection
  • the decomposition is introduced into the calculation of the tensor inner product, and the modified dual problem is obtained.
  • the sequence minimum optimization SMO algorithm is used to solve the modified dual problem, and the optimal combination and offset scalar of Lagrangian are output; the projection tensor is calculated; The rank-decomposition of the projection tensor is performed; the component obtained by the rank-decomposition of the projection tensor is back-projected; the inverse-projected component is subjected to the rank-one decomposition inverse operation to obtain the optimal corresponding to the training tensor data set.
  • Projection tensor W constructing the decision function stage, constructing the decision function by the optimal projection tensor W after the rank-one decomposition and the offset scalar; in the application prediction stage, the predicted tensor data is subjected to rank-one decomposition and input to the In the decision function, the prediction is made.
  • FIG. 1 is a flowchart showing an implementation process of a supervised learning optimization method in a tensor mode according to Embodiment 1 of the present invention, which is described in detail as follows:
  • step S101 the input training tensor data set is received.
  • the training tensor data set is ⁇ Xm, ym
  • m 1, 2...M ⁇ , where Xm represents tensor input data, y m ⁇ +1,- 1 ⁇ indicates the label.
  • the sample points are stored in the form of second-order tensors (matrices). All sample points are composed of column data to form the input data set. Similarly, the label set is also a column vector, and each label is The position corresponds to the position of the corresponding sample point.
  • step S102 an intra-class scatter matrix is introduced into the objective function such that the objective function maximizes the inter-class distance while minimizing the intra-class distance.
  • the objective function optimization framework supporting the Support Tensor Machine (STM) problem is a combination of N vector mode quadratic programming problems, respectively corresponding to a sub-problem, wherein the n-th sub-problem
  • the secondary planning problem is:
  • C is a penalty factor
  • w (n) has the Fisher criterion effect in the n-th order of the training tensor data set to maximize the class spacing.
  • step S103 an optimization framework of the objective function of the optimal projection tensor OPSTM subproblem is constructed.
  • the optimization framework of the objective function of the optimal projection tensor OPSTM problem is a combination of N vector pattern quadratic programming problems, respectively corresponding to a sub-problem, wherein the n-th sub-problem quadratic programming
  • the problem is:
  • Training the nth-order projection vector of the tensor data set, n 1, 2, ... N; w (n) is the optimal projection vector of the nth order of the training tensor data set in equation (1-4); ⁇ (n) and P (n) satisfy E is the unit matrix.
  • step S104 the quadratic programming sub-problems of the N vector patterns are transformed into multiple quadratic programming problems in a single tensor mode, and an optimization framework of the objective function of the OPSTM problem is constructed.
  • W * is the projection tensor and ⁇ > is the inner product operator.
  • the transformed objective function optimization framework is the objective function optimization framework of OPSTM problem.
  • the number of parameters of the model is greatly reduced, and the problems of dimensional disaster, over-learning, small sample, etc. which occur when the vector algorithm processes the tensor data are overcome.
  • step S105 according to the Lagrangian multiplier method, the dual problem of the objective function optimization framework is obtained, and the tensor rank-one decomposition is introduced into the calculation of the tensor inner product to obtain the modified dual problem.
  • the dual problem of the optimization framework [(3-1), (3-2, (3-3)]) of the objective function of the OPSTM problem is obtained, wherein ⁇ m is a Lagrange multiplier.
  • the tensor CP (CANDECOMP/PARAFAC) decomposition is introduced into the calculation of the tensor inner product.
  • the rank-one decomposition of the tensor data V i , V j is:
  • the tensor inner product calculation part is introduced, and the tensor rank-one decomposition auxiliary calculation is introduced. Further reducing the computational complexity and storage cost, and the tensor rank-decomposition can obtain a more compact and meaningful representation of the tensor object, which can more effectively extract the structural information and intrinsic correlation of the tensor data, and effectively avoid the present Some tensor mode algorithms take time-consuming alternating projection iterations.
  • step S107 the projection tensor W * is calculated.
  • step S108 the projection tensor W * is subjected to rank-one decomposition.
  • the projection tensor W * is subjected to rank-one decomposition to obtain
  • step S109 the component obtained by rank-decomposing the projection tensor W * is backprojected.
  • step S110 the inverse-projected component is subjected to a rank-one decomposition inverse operation to obtain an optimal projection tensor W corresponding to the training tensor data set.
  • step S111 a decision function stage is constructed, and the optimal projection tensor W is constructed together with the offset scalar b after the rank-one decomposition.
  • the decision function stage is constructed, and the optimal projection tensor W is subjected to rank-one decomposition, and after decomposition, the decision function is constructed together with the offset scalar b:
  • step S112 in the application prediction stage, the to-be-predicted tensor data is subjected to rank-one decomposition, and then input into a decision function to perform prediction.
  • the tensor data to be predicted is subjected to rank-one decomposition, and then input into a decision function for prediction.
  • the present embodiment has the following advantages: 1) Converting the quadratic programming problem of N vector modes into a multiple quadratic programming problem under a single tensor mode, and optimizing the transformed objective function
  • the framework is the optimization framework of the objective function of the OPSTM problem, which can greatly reduce the number of parameters of the model, and overcome the problems of dimensional disasters, over-learning, small samples, etc., which are caused by the traditional vector pattern algorithm when processing tensor data. At the same time, it highlights its excellent classification effect.
  • the algorithm provided by the embodiment of the present invention can efficiently process tensor data directly in the tensor field, and has the characteristics of optimal classification ability, and has strong practicability and generalization.
  • the tensor inner product calculation part is introduced, and the tensor rank-one decomposition auxiliary calculation is introduced. Further reducing the computational complexity and storage cost, and the tensor rank-decomposition can obtain a more compact and meaningful representation of the tensor object, which can more effectively extract the structural information and intrinsic correlation of the tensor data, and effectively avoid the consumption. Alternate projection iteration process.
  • the size of the sequence numbers of the foregoing processes does not mean the order of execution sequence, and the execution order of each process should be determined by its function and internal logic, and should not be implemented in the embodiment of the present invention. Form any limit.
  • FIG. 2 is a block diagram showing a specific structure of a supervised learning optimization system in a tensor mode according to Embodiment 2 of the present invention.
  • the supervised learning optimization system 2 in the tensor mode includes: a data receiving unit 21, an intra-class scatter introducing unit 22, a sub-question optimization framework building unit 23, a problem optimization framework building unit 24, a dual problem obtaining unit 25, and a dual problem solving.
  • the data receiving unit 21 is configured to receive the input training tensor data set
  • the intra-class scatter introduction unit 22 is configured to introduce an intra-class scatter matrix into the objective function, so that the objective function maximizes the inter-class distance while minimizing the intra-class distance;
  • the sub-problem optimization framework building unit 23 is configured to construct an optimization framework of the objective function of the optimal projection tensor OPSTM sub-problem;
  • the problem optimization framework construction unit 24 is configured to convert the quadratic programming sub-problems of the N vector patterns into multiple quadratic programming problems in a single tensor mode, and construct an optimization framework of the objective function of the OPSTM problem;
  • the dual problem obtaining unit 25 is configured to obtain a dual problem of the optimization framework of the objective function according to the Lagrangian multiplier method, and introduce a tensor rank-one decomposition into the calculation of the tensor inner product to obtain the modified duality. problem;
  • the dual problem solving unit 26 is configured to solve the modified dual problem by using the sequence minimum optimization SMO algorithm, and output the optimal combination of Lagrangian and the offset scalar b;
  • a projection tensor calculation unit 27 for calculating a projection tensor W * ;
  • a projection tensor decomposition unit 28 for performing rank-one decomposition on the projection tensor W * ;
  • a back projection unit 29, configured to perform back projection on a component obtained by performing rank-one decomposition on the projection tensor W * ;
  • the optimal projection tensor calculation unit 210 is configured to perform a rank-one decomposition inverse operation on the component after the back projection, to obtain an optimal projection tensor W corresponding to the training tensor data set;
  • the decision function construction unit 211 is configured to construct a decision function stage, and construct the decision function together with the offset scalar b after the optimal projection tensor W is decomposed by the rank one;
  • the prediction unit 212 is configured to input the prediction tensor data into the decision function after the rank-first decomposition in the application prediction stage, and perform prediction.
  • the intra-class scatter introducing unit 22 introduces the intra-class scatter matrix into the objective function of the STM sub-problem by the eta coefficient ⁇
  • the objective function of the quadratic programming problem of the n-th sub-problem becomes:
  • w (n) is the n-th order optimal projection vector of the training tensor data set
  • n 1, 2, ... N
  • C is a penalty factor
  • It is a slack variable
  • the eta coefficient ⁇ is used to measure the importance of the intra-class scatter matrix.
  • the optimization framework of the objective function of the OPSTM problem is a combination of N vector pattern quadratic programming problems, respectively corresponding to a sub-problem, wherein the n-th sub-problem is twice
  • the planning problem is:
  • E is the unit matrix
  • Is the tensor input data obtained by projecting the tensor input data X m in the tensor data set along each order
  • ⁇ i is the i-mode multiplication operator
  • b (n) is the nth order of the training tensor data set.
  • the problem optimization framework building unit 24 is based on a formula And formula
  • the quadratic programming sub-problems of N vector patterns are transformed into multiple quadratic programming problems in a single tensor mode.
  • the optimization framework of the objective function of the constructed OPSTM problem satisfies:
  • the dual problem solving unit 26 obtains the dual problem of the optimization framework of the objective function according to the Lagrangian multiplier method:
  • the dual problem solving unit 26 introduces the tensor rank-one decomposition into the calculation of the tensor inner product, and the modified dual problem is:
  • the projection tensor calculation unit 27 is based on a formula Calculate the projection tensor W * .
  • the supervised learning optimization system 2 in the tensor mode provided by the embodiment of the present invention can be applied to the foregoing corresponding method embodiment 1.
  • the supervised learning optimization system 2 in the tensor mode provided by the embodiment of the present invention can be applied to the foregoing corresponding method embodiment 1.
  • the disclosed systems, devices, and methods may be implemented in other manners.
  • the device embodiments described above are merely illustrative.
  • the division of the unit is only a logical function division.
  • there may be another division manner for example, multiple units or components may be combined or Can be integrated into another system, or Some features can be ignored or not executed.
  • the mutual coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or unit, and may be in an electrical, mechanical or other form.
  • the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of the embodiment.
  • each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.
  • the functions may be stored in a computer readable storage medium if implemented in the form of a software functional unit and sold or used as a standalone product.
  • the technical solution of the present invention which is essential or contributes to the prior art, or a part of the technical solution, may be embodied in the form of a software product, which is stored in a storage medium, including
  • the instructions are used to cause a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention.
  • the foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, and the like. .

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Abstract

一种张量模式下的有监督学习优化方法及系统，其中，所述方法包括：接收输入的训练张量数据集；将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离；构建OPSTM子问题的目标函数的优化框架；构建OPSTM问题的目标函数的优化框架；求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量b；计算投影张量W *；计算最优投影张量W；根据W和b构建决策函数；待预测张量数据经过秩一分解后，输入到决策函数中进行预测。克服了向量模式算法在处理张量数据时出现的维度灾难、过学习、小样本等问题，并且有效地避免了现有的张量模式算法耗时的交替投影迭代过程。

Description

一种张量模式下的有监督学习优化方法及系统 技术领域
本发明属于模式识别技术领域，尤其涉及一种张量模式下的有监督学习优化方法及系统。
背景技术
随着大数据时代的到来，数据的张量表达逐渐成为主流。然而，在实现本发明过程中，发明人发现现有技术还是采用向量模式算法处理张量数据。根据向量模式算法的观点，须在预处理阶段对原始数据进行特征提取(向量化)，这样，一是容易破坏张量数据特有的空间信息及内在相关性，二是模型参数过多，容易导致维度灾难、过学习、小样本等问题。
许多张量模式算法成为时代的新宠。然而，STM的目标函数求解是非凸优化问题，需要利用交替投影方法求解，算法的时间复杂度很高，并且常遭遇局部最小值问题。
技术问题
有鉴于此，本发明实施例提供一种张量模式下的有监督学习优化方法及系统，以解决现有技术提供的向量模式算法，在处理张量数据时出现的维度灾难、过学习、小样本等问题，克服现有的张量模式算法，本发明的算法是为了解决现有算法的局限，比如存在算法的时间复杂度很高，并且常遭遇局部最小值等问题。
技术解决方案
第一方面，提供一种张量模式下的有监督学习优化方法，所述方法包括：
接收输入的训练张量数据集；
将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小 化类内距离；
构建最优投影张量机OPSTM子问题的目标函数的优化框架；
将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建OPSTM问题的目标函数的优化框架；
根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题；
利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量b；
计算投影张量W*；
对投影张量W*进行秩一分解；
对投影张量W*进行秩一分解后得到的分量进行逆投影；
对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W；
构建决策函数阶段，将最优投影张量W经过秩一分解后和偏移标量b一起构建决策函数；
在应用预测阶段，待预测张量数据经过秩一分解后，输入到所述决策函数中，进行预测。
进一步地，通过eta系数η将类内散布矩阵引入STM子问题的目标函数后，第n个子问题的二次规划问题的目标函数变为：
Figure PCTCN2015096375-appb-000001
其中，
Figure PCTCN2015096375-appb-000002
是训练张量数据集沿第n阶展开后估计的第n阶类内散布矩阵，w(n)是训练张量数据集的第n阶的最优投影向量，n＝1,2，……N，C是惩罚因子，
Figure PCTCN2015096375-appb-000003
是松弛变量，eta系数η用于衡量类内散布矩阵的重要性。
进一步地，OPSTM问题的目标函数的优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
Figure PCTCN2015096375-appb-000004
其中，
Figure PCTCN2015096375-appb-000005
为训练张量数据集的第n阶的投影向量，
Figure PCTCN2015096375-appb-000006
Λ(n)和P(n)满足
Figure PCTCN2015096375-appb-000007
E是单位矩阵，
Figure PCTCN2015096375-appb-000008
是训练张量数据集中的张量输入数据Xm沿各阶投影后得到的张量输入数据，×i是i-mode乘运算符，b(n)为训练张量数据集的第n阶的偏移标量。
进一步地，根据公式
Figure PCTCN2015096375-appb-000009
和公式
Figure PCTCN2015096375-appb-000010
将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建的OPSTM问题的目标函数的优化框架满足：
Figure PCTCN2015096375-appb-000011
其中，<>是内积运算符，
Figure PCTCN2015096375-appb-000012
进一步地，根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题为：
Figure PCTCN2015096375-appb-000013
将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题为：
Figure PCTCN2015096375-appb-000014
进一步地，根据公式
Figure PCTCN2015096375-appb-000015
计算投影张量W*。
第二方面，提供一种张量模式下的有监督学习优化系统，所述系统包括：
数据接收单元，用于接收输入的训练张量数据集；
类内散布引入单元，用于将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离；
子问题优化框架构建单元，用于构建最优投影张量机OPSTM子问题的目标函数的优化框架；
问题优化框架构建单元，用于将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建OPSTM问题的目标函数的优化框架；
对偶问题获得单元，用于根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题；
对偶问题求解单元，用于利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量b；
投影张量计算单元，用于计算投影张量W*；
投影张量分解单元，用于对投影张量W*进行秩一分解；
逆投影单元，用于对投影张量W*进行秩一分解后得到的分量进行逆投影；
最优投影张量计算单元，用于对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W；
决策函数构建单元，用于构建决策函数阶段，将最优投影张量W经过秩一分解后和偏移标量b一起构建决策函数；
预测单元，用于在应用预测阶段，待预测张量数据经过秩一分解后，输入到所述决策函数中，进行预测。
进一步地，所述类内散布引入单元通过eta系数η将类内散布矩阵引入STM子问题的目标函数后，第n个子问题的二次规划问题的目标函数变为：
Figure PCTCN2015096375-appb-000016
其中，
Figure PCTCN2015096375-appb-000017
是训练张量数据集沿第n阶展开后估计的第n阶类内散布矩阵，w(n)是训练张量数据集的第n阶的最优投影向量，n＝1,2，……N，C是惩罚因子，
Figure PCTCN2015096375-appb-000018
是松弛变量，eta系数η用于衡量类内散布矩阵的重要性。
进一步地，所述子问题优化框架构建单元中，OPSTM问题的目标函数的优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
Figure PCTCN2015096375-appb-000019
其中，
Figure PCTCN2015096375-appb-000020
为训练张量数据集的第n阶的投影向量，
Figure PCTCN2015096375-appb-000021
Λ(n)和P(n)满足
Figure PCTCN2015096375-appb-000022
E是单位 矩阵，
Figure PCTCN2015096375-appb-000023
是训练张量数据集中的张量输入数据Xm沿各阶投影后得到的张量输入数据，×i是i-mode乘运算符，b(n)为训练张量数据集的第n阶的偏移标量。
进一步地，所述问题优化框架构建单元根据公式
Figure PCTCN2015096375-appb-000024
和公式
Figure PCTCN2015096375-appb-000025
将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建的OPSTM问题的目标函数的优化框架满足：
Figure PCTCN2015096375-appb-000026
其中，<>是内积运算符，
Figure PCTCN2015096375-appb-000027
进一步地，所述对偶问题求解单元根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题为：
Figure PCTCN2015096375-appb-000028
所述对偶问题求解单元将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题为：
Figure PCTCN2015096375-appb-000029
进一步地，所述投影张量计算单元根据公式
Figure PCTCN2015096375-appb-000030
计算投影张量W*。
有益效果
在本发明实施例，将N个向量模式的二次规划问题转化为单个张量模式下的多重二次规划问题，转化后的目标函数的优化框架即为OPSTM问题的目标函数的优化框架，可以大幅降低模型的参数数量，克服了传统的向量模式算法在处理张量数据时出现的维度灾难、过学习、小样本等问题，在保证高效处理的同时，凸显其极优的分类效果。综上，本发明的实施例提供的算法能够直接在张量领域高效处理张量数据，同时具备最优的分类能力的特点，具有较强的实用性和推广性。
附图说明
图1是本发明张量模式下的有监督学习优化方法实施例的实现流程图；
图2是本发明张量模式下的有监督学习优化系统实施例的结构框图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。
在本发明实施例中，接收输入的训练张量数据集；将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离；构建最优投影 张量机OPSTM子问题的目标函数的优化框架；构建OPSTM问题的目标函数的优化框架；根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题；利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量；计算投影张量；对投影张量进行秩一分解；对投影张量进行秩一分解后得到的分量进行逆投影；对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W；构建决策函数阶段，将最优投影张量W经过秩一分解后和偏移标量一起构建决策函数；在应用预测阶段，待预测张量数据经过秩一分解后，输入到所述决策函数中，进行预测。
以下结合具体实施例对本发明的实现进行详细描述：
实施例一
图1示出了本发明实施例一提供的张量模式下的有监督学习优化方法的实现流程，详述如下：
在步骤S101中，接收输入的训练张量数据集。
在本发明实施例中，假设训练张量数据集为{Xm,ym|m＝1,2.....M}，其中，Xm表示张量输入数据，ym∈{+1，-1}表示标签。
以灰度图像为例，样本点以二阶张量(矩阵)的形式进行数据存储，所有样本点以列向量形式组成输入数据集，同理，标签集也是列向量，并且，每个标签的位置对应着相应样本点的位置。
Figure PCTCN2015096375-appb-000031
在步骤S102中，将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离。
在本发明实施例中，支持张量机(Support Tensor Machine，STM)问题的目标函数优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
Figure PCTCN2015096375-appb-000032
Figure PCTCN2015096375-appb-000033
Figure PCTCN2015096375-appb-000034
其中，w(n)：训练张量数据集的第n阶的最优投影向量，n＝1,2，……N；
b(n)：训练张量数据集的第n阶的偏移标量，n＝1,2，……N。
C：是惩罚因子；
Figure PCTCN2015096375-appb-000035
松弛变量。
通过eta系数η将类内散布矩阵引入STM子问题的目标函数后，第n个子问题的二次规划问题的目标函数变为：
Figure PCTCN2015096375-appb-000036
其中，
Figure PCTCN2015096375-appb-000037
是训练张量数据集沿第n阶展开后估计的第n阶类内散布矩阵，此时的w(n)，在训练张量数据集的第n阶具有Fisher准则效果“最大化类间距，最小化类内距”，eta系数η用于衡量类内散布的重要性。
在步骤S103中，构建最优投影张量机OPSTM子问题的目标函数的优化框架。
在本发明实施例中，最优投影张量机OPSTM问题的目标函数的优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
Figure PCTCN2015096375-appb-000038
Figure PCTCN2015096375-appb-000039
Figure PCTCN2015096375-appb-000040
其中，
Figure PCTCN2015096375-appb-000041
训练张量数据集的第n阶的投影向量，
Figure PCTCN2015096375-appb-000042
n＝1,2，……N；w(n)是公式(1-4)中的训练张量数据集的第n阶的最优投影向 量；Λ(n)和P(n)满足
Figure PCTCN2015096375-appb-000043
E是单位矩阵。
Figure PCTCN2015096375-appb-000044
是张量输入数据Xm沿各阶投影后得到的张量输入数据，×i是i-mode乘运算符。
在步骤S104中，将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建OPSTM问题的目标函数的优化框架。
在本发明实施例中，
Figure PCTCN2015096375-appb-000045
Figure PCTCN2015096375-appb-000046
Figure PCTCN2015096375-appb-000047
其中，
Figure PCTCN2015096375-appb-000048
表示范数，“o”是外积运算符。根据公式Eq.1和Eq.2，有
Figure PCTCN2015096375-appb-000049
因此，可以将N个子问题的向量模式二次规划问题转化为单个张量模式下的多重二次规划问题，即OPSTM问题的目标函数的优化框架为：
Figure PCTCN2015096375-appb-000050
S.t ym(<W*,Vm>+b)≥1-ξm  (3-2)
ξm≥0 m＝1,2,…M  (3-3)
其中，W*是投影张量，<>是内积运算符，
Figure PCTCN2015096375-appb-000051
通过Eq.1和Eq.2，将N个向量模式的二次规划问题转化为单个张量模式下的多重二次规划问题，转化后目标函数优化框架即为OPSTM问题的目标函数优化框架。大幅度降低了模型的参数数量，克服了向量算法在处理张量数据时出现的维度灾难、过学习、小样本等问题。
在步骤S105中，根据拉格朗日乘子法，得到所述目标函数优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题。
在本发明实施例中，根据拉格朗日乘子法，得到OPSTM问题的目标函数的优化框架[(3-1)、(3-2、(3-3)]的对偶问题，其中，αm是拉格朗日乘子。
Figure PCTCN2015096375-appb-000052
Figure PCTCN2015096375-appb-000053
0＜αm＜C m＝1,2,…M  (4-3)
将张量CP(CANDECOMP/PARAFAC)分解引入到张量内积的计算。
张量数据Vi、Vj的秩一分解分别为：
Figure PCTCN2015096375-appb-000054
又
Figure PCTCN2015096375-appb-000055
所以对偶问题可以修改为：
Figure PCTCN2015096375-appb-000056
Figure PCTCN2015096375-appb-000057
0<αm<C m＝1,2,…M  (4-3)
修改后的对偶问题的目标函数(4-1)中，张量内积计算部分，引入张量秩一分解辅助计算，
Figure PCTCN2015096375-appb-000058
进一步降低计算复杂度及储存代价，同时张量秩一分解能够获得张量对象更加紧凑和更有意义的表示，能够更有效提取张量数据的结构信息及内在相关性，并且有效地避免了现有的张量模式算法耗时的交替投影迭代过程。
在步骤S106中，利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合α＝[α1，α2，……αM]及偏移标量b。
在步骤S107中，计算投影张量W*。
在本发明实施例中，根据公式
Figure PCTCN2015096375-appb-000059
计算影张量W*。
在步骤S108中，对投影张量W*进行秩一分解。
在本发明实施例中，对投影张量W*进行秩一分解，得到
Figure PCTCN2015096375-appb-000060
在步骤S109中，对投影张量W*进行秩一分解后得到的分量进行逆投影。
在本发明实施例中，对投影张量W*进行秩一分解后的分量进行逆投影，得到
Figure PCTCN2015096375-appb-000061
w(n)对应(1-4)的最优投影向量，是训练张量数据集的第n阶的最优投影向量，n＝1,2，……N。
在步骤S110中，对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W。
在本发明实施例中，将逆投影后得到的分量融合(秩一分解逆运算)成最优投影张量W，W＝w(1)οw(2)ο…w(N)，所以，最优投影张量W在各阶都能体现Fisher准则。
在步骤S111中，构建决策函数阶段，最优投影张量W经过秩一分解后和偏移标量b一起构建决策函数。
在本发明实施例中，构建决策函数阶段，最优投影张量W须经过秩一分解，分解后和偏移标量b一起构建决策函数:
Figure PCTCN2015096375-appb-000062
在步骤S112中，在应用预测阶段，待预测张量数据经过秩一分解后，输入到决策函数中，进行预测。
在本发明实施例中，在应用预测阶段，待预测张量数据须经过秩一分解后，输入到决策函数中进行预测。
本实施例，相比现有的技术，具有以下的优点：1)、将N个向量模式的二次规划问题转化为单个张量模式下的多重二次规划问题，转化后的目标函数的优化框架即为OPSTM问题的目标函数的优化框架，可以大幅降低模型的参数数量，克服了传统的向量模式算法在处理张量数据时出现的维度灾难、过学习、小样本等问题，在保证高效处理的同时，凸显其极优的分类效果。综上，本发明的实施例提供的算法能够直接在张量领域高效处理张量数据，同时具备最优的分类能力的特点，具有较强的实用性和推广性。2)、将类内散布矩阵引入目标函数，，能够直接在张量领域接收处理张量数据，输出的最优投影张量W在 各阶都能体现Fisher准则“最大化类间距，最小化类内距”。3)、对偶问题的目标函数(4-1)中，张量内积计算部分，引入张量秩一分解辅助计算，
Figure PCTCN2015096375-appb-000063
进一步降低计算复杂度及储存代价，同时张量秩一分解能够获得张量对象更加紧凑和更有意义的表示，能够更有效提取张量数据的结构信息及内在相关性，并且有效地避免了耗时的交替投影迭代过程。
应理解，在本发明实施例中，上述各过程的序号的大小并不意味着执行顺序的先后，各过程的执行顺序应以其功能和内在逻辑确定，而不应对本发明实施例的实施过程构成任何限定。
本领域普通技术人员可以理解实现上述各实施例方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，相应的程序可以存储于一计算机可读取存储介质中，所述的存储介质，如ROM/RAM、磁盘或光盘等。
实施例二
图2示出了本发明实施例二提供的张量模式下的有监督学习优化系统的具体结构框图，为了便于说明，仅示出了与本发明实施例相关的部分。该张量模式下的有监督学习优化系统2包括：数据接收单元21、类内散布引入单元22、子问题优化框架构建单元23、问题优化框架构建单元24、对偶问题获得单元25、对偶问题求解单元26、投影张量计算单元27、投影张量分解单元28、逆投影单元29、最优投影张量计算单元210、决策函数构建单元211和预测单元212。
其中，数据接收单元21，用于接收输入的训练张量数据集；
类内散布引入单元22，用于将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离；
子问题优化框架构建单元23，用于构建最优投影张量机OPSTM子问题的目标函数的优化框架；
问题优化框架构建单元24，用于将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建OPSTM问题的目标函数的优化框架；
对偶问题获得单元25，用于根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题；
对偶问题求解单元26，用于利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量b；
投影张量计算单元27，用于计算投影张量W*；
投影张量分解单元28，用于对投影张量W*进行秩一分解；
逆投影单元29，用于对投影张量W*进行秩一分解后得到的分量进行逆投影；
最优投影张量计算单元210，用于对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W；
决策函数构建单元211，用于构建决策函数阶段，将最优投影张量W经过秩一分解后和偏移标量b一起构建决策函数；
预测单元212，用于在应用预测阶段，待预测张量数据经过秩一分解后，输入到所述决策函数中，进行预测。
进一步地，所述类内散布引入单元22通过eta系数η将类内散布矩阵引入STM子问题的目标函数后，第n个子问题的二次规划问题的目标函数变为：
Figure PCTCN2015096375-appb-000064
其中，
Figure PCTCN2015096375-appb-000065
是训练张量数据集沿第n阶展开后估计的第n阶类内散布矩阵，w(n)是训练张量数据集的第n阶的最优投影向量，n＝1,2，……N，C是惩罚因子，
Figure PCTCN2015096375-appb-000066
是松弛变量，eta系数η用于衡量类内散布矩阵的重要性。
进一步地，所述子问题优化框架构建单元23中，OPSTM问题的目标函数的优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
Figure PCTCN2015096375-appb-000067
其中，
Figure PCTCN2015096375-appb-000068
为训练张量数据集的第n阶的投影向量，
Figure PCTCN2015096375-appb-000069
Λ(n)和P(n)满足
Figure PCTCN2015096375-appb-000070
E是单位矩阵，
Figure PCTCN2015096375-appb-000071
是训练张量数据集中的张量输入数据Xm沿各阶投影后得到的张量输入数据，×i是i-mode乘运算符，b(n)为训练张量数据集的第n阶的偏移标量。
进一步地，所述问题优化框架构建单元24根据公式
Figure PCTCN2015096375-appb-000072
和公式
Figure PCTCN2015096375-appb-000073
将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建的OPSTM问题的目标函数的优化框架满足：
Figure PCTCN2015096375-appb-000074
其中，<>是内积运算符，
Figure PCTCN2015096375-appb-000075
进一步地，所述对偶问题求解单元26根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题为：
Figure PCTCN2015096375-appb-000076
所述对偶问题求解单元26将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题为：
Figure PCTCN2015096375-appb-000077
进一步地，所述投影张量计算单元27根据公式
Figure PCTCN2015096375-appb-000078
计算投影张量W*。
本发明实施例提供的张量模式下的有监督学习优化系统2可以应用在前述对应的方法实施例一中，详情参见上述实施例一的描述，在此不再赘述。
本领域普通技术人员可以意识到，结合本文中所公开的实施例描述的各示例的单元及算法步骤，能够以电子硬件、或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本发明的范围。
所属领域的技术人员可以清楚地了解到，为描述的方便和简洁，上述描述的系统、装置和单元的具体工作过程，可以参考前述方法实施例中的对应过程，在此不再赘述。
在本申请所提供的几个实施例中，应该理解到，所揭露的系统、装置和方法，可以通过其它的方式实现。例如，以上所描述的装置实施例仅仅是示意性的，例如，所述单元的划分，仅仅为一种逻辑功能划分，实际实现时可以有另外的划分方式，例如多个单元或组件可以结合或者可以集成到另一个系统，或 一些特征可以忽略，或不执行。另一点，所显示或讨论的相互之间的耦合或直接耦合或通信连接可以是通过一些接口，装置或单元的间接耦合或通信连接，可以是电性，机械或其它的形式。
所述作为分离部件说明的单元可以是或者也可以不是物理上分开的，作为单元显示的部件可以是或者也可以不是物理单元，即可以位于一个地方，或者也可以分布到多个网络单元上。可以根据实际的需要选择其中的部分或者全部单元来实现本实施例方案的目的。
另外，在本发明各个实施例中的各功能单元可以集成在一个处理单元中，也可以是各个单元单独物理存在，也可以两个或两个以上单元集成在一个单元中。
所述功能如果以软件功能单元的形式实现并作为独立的产品销售或使用时，可以存储在一个计算机可读取存储介质中。基于这样的理解，本发明的技术方案本质上或者说对现有技术做出贡献的部分或者该技术方案的部分可以以软件产品的形式体现出来，该计算机软件产品存储在一个存储介质中，包括若干指令用以使得一台计算机设备(可以是个人计算机，服务器，或者网络设备等)执行本发明各个实施例所述方法的全部或部分步骤。而前述的存储介质包括：U盘、移动硬盘、只读存储器(ROM，Read-Only Memory)、随机存取存储器(RAM，Random Access Memory)、磁碟或者光盘等各种可以存储程序代码的介质。
以上所述，仅为本发明的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应所述以权利要求的保护范围为准。

Claims (12)

  1. 一种张量模式下的有监督学习优化方法，其特征在于，所述方法包括：
    接收输入的训练张量数据集；
    将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离；
    构建最优投影张量机OPSTM子问题的目标函数的优化框架；
    将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建OPSTM问题的目标函数的优化框架；
    根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题；
    利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量b；
    计算投影张量W*；
    对投影张量W*进行秩一分解；
    对投影张量W*进行秩一分解后得到的分量进行逆投影；
    对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W；
    构建决策函数阶段，将最优投影张量W经过秩一分解后和偏移标量b一起构建决策函数；
    在应用预测阶段，待预测张量数据经过秩一分解后，输入到所述决策函数中，进行预测。
  2. 如权利要求1所述的方法，其特征在于，通过eta系数η将类内散布矩阵引入STM子问题的目标函数后，第n个子问题的二次规划问题的目标函数变为：
    Figure PCTCN2015096375-appb-100001
    其中，
    Figure PCTCN2015096375-appb-100002
    是训练张量数据集沿第n阶展开后估计的第n阶类内散布矩阵，w(n)是训练张量数据集的第n阶的最优投影向量，n＝1,2，……N，C是惩罚因子，
    Figure PCTCN2015096375-appb-100003
    是松弛变量，eta系数η用于衡量类内散布矩阵的重要性。
  3. 如权利要求2所述的方法，其特征在于，OPSTM问题的目标函数的优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
    Figure PCTCN2015096375-appb-100004
    Figure PCTCN2015096375-appb-100005
    Figure PCTCN2015096375-appb-100006
    其中，
    Figure PCTCN2015096375-appb-100007
    为训练张量数据集的第n阶的投影向量，
    Figure PCTCN2015096375-appb-100008
    Λ(n)和P(n)满足
    Figure PCTCN2015096375-appb-100009
    E是单位矩阵，
    Figure PCTCN2015096375-appb-100010
    是训练张量数据集中的张量输入数据Xm沿 各阶投影后得到的张量输入数据，×i是i-mode乘运算符，b(n)为训练张量数据集的第n阶的偏移标量。
  4. 如权利要求3所述的方法，其特征在于，根据公式
    Figure PCTCN2015096375-appb-100011
    和公式
    Figure PCTCN2015096375-appb-100012
    将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建的OPSTM问题的目标函数的优化框架满足：
    Figure PCTCN2015096375-appb-100013
    ym(<W*,Vm>+b)≥1-ξm
    S.t
    ξm≥0 m＝1,2,…M
    其中，<>是内积运算符，
    Figure PCTCN2015096375-appb-100014
  5. 如权利要求4所述的方法，其特征在于，根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题为：
    Figure PCTCN2015096375-appb-100015
    Figure PCTCN2015096375-appb-100016
    S.t
    0<αm<C m＝1,2,…M；
    将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题为：
    Figure PCTCN2015096375-appb-100017
    Figure PCTCN2015096375-appb-100018
    S.t
    0<αm<C m＝1,2,…M。
  6. 如权利要求5所述的方法，其特征在于，根据公式
    Figure PCTCN2015096375-appb-100019
    计算投影张量W*。
  7. 一种张量模式下的有监督学习优化系统，其特征在于，所述系统包括：
    数据接收单元，用于接收输入的训练张量数据集；
    类内散布引入单元，用于将类内散布矩阵引入目标函数，使得目标函数最大化类间距离的同时最小化类内距离；
    子问题优化框架构建单元，用于构建最优投影张量机OPSTM子问题的目标函数的优化框架；
    问题优化框架构建单元，用于将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建OPSTM问题的目标函数的优化框架；
    对偶问题获得单元，用于根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题，并将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题；
    对偶问题求解单元，用于利用序列最小优化SMO算法，求解修改后的对偶问题，输出拉格朗日的最优组合及偏移标量b；
    投影张量计算单元，用于计算投影张量W*；
    投影张量分解单元，用于对投影张量W*进行秩一分解；
    逆投影单元，用于对投影张量W*进行秩一分解后得到的分量进行逆投影；
    最优投影张量计算单元，用于对经过逆投影后的分量，进行秩一分解逆运算，得到训练张量数据集对应的最优投影张量W；
    决策函数构建单元，用于构建决策函数阶段，将最优投影张量W经过秩一分解后和偏移标量b一起构建决策函数；
    预测单元，用于在应用预测阶段，待预测张量数据经过秩一分解后，输入到所述决策函数中，进行预测。
  8. 如权利要求7所述的系统，其特征在于，所述类内散布引入单元通过eta系数η将类内散布矩阵引入STM子问题的目标函数后，第n个子问题的二次规划问题的目标函数变为：
    Figure PCTCN2015096375-appb-100020
    其中，
    Figure PCTCN2015096375-appb-100021
    是训练张量数据集沿第n阶展开后估计的第n阶类内散布矩阵，w(n)是训练张量数据集的第n阶的最优投影向量，n＝1,2，……N，C是惩罚因子，
    Figure PCTCN2015096375-appb-100022
    是松弛变量，eta系数η用于衡量类内散布矩阵的重要性。
  9. 如权利要求8所述的系统，其特征在于，所述子问题优化框架构建单元中，OPSTM问题的目标函数的优化框架是N个向量模式二次规划问题的组合，分别对应着一个子问题，其中，第n个子问题的二次规划问题为：
    Figure PCTCN2015096375-appb-100023
    Figure PCTCN2015096375-appb-100024
    Figure PCTCN2015096375-appb-100025
    其中，
    Figure PCTCN2015096375-appb-100026
    为训练张量数据集的第n阶的投影向量，
    Figure PCTCN2015096375-appb-100027
    Λ(n)和P(n)满足
    Figure PCTCN2015096375-appb-100028
    E是单位矩阵，
    Figure PCTCN2015096375-appb-100029
    是训练张量数据集中的张量输入数据Xm沿各阶投影后得到的张量输入数据，×i是i-mode乘运算符，b(n)为训练张量数据集的第n阶的偏移标量。
  10. 如权利要求9所述的系统，其特征在于，所述问题优化框架构建单元根据公式
    Figure PCTCN2015096375-appb-100030
    和公式
    Figure PCTCN2015096375-appb-100031
    将N个向量模式的二次规划子问题转化为单个张量模式下的多重二次规划问题，构建的OPSTM问题的目标函数的优化框架满足：
    Figure PCTCN2015096375-appb-100032
    ym(<W*,Vm>+b)≥1-ξm
    S.t
    ξm≥0 m＝1,2,…M
    其中，<>是内积运算符，
    Figure PCTCN2015096375-appb-100033
  11. 如权利要求10所述的系统，其特征在于，所述对偶问题求解单元根据拉格朗日乘子法，得到所述目标函数的优化框架的对偶问题为：
    Figure PCTCN2015096375-appb-100034
    Figure PCTCN2015096375-appb-100035
    0<αm<C m＝1,2,…M；
    所述对偶问题求解单元将张量秩一分解引入到张量内积的计算，得到修改后的对偶问题为：
    Figure PCTCN2015096375-appb-100036
    Figure PCTCN2015096375-appb-100037
    0<αm<C m＝1,2,…M。
  12. 如权利要求11所述的系统，其特征在于，所述投影张量计算单元根据公式
    Figure PCTCN2015096375-appb-100038
    计算投影张量W*。
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