CN103020116B - The method of the powerful user of automatic screening on social media network - Google Patents

Abstract

The present invention is a kind of method of powerful user of automatic screening on social media network, comprises step as follows: step S1: utilize hypergraph model for the user in interest social media network, object of interest and interaction relationship modeling thereof; Step S2: the regularization theme probability model adopting hypergraph constraint, utilize similarity relationships between the content information of object of interest and content information as constraint, automatic learning obtains the interest topic implied; Step S3: the sequence of theme influence power is carried out to each user and object of interest, similarity propagation model and the user on hypergraph and object of interest and super limit is each other adopted to propagate theme influence power, until stable state, then sequence can obtain the influential user under particular topic.The present invention truly and exactly can reflect the distribution of user force in social media network.

Description

The method of the powerful user of automatic screening on social media network

Technical field

The invention belongs to digital information processing field, be specifically related to a kind of data screening technology of social media network, particularly based on the screening technique of the responsive powerful user of theme of content of multimedia and link analysis.

Background technology

The appearance of social media network and prosperity and development, change the mode of people's acquisition and consumption information.Various social media network be people provide one can convenient creation and the platform sharing interest content.Such as, the news in brief picture of Sina, Tengxun's microblogging is shared, the news in brief of twitter, and the picture of Flickr is shared.But one has problems significantly is that people, while convenient obtaining information, also face the problem of information overload.During people's obtaining information, can tend to obtain oneself interested content and using influential user as information source.From social media network, filter out influential user or object of interest under a certain field or theme, become the focus of current academia and industry member concern.By filtering out the user of theme sensitivity, a kind of " interest intelligent " or " leader of opinion ", thus businessman can carry out influence power promotion, user can obtain interested required knowledge information with having Objective better.

At present for the screening of powerful user, existing method has: one is expert's discover method, and namely a given theme, identifies relevant technical ability or the people of experience.Existing work mainly concentrates on text data, does not relate to multi-medium data, i.e. the interested information carrier of various user, such as audio frequency, picture, video etc.Another kind is the influence power analysis of social media network, namely analyzes social media network and carries out modeling to the influence power in social media network, understands the active development situation of social media network.Existing groundwork be differentiate in social networks influence power existence or in homogenous network quantization influence power.

But, said method can not reflect the distribution of user force in social networks completely truely and accurately, user force is a successional quantifiable variable in social networks, and the influence power of user is theme sensitivity, namely, on different themes, the influence power distribution of user is different.Traditional method, on the one hand large multi-method is confined to text data process measure user influence power, and in fact comprises abundant multi-medium data in social networks, and these information have important effect to user force modeling.Classic method is to the general influence power modeling of user on the other hand, does not consider the influence power modeling of theme sensitivity.

Summary of the invention

(1) technical matters that will solve

Technical matters to be solved by this invention is the user how automatically filtering out influence power from social media network about specific theme, and to overcome current method be only the limitation of customer impact force modeling and the tolerance being only limitted to user's global impact power on text data.

(2) technical scheme

For solving the problems of the technologies described above, the present invention proposes a kind of method of powerful user of automatic screening on social media network, and it is as follows that the method comprising the steps of: step S1: utilize hypergraph model for the user in interest social media network, object of interest and interaction relationship modeling thereof; Step S2: the regularization theme probability model adopting hypergraph constraint, utilize similarity relationships between the content information of object of interest and content information as constraint, automatic learning obtains the interest topic implied; Step S3: the sequence of theme influence power is carried out to each user and object of interest, similarity propagation model and the user on hypergraph and object of interest and super limit is each other adopted to propagate theme influence power, until stable state, then sequence can obtain the influential user under particular topic.

(3) beneficial effect

The present invention utilizes in social media network the various media contents comprised automatically to find potential theme, and the powerful user under analyzing corresponding theme, multi-medium data and various social linking relationship can be utilized in multi-modal heterogeneous network to excavate the user of theme sensitivity.Further, the present invention truly and exactly can reflect the distribution of user force in social media network, filters out the powerful user of theme sensitivity in social media network.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the present invention's method of the powerful user of automatic screening on social media network;

Fig. 2 is that the homogeneity built according to view-based access control model content of the present invention surpasses limit schematic diagram;

Fig. 3 is that the homogeneity built based on content of text according to the present invention surpasses limit schematic diagram;

Fig. 4 is according to heterogeneous super limit of the present invention schematic diagram;

Fig. 5 is influence power message propagation schematic diagram in hypergraph of the present invention;

Fig. 6 a and Fig. 6 b is the representative user that obtains of method according to an embodiment of the invention and picture.

Embodiment

For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in further detail.

Target of the present invention is the powerful user filtering out theme sensitivity in social media network.Social media network in the present invention refers to of providing for user and can create and the platform sharing media information, such as picture sharing website Flickr.User alleged in the present invention refers to agent object in social media network and people, and alleged object of interest refers to be created and the special object shared, as picture, video, music by user.So-called theme refers to the polymerization of object of interest on semantic hierarchies and expresses, and concrete manifestation form is the probability distribution of the word of semantic similarity.Powerful user refer to such as can to forward the network behavior of other users in social networks, user that comment etc. produces directly or indirectly impact, so-called influence power is defined as when the mood of user, suggestion or behavior are subject to a kind of form of expression of other people effect.

Social media network of the present invention refers to centered by object of interest, create and the platform sharing object of interest for one that provides for user, object of interest can be news in brief, picture, video, music etc., abundant multi-medium data is there is in social media network, multi-modal and heterogeneous, such as in Flickr, there is text, picture, video, and exist between user and picture and comment on, forward, the linking relationship such as to like.

Put it briefly, the present invention utilizes in social media network the various media contents comprised automatically to find potential theme, and the powerful user under analyzing corresponding theme.The present invention can utilize multi-medium data and various social linking relationship to excavate the user of theme sensitivity in multi-modal heterogeneous network.Illustrate embodiments of the present invention below.

Figure 1 shows that the process flow diagram of powerful user's screening technique of the present invention.As shown in Figure 1, the present invention includes three step: S1, hypergraph builds (hypergraphconstruction); S2, interest topic Distributed learning (Topicofinterestdistributionlearning); Responsive influence power sequence (Topicsensitiveinfluenceranking) of S3, theme.Each step is described respectively below.

S1, hypergraph build

So-called hypergraph refers to the figure that can represent multistage relation.In hypergraph, comprise node and super limit G=(V, E, w), wherein node represents dissimilar object, and super limit can connect and represents higher order relationship each other more than two nodes.Hypergraph can carry out modeling to the object network comprising higher order relationship.

Step S1 uses hypergraph model to carry out the step of modeling for the user in social media network, object of interest and interaction relationship thereof.In social media network, to similarly being the most basic element, there is multiple linking relationship therebetween in user and interest, such as user can comment on, forwards, likes and comment on an object of interest.

In the present invention, user (user) in social media network and object of interest (objectofinterest, OI) is represented with hypergraph node; Super limit is divided into two types: homogeneity (homogeneous) super limit and heterogeneous (heterogeneous) super limit.

Homogeneity surpasses limit for representing the content similarities between object of interest, comprise vision content similarity and content of text similarity, heterogeneous super limit for representing the social linking relationship of high-order between user and object of interest, as liking and comment relation of existing between user and object of interest.

Fig. 2 is the schematic diagram that the homogeneity building view-based access control model content similarities surpasses limit, and as shown in Figure 2, the present invention adopts the method for k nearest neighbor, namely for each object of interest, find the object of interest of its K arest neighbors, then surpass limit by a homogeneity and connect these nodes, and weight is set to 1.

For content of text similarity, the homogeneity that the present invention builds based on text label surpasses limit, Fig. 3 builds the schematic diagram based on the super limit of text similarity, as shown in Figure 3, first a dictionary is extracted from the text meta-data of all object of interest, then for each word, for all object of interest comprising this word set up a super limit, and weight is set to 1.

For heterogeneous super limit, the present invention mainly considers two kinds:

A kind of heterogeneous super limit is the super limit of " owner-multiple object of interest-sole user " (owner-OIs-user), what it connected is owner (user A) and another user B and the mutual multiple object of interest between them, the multiple object of interest of user B to user A show interest behavior, such as comment on or like; The weight on this super limit is 1.

Another kind of heterogeneous super limit is the super limit of owner-single object of interest-multiple user (owner-OI-users), multiple users of what it connected is owner (user A) and an object of interest and behavior of becoming interested to this object of interest.The weight on this super limit is 1.

Fig. 4 is the schematic diagram on above-mentioned two kinds of heterogeneous super limits, and arrow represents certain linking relationship between user and object of interest.

S2, interest topic Distributed learning

In social media network, each object of interest both included content information, also included context metadata information, and content information comprises the information such as text, audio frequency, video, and context metadata information comprises the information such as label, time, position.This step S2 adopts hypergraph regularization theme probability model, and utilize similarity between the content information of object of interest and content information as constraint, automatic learning obtains the interest topic implied.

Suppose that a set includes N number of object of interest O={o ₁, o ₂..., o _n, enjoy K theme Z={z ₁..., z _k, each object of interest is expressed as a characteristic vector W based on word bag={ w ₁, w ₂..., w _m.Each object of interest is regarded as a document, word in subsidiary text is as word, the theme jointly enjoyed is as theme, and we adopt probability potential applications index (PLSI) to the generation of each object of interest and symbiosis word rate to carry out modeling, and production process is as follows:

With probability P (o _i) select an object of interest o _i;

With probability P (z _k| o _i) select a potential interest topic z _k;

With probability P (w _j| z _k) produce a word w _j.

The observation probability of a pair object of interest and word calculates as follows:

$P(o_i,w_j)=P\left(o_i\right)P\left(w_j\right|o_i)=P\left(o_i\right)\underset{k=1}{\overset{K}{\mathrm{\Σ}}}P\left(w_j\right|z_k)P\left(z_k\right|o_i)---\left(1\right)$

Comprising parameter has { P (w _j| z _k), P (z _k| o _i), we can obtain by optimizing likelihood,

$L^{\′}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}n(o_i,w_j)\log \underset{k=1}{\overset{K}{\mathrm{\Σ}}}P\left(w_j\right|z_k)P\left(z_k\right|o_i)---\left(2\right)$

The theme distribution of the object of interest gone out to make study keeps local similarity, we add the content of object of interest, comprise text, visual signature and content consistency therebetween as bound term, finally we obtain the theme probability model of hypergraph regularization.Obtain by maximizing plausible goals formula below:

$\begin{array}{c}L=L^{\′}-\mathrm{\λR}\\ =\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}n(o_i,w_j)\log \underset{k=1}{\overset{K}{\mathrm{\Σ}}}P\left(w_j\right|z_k)P\left(z_k\right|o_i)-\mathrm{\λ}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{f}_k^{T}L{f}_k\end{array}---\left(3\right)$

Wherein, L is hypergraph Laplacian Matrix, expresses as follows

$\begin{array}{c}R=\frac{1}{2}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{e\∈E_o}{\mathrm{\Σ}}\underset{o_i,o_j\∈V_o}{\mathrm{\Σ}}\frac{w\left(e\right)h(o_i,e)h(o_i,e)}{\mathrm{\δ}\left(e\right)}(\frac{P\left(z_k\right|o_i\left)\right)}{\sqrt{d\left(o_i\right)}}-\frac{P\left(z_k\right|o_j\left)\right)}{\sqrt{d}\left(o_j\right)})\\ =\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{f}_k^T(I-{D_v}^{-\frac{1}{2}}{\mathrm{HWD}}_e^{-1}{H}^T{D_v}^{-\frac{1}{2}})f_k\\ =\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{f}_k^T\mathrm{Lf}\end{array}---\left(4\right)$

We adopt extensive expectation-maximization algorithm to carry out optimized-type (3) and obtain theme probability model parameter { P (w _j| z _k), P (z _k| o _i).Extensive expectation maximization (generalizedEM) algorithm comprises desired step and maximization steps iteration is carried out.In desired step, calculate the posterior probability of hidden variable based on current parameter estimation; In maximization steps, optimize plausible goals formula, undated parameter obtains one and better separates.By extensive maximization algorithm, we obtain each object of interest o _itheme distribution P (z _k| o _i) and each theme z _kword probability distribution P (w _j| z _k).After obtaining the theme distribution of object of interest, the theme distribution that we obtain each user by the object of interest of being polymerized each user is as follows,

$P\left(z_k\right|u)=\underset{o_i\∈O_u}{\mathrm{\Σ}}P\left(z_k\right|o_i)P\left(o_i\right|u)=\underset{o_i\∈O_u}{\mathrm{\Σ}}\frac{P\left(z_k\right|o_i)}{\left|O_u\right|}---\left(5\right)$

The responsive influence power sequence of S3, theme

After the theme distribution obtaining each user and object of interest, this step S3 carries out the sequence of theme influence power, adopt user on hypergraph of similarity propagation model and object of interest and super limit propagation effect power each other, until stable state, then sequence can obtain the influential user under particular topic.

Fig. 5 is influence power message propagation schematic diagram.As shown in Figure 5, theme influence power at user's node of hypergraph and object of interest node, and between super limit propagate and until convergence.

As previously mentioned, heterogeneous super limit is divided into two kinds, and one is the super limit of owner-multiple object of interest-sole user (owner-OIs-user), and another kind is owner-single object of interest-multiple user.

First, in the responsive influence power of theme of the super limit study user of owner-multiple object of interest-sole user.With represent user u _iinfluence power score on theme k, s ^k(o _p) represent object of interest o _pinfluence power score on theme k.First two user u are calculated _i, u _jtopic Similarity f ^k(i, j) is as follows:

$f^k(i,j)=\log \frac{g(u_i,u_j,k)}{\underset{z\∈S}{\mathrm{\Σ}}g(u_i,u_z,k)},g(u_i,u_j,k)=\underset{o_p\∈O_{\mathrm{uj}}}{\mathrm{\Σ}}{s}^k\left(o_p\right)---\left(6\right)$

Topic Similarity f ^k(i, j) for calculating the influence power of user in similarity propagation introduce two groups of variablees with represent influence power message, r ^k(i, j) is by user's node u _isend to u _j, represent from user u _iangle see, he consenting user u _jtheme k affects his degree; a ^k(i, j) is by user's node u _jsend to u _i, represent from user u _jangle see, he thinks that he is to user u _ieffect on theme k.

By the super limit pass-along message owner-multiple object of interest-sole user, upgrade user force score as follows:

$\begin{array}{c}{r}^k(i,j)\←f^k(i,j)-\underset{z\∈S\left(i\right)}{\max }\{f^k(i,z)+a^k(i,z)\}\\ a^k(i,j)\←\min \{0,r^k(i,j)+\underset{z\∉\{i,j\}}{\mathrm{\Σ}}\max \{0,r^k(z,j)\left\}\right\}\\ a^k(j,j)\←\underset{i^{\′}\≠j}{\mathrm{\Σ}}\max \{0,r^k(i^{\′},j)\}\end{array}---\left(7\right)$

Wherein S (i) represents user u _ithe set having user of interested object of interest.By similar propagation algorithm above, we obtain stable state with based on this, the influence power that we define between user is: use q ^k(i, j) represents user u _jto user u _iinfluence power on theme k, is calculated as follows:

$q^k(i,j)=\frac{1}{1+e^{-(r^k(i,j)+a^k(i,j))}}---\left(8\right)$

Then we calculate the global impact power of user at theme:

$s^k\left(j\right)=\mathrm{\η}\underset{i:i\→j}{\mathrm{\Σ}}{s}^k\left(i\right)p^k\left(j\right|i)+(1-\mathrm{\η})v_j^k---\left(9\right)$

η is a controling parameters.P ^k(j|i) user u is represented _ito user u _jtransition probability calculate as follows:

$p^k\left(j\right|i)=\frac{q^k(i,j)}{\underset{j^{\′}:i\→j^{\′}}{\mathrm{\Σ}}{q}^k(i,j^{\′})}---\left(10\right)$

user u _jinitialization in the influence power of theme k, solving to formula (9) user force obtaining stable state is

$s_u^k=(1-\mathrm{\η}){(I-\mathrm{\η}{Q}_k)}^{-1}{v}^k---\left(11\right)$

For the super limit based on user force and owner-single object of interest-multiple user, the influence power that we calculate each object of interest is as follows:

$s_o^k\left(o_p\right)=P\left(z_k\right|o_p)(\mathrm{\β}\underset{z=1}{\overset{C}{\mathrm{\Σ}}}{s}^k\left(u_z\right)+(1-\mathrm{\β})s^k\left(u_h\right))---\left(12\right)$

Wherein C is to object of interest o _pthe user become interested.β is a controling parameters.

Upgrade the influence power iteration of user and object of interest, until reach stable state, finally we obtain the influence power of the theme sensitivity of each user and object of interest

Specific embodiment:

In order to assess the present invention, one embodiment of the present of invention, based on the api interface of the community Media picture sharing website Flickr of interest, have captured 2,314 users, and 556942 pictures altogether.Fig. 6 a show method of the present invention screening four influential representative users of theme.The theme probability model study of each theme hypergraph regularization obtains, and show with the most significant vocabulary, word is more relevant important, and its font is larger.Can find out that four themes are relevant to flower, girl, city, seabeach scenery respectively from Fig. 6 a.Under each theme, point the highest user of influence power and the picture that influence power mark is the highest under this theme of Ta are enumerated out, and as can be seen from the figure, theme vocabulary is relevant to picture.Fig. 6 b show method of the present invention screening at four influential representative pictures of theme.The picture that under each theme, influence power mark is the highest is enumerated out.Four themes are relevant with sky cloud, dark scene, portrait, seashore sunrise respectively, and picture vision content and word keep good consistance to explain.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (8)

1. the powerful user's of an automatic screening method on social media network, it is characterized in that, it is as follows that the method comprising the steps of:

Step S1: adopt probability potential applications index (PLSI) to carry out modeling to the generation of each object of interest and symbiosis word rate, obtain the observation probability of object of interest and word, add the content of object of interest again, comprise text, visual signature and content consistency therebetween as bound term to obtain the theme probability model of hypergraph constraint regularization;

Step S2: the theme probability model adopting hypergraph constraint regularization, utilize similarity relationships between the content information of object of interest and content information as constraint, automatic learning obtains the interest topic implied;

Step S3: the sequence of theme influence power is carried out to each user and object of interest, similarity propagation model and the user on hypergraph and object of interest and super limit is each other adopted to propagate theme influence power, until stable state, then sequence can obtain the influential user under particular topic.

2. the method for the powerful user of automatic screening on social media network according to claim 1, it is characterized in that, described step S1 comprises: represent user in social media network and object of interest with hypergraph node, surpass limit by homogeneity and represent content similarities between object of interest, represent the social linking relationship of high-order between user and object of interest with heterogeneous super limit.

3. the method for the powerful user of automatic screening on social media network according to claim 2, is characterized in that, the content similarities between described object of interest comprises vision content similarity and content of text similarity, and,

For representing that the super limit construction step of vision content similarity is: for each object of interest, find the object of interest of its K arest neighbors, then surpass limit by a homogeneity and connect these nodes, and weight is set to 1;

For representing that the super limit construction step of content of text similarity is: first extract a dictionary from the text meta-data of all object of interest, then for each word, for all object of interest comprising this word set up a super limit, and weight is set to 1.

4. the method for the powerful user of automatic screening on social media network according to claim 2, is characterized in that, described heterogeneous super limit comprises:

The super limit of owner-multiple object of interest-sole user, the weight on this super limit is set to 1; And,

The super limit of owner-single object of interest-multiple user, the weight on this super limit is set to 1.

5. the method for the powerful user of automatic screening on social media network according to claim 1, is characterized in that, the theme probability model of described hypergraph constraint regularization is: object keeps local similarity in the distribution of theme semantic space.The theme distribution p (z|o) calculating object of interest o is as follows with semantic space theme p (w|z) formula:

$L^{\′}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{M}{\mathrm{\Σ}}}n(o_i,w_j)\log \underset{k=1}{\overset{K}{\mathrm{\Σ}}}P\left(w_j\right|z_k)P\left(z_k\right|o_i)$

P (z|o) and p (w|z) can be obtained by optimizing above formula.Wherein, N is object of interest number, and M is the total number of word, and K is the number of implicit theme.N (o _i, w _j) be the symbiosis number of word and object of interest, what above formula represented is meant to solve parameter by optimizing likelihood.

6. the method for the powerful user of automatic screening on social media network according to claim 1, it is characterized in that, described step S3 comprises:

Based on the super limit of owner-multiple object of interest-sole user, calculate user force;

Based on the super limit of user force and owner-single object of interest-multiple user, calculate each object of interest influence power;

User force and object of interest influence power iteration are upgraded, until reach stable state, obtains the influence power of each user and object of interest.

7. the method for the powerful user of automatic screening on social media network according to claim 6, is characterized in that, the step of the calculating user force of described step S3 comprises:

Two user u are calculated by following formula _i, u _jtopic Similarity f ^k(i, j):

$f^k(i,j)=\log \frac{g(u_i,u_j,k)}{\underset{z\∈S}{\mathrm{\Σ}}g(u_i,u_z,k)},g(u_i,u_j,k)=\underset{o_p\∈O_{u_j}}{\mathrm{\Σ}}{s}^k\left(o_p\right),$ Wherein, variable with represent influence power message, r ^k(i, j) is by user's node u _isend to u _j, represent from user u _iangle see, he consenting user u _jtheme k affects his degree; a ^k(i, j) is by user's node u _jsend to u _i, represent from user u _jangle see, he thinks that he is to user u _ieffect on theme k; s ^k(o _p) represent object of interest o _pinfluence power score on theme k, g (u _i, u _j, k) be an intermediate variable;

By the super limit pass-along message owner-multiple object of interest-sole user, upgrade user force score as follows:

$r^k(i,j)\←f^k(i,j)-\underset{z\∈S\left(i\right)}{\max }\{f^k(i,z)+a^k(i,z)\}$

$a^k(i,j)\←\min \{0,r^k(j,j)+\underset{z\∉\{i,j\}}{\mathrm{\Σ}}\max \{0,r^k(z,j)\left\}\right\},$

$a^k(j,j)\←\underset{i^{\′}\≠j}{\mathrm{\Σ}}\max \{0,r^k(i^{\′},j)\}$

By similar propagation algorithm above, we obtain stable state with wherein S (i) represents user u _ithe set having user of interested object of interest;

Influence power between definition user is: use q ^k(i, j) represents user u _jto user u _iinfluence power on theme k:

$q^k(i,j)=\frac{1}{1+e^{-(r^k(i,j)+a^k(i,j))}};$

Calculate the global impact power of user at theme:

$s^k\left(j\right)=\mathrm{\η}\underset{i:i\→j}{\mathrm{\Σ}}{s}^k\left(i\right)p^k\left(j\right|i)+(1-\mathrm{\η})v_j^k,$ Wherein η is a controling parameters,

P ^k(j|i) user u is represented _ito user u _jtransition probability, and

wherein user u _jinitialization in the influence power of theme k, $v_j^k=\underset{o_i\∈O_{v_j}}{\mathrm{\Σ}}P\left(z_k\right|o_i);$

To formula $s^k\left(j\right)=\mathrm{\η}\underset{i:i\→j}{\mathrm{\Σ}}{s}^k\left(i\right)p^k\left(j\right|i)+(1-\mathrm{\η})v_j^k$ Solving the user force obtaining stable state is

$s_u^k=(1-\mathrm{\η}){(I-\mathrm{\η}{Q}_k)}^{-1}{v}^k.$

8. the method for the powerful user of automatic screening on social media network according to claim 6, is characterized in that, the formula calculating object of interest influence power in described step S3 is:

Utilize $s_o^k\left(o_p\right)=P\left(z_k\right|o_p)(\mathrm{\β}\underset{z=1}{\overset{C}{\mathrm{\Σ}}}{s}^k\left(u_z\right)+(1-\mathrm{\β})s^k\left(u_h\right)),$ Wherein C is to object of interest o _pthe user become interested, β is a controling parameters.