CN104331816A - Knowledge learning and privacy protection based big-data user purchase intention predicating method - Google Patents

Abstract

The invention discloses a knowledge learning and privacy protection based big-data user purchase intention predicating method which comprises following steps of: (1) performing normalization processing on a large number of historical data and a small number of current data; (2) grouping the data and establishing a training sample set; (3) counting user purchase intention probability of each group; (4) calculating group labels; (5) training the training set by using an improved support vector machine; (6) constructing a prediction function; (7) inputting to-be-predicted data into the predication function to obtain a prediction result. As the improved support vector machine is used in the method, the small number of current data set probability information and the large number of historical data set probability information are blended into a structural risk minimization learning framework, learning of knowledge in different periods is realized by virtue of constructing similar distance items among data, and accordingly, the knowledge learning and privacy protection based big-data user purchase intention predicating method which is applicable for learning problems of big samples is constructed.

Description

Large data user's purchase intention Forecasting Methodology of knowledge based study and secret protection

Technical field

The invention belongs to marketing technical field, relate to mode identification technology, is knowledge based study and large data user's purchase intention Forecasting Methodology of secret protection.

Background technology

The invention belongs to marketing technical field, relate to mode identification technology, is knowledge based study and large data user's purchase intention Forecasting Methodology of secret protection.

Consumer is the guide of the various business activities of enterprise, and the purchase intention of consumer is the basis of buying behavior, can be used for predicting the behavior of consumer.From marketing angle, after enterprise grasps the purchase intention of consumer, just can the raw-material purchase of reasonable arrangement, the structure of adjustment product, the production schedule of formulation product; After marketing personnel grasp the purchase intention of consumer, just can recommend dependent merchandise to consumer targetedly, improve sales volume; After the purchase intention of consumer is grasped in market, supermarket, just can on purpose commodities purchased, the revolution of acceleration commodity.Therefore, the purchase intention of research user is the important content of marketing research, all has important theory and realistic meaning to correctly guiding consumption of resident and instructing enterprise to formulate scientific and reasonable production, marketing strategy.

The measuring method of generally common user's purchase intention has two classes: the first kind measures the purchase intention of user, as Choice Based model, this model is provided with eight ATTRIBUTE INDEX, to each index determination weight, then user is to this eight indexs scoring, finally according to weight and score calculation user to the purchase intention of this product.Equations of The Second Kind uses infotech, as Wang Ping uses decision tree and neural net method to set up client's purchase intention disaggregated model to predict the purchase intention (" maintenance data digging technology prediction client purchase intention---method and positive research " of client, information science, in May, 2005); The people such as Wu Guohua introduce several attribute variable, build the probabilistic model (" customer purchasing behavior analysis of Influential Factors and heavily purchase the prediction of probability ", management engineering journal, in January, 2005) describing customer purchasing behavior or prediction purchase probability.But these two class methods all existing defects, first kind method is simple, but the weight of index is wayward, estimation precision is low, and the historical data used in method is not enough to the whole features reflecting current data, the prerequisite of Equations of The Second Kind method buys before and after client to obey Gamma distribution interval time, and this exists significant limitation in actual use; And under these two class methods are not all suitable for large data cases, in model use procedure, particularly disclose the purchase intention of user, do not consider the confidentiality of userspersonal information.

Summary of the invention

Technical matters to be solved by this invention is: the first, and existing user's purchase intention Forecasting Methodology is under the scene of a large amount of historical correlation data and a small amount of latest data, and the accuracy of prediction is not high; The second, existing method is not suitable for large data scene, and the time needed for training pattern is longer; 3rd, existing method can not the privacy of available protecting userspersonal information.

Technical scheme of the present invention is: large data user's purchase intention Forecasting Methodology of knowledge based study and secret protection; use the support vector machine technology improved; current a small amount of data group purchase intention probabilistic information and a large amount of history data set purchase intention probabilistic informations are incorporated in structural risk minimization learning framework; the study of knowledge is realized by structure different times data similarity distance item; user's purchase intention is predicted, comprises the following steps:

Step one: normalized is done to a large amount of historical data sample and a small amount of current data sample, obtains initial sample set (x _i, y _i) _{i=1 ..., N}, wherein x _ifor the proper vector of sample, y _i={+1 ,-1} is the class label of sample, and N is total number of sample;

Step 2: to historical data sample and current data sample division group, divide that often to organize data amount check roughly the same, build training sample set D={D ₁..., D _n, D _n+1..., D _n+d, wherein, n group is historical data sample, and rear d group is current data sample;

Step 3: the Probability p of counting user purchase intention in each grouping _i, calculate such as formula (1):

$p_i=\frac{\underset{i\∈S_i}{\mathrm{\Σ}}{y}_i}{\left|S_i\right|},(y_i=1)---\left(1\right)$

Wherein, | S _i| be the number of samples that each grouping comprises;

Step 4: calculating group label l _i, calculate such as formula (2):

$l_i=-\log (\frac{1}{p_i}-1)---\left(2\right)$

Step 5: use the support vector machine improved to train training set, the form of training pattern is such as formula (3):

$\underset{w_c,w_h,b_c,b_h}{\min }\frac{1}{2}{\left|\right|w_c\left|\right|}^2+\frac{1}{2}{\left|\right|w_h\left|\right|}^2+C_h\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i^h+{\mathrm{\ξ}}_i^{h*})+C_c\underset{i=n+1}{\overset{n+d}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i+{\mathrm{\ξ}}_i^{*})+\frac{\mathrm{\λ}}{2}{\left|\right|w_c-w_h\left|\right|}^2---\left(3\right)$

Wherein, for for nuclear space mapping function, w _hwith the weight vector of historical data sample and current data sample respectively, C _hand C _chistorical data sample and current data sample regularization parameter respectively, ξ _iwith be respectively the slack variable of historical data sample, ξ _jand ξ _i ^*be respectively the slack variable of current data sample, λ is balance parameters is a normal number, l _ifor the group label often organized obtained in described step 4, ε _i(i=1 ..., n) with ε ' _i(i=n+1 ..., n+d) and be respectively the approximation accuracy often organizing sample in historical data sample and current data sample, computing formula is as following form:

${\mathrm{\ϵ}}_i=\frac{\mathrm{\Δ}}{p_i(1-p_i)}---\left(4\right)$

Wherein p _ifor the probability calculated in described step 3, Δ is a less normal number;

Above formula (3) can convert following quadratic programming form to:

$\underset{\mathrm{\β}}{\min }\frac{1}{2}{\mathrm{\β}}^T\tilde{K}\mathrm{\β}+{\tilde{e}}^T\mathrm{\β},---\left(5\right)$

s.t.f ^Tβ＝0.

Wherein β=[α ^h, α ^h*, α, α ^*] ^t,

$\tilde{e}=[\mathrm{\ϵ}-L_h,\mathrm{\ϵ}+L_h,{\mathrm{\ϵ}}^{\′}-L_c,{\mathrm{\ϵ}}^{\′}+L_c],$

L _h＝[l ₁,...,l _n],L _c＝[l _n+1,...,l _n+d],

$\tilde{K}=\frac{1}{1+2\mathrm{\λ}}{\left[\begin{array}{ccc}1+\mathrm{\λ}{K}_{h,h}& \mathrm{\λ}{K}_{h,c}& -\mathrm{\λ}{K}_{h,c}\\ \mathrm{\λ}{K}_{h,c}^T& 1+\mathrm{\λ}{K}_{c,c}& -1+\mathrm{\λ}{K}_{c,c}\\ -\mathrm{\λ}{K}_{h,c}^T& -1+\mathrm{\λ}{K}_{c,c}& 1+\mathrm{\λ}{K}_{c,c}\end{array}\right]}_{(n+2d)\×(n+2d)},$

$K_{h,h}={\left(\frac{1}{\left|S_i\right|\left|S_j\right|}\underset{i\∈S_i}{\mathrm{\Σ}}\underset{j\∈S_j}{\mathrm{\Σ}}k(x_i,x_j)\right)}_{i,j=1,\·\·\·,n},K_{h,c}={\left(\frac{1}{\left|S_i\right|\left|S_j\right|}\underset{i\∈S_i}{\mathrm{\Σ}}\underset{j^{\′}\∈S_j}{\mathrm{\Σ}}k(x_i,x_{j^{\′}})\right)}_{i=1,\·\·\·,n,j^{\′}=1,...,d},$

$K_{c,c}={\left(\frac{1}{\left|S_{i^{\′}}\right|\left|S_{j^{\′}}\right|}\underset{i^{\′}\∈S_i}{\mathrm{\Σ}}\underset{j^{\′}\∈S_j}{\mathrm{\Σ}}k(x_{i^{\′}},x_{j^{\′}})\right)}_{i^{\′}{,j}^{\′}=1,...,d},$ kernel function, x _i, x _jbe respectively the proper vector of i-th and a jth sample,

By solving formula (3) and formula (5) can obtain w, the optimum solution w of b _c ^*, b _c ^*, wherein w _c ^*formula (6) can be expressed as:

B _c ^*formula (7) can be expressed as:

${b_c}^{*}=l_i-\frac{\mathrm{\λ}}{1+2\mathrm{\λ}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\widetilde{\mathrm{\α}}}_j^h-{\widetilde{\mathrm{\α}}}_j^{h*}}{\left|S_j\right|\left|S_i\right|}\underset{l\∈S_j}{\mathrm{\Σ}}\underset{k\∈S_i}{\mathrm{\Σ}}k(x_l,x_k)-\frac{1+\mathrm{\λ}}{1+2\mathrm{\λ}}\underset{j=n+1}{\overset{n+d}{\mathrm{\Σ}}}\frac{{\widetilde{\mathrm{\α}}}_j-{\widetilde{\mathrm{\α}}}_j^{*}}{\left|S_j\right|\left|S_i\right|}\underset{l\∈S_j}{\mathrm{\Σ}}\underset{k\∈S_i}{\mathrm{\Σ}}k(x_l,x_k)---\left(7\right)$

Step 6: structure forecast function, the form of anticipation function is formula (8):

Wherein, w _c ^*and b _c ^*for the optimum solution that described step 5 obtains;

Step 7: be input to after user data normalization to be predicted in described anticipation function, obtain predicting the outcome of user's purchase intention, if:

Beneficial effect of the present invention shows: 1) the present invention utilizes a large amount of historical datas to obtain relevant knowledge, auxiliary only comprise a small amount of current data and carry out knowledge learning, set up the forecast model based on the support vector machine improved, inherit the advantage of support vector machine based on empirical risk minimization framework largest interval, and reach the effect that current data better predicts.2) replace sample label when carrying out historical data sample and current data sample training with group probability, therefore space complexity of the present invention is (O (N ²)), time complexity is (O (N ³)) (wherein N is the group number that historical data and current data are divided into), under being applicable to large data environment than traditional SVM, (traditional SVM space complexity is (O (M in use ²)), time complexity is (O (M ³)) (wherein M is all sample number of historical data and current data), wherein N M.3) sample label contains very important privacy information; sample label is replaced with group probability when carrying out historical data sample and current data sample training; advantage is the Privacy Safeguarding provided raw data, can not reveal in the training process the privacy information of available protecting user.

Accompanying drawing explanation

Fig. 1 is the general flow chart of large data user's purchase intention Forecasting Methodology of knowledge based of the present invention study and secret protection.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with Concrete facts example, and with reference to accompanying drawing, the present invention is described in more detail.

The present embodiment chooses the enquiry data of certain digital product as research object, wherein historical data is the enquiry data of other model digital products of this brand before half a year, comprise 10000 samples altogether, current data is the enquiry data of the same brand new model digital product recently released, and comprises 100 samples altogether.All data comprise 40 attributes altogether, comprising: AGE, SEX, MARITAL, JOB, TRAVTIME, STATECOD, DOMESTIC, BRAND, MODEL NUMBER, AMOUNT, PRICE, RETURN etc.

Step one: normalized is done to a large amount of historical data sample and a small amount of current data sample;

In order to improve the accuracy rate of Forecasting Methodology, need data normalization in [0,1] or [-1,1] interval.The present embodiment adopts method for normalizing: according to maximal value and the minimum value of every eigenwert, all data of every eigenwert be transformed into linearly in [0,1] interval, conversion formula is as follows:

$\left\{\begin{array}{cc}{x}^{\′}=\frac{x-\min \left(x\right)}{\max \left(x\right)-\min x}& \max \left(x\right)\≠\min \left(x\right)\\ x^{\′}=1& \max \left(x\right)=\min \left(x\right)\end{array}\right.---\left(1\right)$

Wherein x is the eigenwert before normalization, and max (x) and min (x) represent respectively and get maximal value and minimum value to x, and x' is the eigenwert after normalization.After completing the normalization of eigenwert, by all eigenwerts composition proper vector, proper vector x is expressed as x={x ₁..., x ₄₀} ^t, wherein x ₁..., x ₄₀represent the concrete numerical value after above-mentioned 40 attribute normalization respectively.

Initial training sample set comprises 10000 historical data sample and 50 current data sample samples, is expressed as (x _i, y _i) _{i=1 ..., N}, wherein x _ifor the proper vector of sample, y _i={+1 ,-1} is the class label of sample, N=10050, and test sample book collection is 50 remaining current data samples, is expressed as (x _i, y _i) _{i=1 ..., M}, M=50, the y in test set _ibe used for the accuracy rate of verification method;

Step 2: to historical data sample and current data sample according to the principle division group often organizing 10 samples, historical data sample is divided into 100 groups, and current data sample is divided into 5 groups, builds training sample set D={D ₁..., D _n, D _n+1..., D _n+d, wherein, n group is historical data sample, and rear d group is current data sample, n=100, d=5;

Step 3: the purchase intention Probability p of counting user in each grouping _i, computing formula is as follows:

The purchase probability of user intention $p_i=\frac{\underset{i\∈S_i}{\mathrm{\Σ}}{y}_i}{\left|S_i\right|},(y_i=1)---\left(2\right)$

Wherein, | S _i| be the number of samples that each grouping comprises, in the present embodiment | S _i|=10;

Step 4: calculating group label l _i, as shown in the formula calculating:

$l_i=-\log (\frac{1}{p_i}-1)---\left(3\right)$

Step 5: use the support vector machine improved to train training set, the form of training pattern is such as formula (4):

$\underset{w_c,w_h,b_c,b_h}{\min }\frac{1}{2}{\left|\right|w_c\left|\right|}^2+\frac{1}{2}{\left|\right|w_h\left|\right|}^2+C_h\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i^h+{\mathrm{\ξ}}_i^{h*})+C_c\underset{i=n+1}{\overset{n+d}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i+{\mathrm{\ξ}}_i^{*})+\frac{\mathrm{\λ}}{2}{\left|\right|w_c-w_h\left|\right|}^2---\left(4\right)$

Wherein, for for nuclear space mapping function, w _hwith the weight vector of historical data sample and current data sample respectively, C _hand C _chistorical data sample and current data sample regularization parameter respectively, C in the present embodiment _hand C _cat grid { 2 ^-8, 2 ^-7, 2 ^-6, 2 ^-5, 2 ^-4, 2 ^-3, 2 ^-2, 2 ^-1, 2 ⁰, 2 ¹, 2 ², 2 ³, 2 ⁴, 2 ⁵, 2 ⁶, 2 ⁷, 2 ⁸, 2 ⁹, 2 ¹⁰middle search optimal value, ξ _iwith be respectively the slack variable of historical data sample, ξ _jand ξ _i ^*be respectively the slack variable of current data sample, λ is balance parameters, is a normal number, and in the present embodiment, balance parameters λ is interval { 2 ^-6, 2 ^-5, 2 ^-4, 2 ^-3, 2 ^-2, 2 ^-1, 2 ⁰, 2 ¹, 2 ², 2 ³, 2 ⁴, 2 ⁵, 2 ⁶, 2 ⁷, 2 ⁸, 2 ⁹, 2 ¹⁰, 2 ¹¹middle search optimal value, l _ifor the group label using formula (3) to calculate, ε _iwith ε ' _ibe respectively the approximation accuracy often organizing sample in historical data sample and current data sample, computing formula as shown in the formula:

${\mathrm{\ϵ}}_i=\frac{\mathrm{\Δ}}{p_i(1-p_i)}---\left(5\right)$

Wherein p _icalculated by formula (2), Δ is a less normal number, and in the present embodiment, Δ gets 0.1;

Above formula can convert following quadratic programming form to:

$\underset{\mathrm{\β}}{\min }\frac{1}{2}{\mathrm{\β}}^T\tilde{K}\mathrm{\β}+{\tilde{e}}^T\mathrm{\β},---\left(6\right)$

s.t.f ^Tβ＝0

Wherein β=[α ^h, α ^h*, α, α ^*] ^t,

$\tilde{e}=[\mathrm{\ϵ}-L_h,\mathrm{\ϵ}+L_h,{\mathrm{\ϵ}}^{\′}-L_c,{\mathrm{\ϵ}}^{\′}+L_c],$

L _h＝[l ₁,...,l _n],L _c＝[l _n+1,...,l _n+d],

$\tilde{K}=\frac{1}{1+2\mathrm{\λ}}{\left[\begin{array}{ccc}1+\mathrm{\λ}{K}_{h,h}& \mathrm{\λ}{K}_{h,c}& -\mathrm{\λ}{K}_{h,c}\\ \mathrm{\λ}{K}_{h,c}^T& 1+\mathrm{\λ}{K}_{c,c}& -1+\mathrm{\λ}{K}_{c,c}\\ -\mathrm{\λ}{K}_{h,c}^T& -1+\mathrm{\λ}{K}_{c,c}& 1+\mathrm{\λ}{K}_{c,c}\end{array}\right]}_{(n+2d)\×(n+2d)},$

$K_{h,h}={\left(\frac{1}{\left|S_i\right|\left|S_j\right|}\underset{i\∈S_i}{\mathrm{\Σ}}\underset{j\∈S_j}{\mathrm{\Σ}}k(x_i,x_j)\right)}_{i,j=1,\·\·\·,n},K_{h,c}={\left(\frac{1}{\left|S_i\right|\left|S_j\right|}\underset{i\∈S_i}{\mathrm{\Σ}}\underset{j^{\′}\∈S_j}{\mathrm{\Σ}}k(x_i,x_{j^{\′}})\right)}_{i=1,\·\·\·,n,j^{\′}=1,...,d},$

$K_{c,c}={\left(\frac{1}{\left|S_{i^{\′}}\right|\left|S_{j^{\′}}\right|}\underset{i^{\′}\∈S_i}{\mathrm{\Σ}}\underset{j^{\′}\∈S_j}{\mathrm{\Σ}}k(x_{i^{\′}},x_{j^{\′}})\right)}_{i^{\′}{,j}^{\′}=1,...,d},$ kernel function, x _i, x _jbe respectively the proper vector of i-th and a jth sample.

In the present embodiment, kernel function selects gaussian kernel function K (x _i, x _j)=exp (-r||x _i-x _j|| ²), wherein r is the wide parameter of core, and in the present embodiment, r is interval { 2 ^-15, 2 ^-13..., 2 ³middle search optimal value, x _i, x _jbe respectively the proper vector of i-th and a jth sample, || || ²represent Euclidean distance.

By solving formula (3) and formula (5) can obtain w, the optimum solution w of b _c ^*, b _c ^*, wherein w _c ^*formula (7) can be expressed as:

B _c ^*formula (8) can be expressed as:

${b_c}^{*}=l_i-\frac{\mathrm{\λ}}{1+2\mathrm{\λ}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\widetilde{\mathrm{\α}}}_j^h-{\widetilde{\mathrm{\α}}}_j^{h*}}{\left|S_j\right|\left|S_i\right|}\underset{l\∈S_j}{\mathrm{\Σ}}\underset{k\∈S_i}{\mathrm{\Σ}}k(x_l,x_k)-\frac{1+\mathrm{\λ}}{1+2\mathrm{\λ}}\underset{j=n+1}{\overset{n+d}{\mathrm{\Σ}}}\frac{{\widetilde{\mathrm{\α}}}_j-{\widetilde{\mathrm{\α}}}_j^{*}}{\left|S_j\right|\left|S_i\right|}\underset{l\∈S_j}{\mathrm{\Σ}}\underset{k\∈S_i}{\mathrm{\Σ}}k(x_l,x_k)---\left(7\right)$

Step 6: structure forecast function, the form of anticipation function is:

Wherein, w _c ^*, b _c ^*for optimum solution obtained above;

Step 7: the test set comprising 50 samples is input to anticipation function in, if:

Accuracy rate of the present invention, working time are as shown in table 1, and using the result of the inventive method with use 10000 historical data sample, 50 current data samples, 10000 historical data sample and 50 current data samples to merge the sample set in three kinds of situations to carry out training predicting the outcome of obtaining to compare as the training set of common support vector machine (SVM) (three kinds of methods are respectively SVM _{10000 historical datas}, SVM _{50 current datas}and SVM _{10050 blended datas}), experiment porch is MATLAB 2009 (a).Data as can be seen from table 1, other three kinds of methods accuracy rate compared with the inventive method is lower, and its reason is SVM _{10000 historical datas}only use historical data to train, have ignored the change between different times data; SVM _{50 current datas}only use 50 current data samples to predict, be not enough to acquisition good forecast model because training sample is very few; SVM _{10050 blended datas}then do not consider the difference between different times data, these three kinds of methods all disclose the label information of sample in training in addition, do not carry out secret protection to this important information of user's purchase intention.

Table 1: the inventive method and SVM _{10000 historical datas}, SVM _{50 current datas}, SVM _{10050 blended datas}discriminating accuracy rate (%) and compare working time (second)

	Accuracy rate (%)	Working time (second)
			The present invention	94％	215
SVM 10000 historical datas	88％	90681
			SVM 50 current datas	64％	213
SVM 10050 blended datas	90％	91190

above-described example just for illustration of the present invention, and is not construed as limiting the invention.Those skilled in the art can make various other various modifications and changes not departing from essence of the present invention according to these technology enlightenment disclosed by the invention, and these modifications and changes are still in protection scope of the present invention.

Claims (1)

1. large data user's purchase intention Forecasting Methodology of knowledge based study and secret protection, its feature comprises the steps:

Step one: normalized is done to a large amount of historical data sample and a small amount of current data sample, obtains initial sample set (x _i, y _i) _{i=1 ..., N}, wherein x _ifor the proper vector of sample, y _i={+1 ,-1} is the class label of sample, and N is total number of sample;

Step 2: to historical data sample and current data sample division group, divide that often to organize data amount check roughly the same, build training sample set D={D ₁..., D _n, D _n+1..., D _n+d, wherein, n group is historical data sample, and rear d group is current data sample;

Step 3: the Probability p of counting user purchase intention in each grouping _i, calculate such as formula (1):

$p_i=\frac{\underset{i\∈S_i}{\mathrm{\Σ}}{y}_i}{\left|S_i\right|}(y_i=1)---\left(1\right)$

Wherein, | S _i| be the number of samples that each grouping comprises;

Step 4: calculating group label l _i, calculate such as formula (2):

$l_i=-\log (\frac{1}{p_i}-1)---\left(2\right)$

Step 5: train the support vector machine that training set improves, the form of training pattern is such as formula (3):

$\underset{w_c,w_h,b_c,b_h}{\min }\frac{1}{2}{\left|\right|w_c\left|\right|}^2+\frac{1}{2}{\left|\right|w_h\left|\right|}^2+C_h\underset{i=1}{\overset{n}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i^h+{\mathrm{\ξ}}_i^{h*})+C_c\underset{i=n+1}{\overset{n+d}{\mathrm{\Σ}}}({\mathrm{\ξ}}_i+{\mathrm{\ξ}}_i^{*})+\frac{\mathrm{\λ}}{2}{\left|\right|w_c-w_h\left|\right|}^2---\left(3\right)$

Wherein, for for nuclear space mapping function, w _hwith the weight vector of historical data sample and current data sample respectively, C _hand C _chistorical data sample and current data sample regularization parameter respectively, ξ _iwith be respectively the slack variable of historical data sample, ξ _jwith be respectively the slack variable of current data sample, λ is balance parameters, is a normal number, l _ifor the group label that formula (2) calculates, ε _iwith ε ' _ibe respectively the approximation accuracy often organizing sample in historical data sample and current data sample, computing formula is as following form:

${\mathrm{\ϵ}}_i=\frac{\mathrm{\Δ}}{p_i(1-p_i)}---\left(4\right)$

Wherein p _icalculated by formula (1), Δ is a less normal number;

Above formula can convert following quadratic programming form to:

$\underset{\mathrm{\β}}{\min }\frac{1}{2}{\mathrm{\β}}^T\tilde{K}\mathrm{\β}+{\tilde{e}}^T\mathrm{\β},---\left(5\right)$

s.t.f ^Tβ＝0.

Wherein

L _h＝[l ₁,...,l _n],L _c＝[l _n+1,...,l _n+d],

$\tilde{K}=\frac{1}{1+2\mathrm{\λ}}{\left[\begin{array}{ccc}1+{\mathrm{\λK}}_{h,h}& {\mathrm{\λK}}_{h,c}& -{\mathrm{\λK}}_{h,c}\\ {\mathrm{\λK}}_{h,c}^T& 1+{\mathrm{\λK}}_{c,c}& -1+{\mathrm{\λK}}_{c,c}\\ -{\mathrm{\λK}}_{h,c}^T& -1+{\mathrm{\λK}}_{c,c}& 1+{\mathrm{\λK}}_{c,c}\end{array}\right]}_{(n+2d)\×(n+2d)},$

$K_{h,h}={\left(\frac{1}{\left|S_i\right|\left|S_j\right|}\underset{{i\∈S}_i}{\mathrm{\Σ}}\underset{j\∈S_j}{\mathrm{\Σ}}k(x_i,x_j)\right)}_{i,j=1,\·\·\·,n},K_{h,c}={\left(\frac{1}{\left|S_i\right|\left|S_j\right|}\underset{{i\∈S}_i}{\mathrm{\Σ}}\underset{j^{\′}{\∈S}_j}{\mathrm{\Σ}}k(x_i,x_{j^{\′}})\right)}_{i=1,\·\·\·,n,j^{\′}=1,...,d},$

kernel function, x _i, x _jbe respectively the proper vector of i-th and a jth sample,

By solving formula (3) and formula (5) can obtain w, the optimum solution w of b _c ^*, b _c ^*, wherein w _c ^*formula (6) can be expressed as:

B _c ^*formula (7) can be expressed as:

${b_c}^{*}=l_i-\frac{\mathrm{\λ}}{1+2\mathrm{\λ}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\widetilde{\mathrm{\α}}}_j^h-{\widetilde{\mathrm{\α}}}_j^{h*}}{\left|S_j\right|\left|S_i\right|}\underset{l\∈S_j}{\mathrm{\Σ}}\underset{k\∈S_i}{\mathrm{\Σ}}k(x_l,x_k)-\frac{1+\mathrm{\λ}}{1+2\mathrm{\λ}}\underset{j=n+1}{\overset{n+d}{\mathrm{\Σ}}}\frac{{\widetilde{\mathrm{\α}}}_j-{\widetilde{\mathrm{\α}}}_j^{*}}{\left|S_j\right|\left|S_i\right|}\underset{l\∈S_j}{\mathrm{\Σ}}\underset{k\∈S_i}{\mathrm{\Σ}}k(x_l,x_k)---\left(7\right)$

Step 6: structure forecast function, the form of anticipation function is formula (8):

Wherein, w _c ^*and b _c ^*for the optimum solution that step 5 obtains;

Step 7: be input to after user data normalization to be predicted in described anticipation function, obtain predicting the outcome of user's purchase intention, if: