CN102693335B - The user interest pattern division methods estimated based on Gini coefficient - Google Patents

Abstract

The invention discloses a kind of user interest pattern division methods estimated based on Gini coefficient, relate to microcomputer modelling technical field, comprising: S1: based on vector space model framework user interest model；S2: according to user interest degree ascending order, the interest-degree after being sorted is ranked up to user interest modelS3: by step S2Interest-degree changes into the percentage taking family total interest degree own:S4: according toCalculate each user'sFor generating the vector of lorenz curve；S5: withValue be ordinate, be arranged as abscissa from low to high with the interest-degree in field, draw the lorenz curve of user interest pattern, and calculate Gini coefficient, by Gini coefficient divide user interest mode.Present invention achieves the accurate division to user interest pattern.

Description

The user interest pattern division methods estimated based on Gini coefficient

Technical field

The present invention relates to microcomputer modelling technical field, survey based on Gini coefficient particularly to one The user interest pattern division methods of degree.

Background technology

User interest pattern is diversified, and some users belong to the extensive type of interest, and it is to respectively Field to like degree to be distributed relatively uniform；Some users are then single-minded to like few class Other things, each field is liked the distribution of degree relative and uneven by it.Many times, i.e. Just different user Cup of tea thing is different, but has identical interest mode, such as one user Being that audiophile only likes music, another user is that military fan only likes military, to the greatest extent Pipe music and military art differ widely, but the two user is single interest pattern to be used Family, they have same interest pattern.And the research of relevant user interest lacks to user at present The measure of interest mode.It is therefore desirable to find a kind of side estimating user interest pattern Method.

In economics, Gini coefficient has very big reference to anticipate for research user interest pattern classification Justice.Gini coefficient is a kind of tolerance of the social rich or poor difference of assessment general in the world in economics Method, tolerance is distribution situation in all population for society's total income, this and user interest Pattern research measure user interest problem of Relative distribution between each field have similar very greatly it Place.

In order to study wealth of society inequitable distribution problem, U.S. statistician M.O. in 1905 Long-range navigation thatch (Max Otto Lorenz) proposes famous lorenz curve (lurenz curve). Lorenz curve (solid wire in Fig. 1) in economics is a kind of wealth distribution aggregation function Graph-based method.

For any point (x%, y%) on lorenz curve in Fig. 1, it is meant that lean to richness The ratio that before arrangement, the accumulative total income of the population of x% accounts for society's total income is y%.In figure " absolutely To fair line " (curve of absolute equality) represent society's total income in city Distribution of earnings curve during absolute mean allocation, is the straight line of " y=x "；" definitely unjust Horizontal line " (Curve of absolute inequality) is that all incomes of society are uniquely accounted for by a people According to when distribution of earnings curve, be a straight line being perpendicular to x-axis.The general position of lorenz curve Between absolute fair line and absolutely not fair line.

1912, Italy's economist's Geordie was according to lorenz curve, it is proposed that Geordie system Number (Gini coefficient).Gini coefficient is (uneven as estimating a variable distribution concentration degree Equal character) index, modern economics often uses it to measure gap between the rich and the poor.As it is shown in figure 1, If the area between lorenz curve and definitely fair line is A, lorenz curve is unjust with absolute The graphics area that horizontal line and x-axis surround is B.And it is unequal divided by the quotient representation of A+B with A Degree is Gini coefficient.It is expressed as by below equation (1):

$\mathrm{Gini\; coefficient}=\frac{A}{A+B}---\left(1\right)$

This numerical value is referred to as Gini coefficient or claims Lorenz coefficient, and size is positioned between 0 to 1. Area A between lorenz curve and definitely fair line is less, and distribution of earnings tends to flat Deng the radian of lorenz curve is also less, and Gini coefficient is also less；Otherwise, distribution of earnings Tending to inequality, the radian of lorenz curve is bigger, then Gini coefficient is also bigger.

Gini coefficient is when measuring gap between the rich and the poor, and the total income that it is social that its essence is assumed is homogeneity , measure its distribution situation at all population.

Prior art concentrates on according to user interest similarity research user preference.Lack from user Interest mode angle research user interest, it is impossible to exactly user interest pattern is divided.

Content of the invention

(1) to solve the technical problem that

The technical problem to be solved in the present invention is: how to carry out to user interest pattern exactly drawing Point.

(2) technical scheme

For solving above-mentioned technical problem, the invention provides one and estimate user based on Gini coefficient Interest division methods, comprises the following steps:

S1: based on vector space model framework user interest model, user interest field Collect and be combined into T={ interest 1, interest 2 ..., interest N}, for any one user, its user Interest model can be expressed as U={<interest 1, interest-degree 1>...,<interest N, interest-degree N>}；

S2: user interest model is ranked up according to user interest degree ascending order, after being sorted User interest degree be:

$U_{\mathrm{User}}^{\mathrm{Sorted}}=\{w_1^{\mathrm{sorted}},w_2^{\mathrm{sorted}},...,w_N^{\mathrm{Sorted}}\};$

S3: by step S2 Interest-degree Change into that to take family itself totally emerging The percentage of interest degree:

$U_{\mathrm{User}}^{\%}=\{w_1^{\%},w_2^{\%},...,w_N^{\%}\};$

S4: according to Calculate each user's Make a living Become the vector of lorenz curve, wherein:

$w_i=\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{w}_j^{\%}(1\&le;i\&le;N);$

S5: with Value be ordinate, be arranged as horizontal seat from low to high with the interest-degree in field Mark, draws the lorenz curve of user interest pattern, and calculates Gini coefficient, by Gini coefficient Divide the interest mode of user.

Wherein, it, in described step S5, is calculated as follows Gini coefficient:

$G_{\mathrm{User}}=1-\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[\frac{1}{2}\&times;(w_i+w_{i-1})\&times;\frac{1}{N}]}{\frac{1}{2}}=1-\frac{1}{N}\&times;\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_i+w_{i+1}).$

Wherein, the less user of described Gini coefficient difference, interest mode is more similar.

(3) beneficial effect

The present invention by utilize lorenz curve and Gini coefficient qualitative and quantitative estimate user The method of interest mode so that the division to user interest pattern is more accurate.

Brief description

Fig. 1 is lorenz curve schematic diagram；

Fig. 2 is that a kind of of the embodiment of the present invention draws based on the user interest pattern that Gini coefficient is estimated Divide method flow diagram；

Fig. 3 is the lorenz curve schematic diagram representing user's A, B, C interest in embodiment；

Fig. 4 is that the ladder approximation decomposition of the lorenz curve representing user's A interest in embodiment is shown It is intended to；

Fig. 5 is 943 user's lorenz curve schematic diagrames in movielens data set；

Fig. 6 is 943 user's Gini coefficient frequency disribution schematic diagrames in movielens data set；

Fig. 7 is the Gini coefficient distribution feelings dividing according to reference user in Movielens data set Condition.

Detailed description of the invention

Below in conjunction with the accompanying drawings and embodiment, the detailed description of the invention of the present invention is made further in detail Describe.Following example are used for illustrating the present invention, but are not limited to the scope of the present invention.

User interest pattern division methods flow process such as Fig. 1 estimating based on Gini coefficient of the present invention Shown in, comprising:

Step S201, based on vector space model (Vector Space Model, VSM) frame Structure user interest model, user interest field collection is combined into T={ interest 1, interest 2 ..., interest N}, for any one user, his user interest can be expressed as U={ < interest 1, interest Degree 1>...,<interest N, interest-degree N>.

U_user={ < theme₁, weight₁>...,<theme_N, weight_N>}

Theme is the theme in corresponding set T, and weight is that user is big to corresponding field interest-degree Little, it is weight user being previously set to certain field interest level, represent user to certain field Degree interested, it is possible to be directly expressed as:

U_user={ weight₁, weight₂..., weight_N}。

Step S202, is ranked up according to user interest degree ascending order to user interest model, obtains User interest after sequence is:

$U_{\mathrm{User}}^{\mathrm{Sorted}}=\{w_1^{\mathrm{sorted}},w_2^{\mathrm{sorted}},...,w_N^{\mathrm{Sorted}}\}$

Wherein $w_1^{\mathrm{sorted}}\&le;w_2^{\mathrm{sorted}}\&le;,...,\&le;w_N^{\mathrm{Sorted}},$

Step S203, then by second step Interest-degree changes into and always takies family itself The percentage of body interest-degree Obviously, numerical value sum in each user vector after percentage It is all 100%:

$U_{\mathrm{User}}^{\%}=\{w_1^{\%},w_2^{\%},...,w_N^{\%}\}$

Wherein:

$\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{w}_i^{\mathrm{Sorted}}=100\%$

Step S204, according to calculate in S203 Calculate each user's It is used to generate the vector of lorenz curve, w_i, (1≤i≤n) Represent that the percentage of in expression step S202 the 1st group is added to i-th group of interest-degree sum and accounts for entirely The percentage of body interest-degree.That is:

$w_i=\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{w}_j^{\mathrm{Sorted}}(1\&le;i\&le;N)$

Step S204, with Value be ordinate, low to high be arranged as by interested with field Abscissa, gets final product described point and draws the lorenz curve of user interest pattern, and Gini coefficient is:

$G_{\mathrm{User}}=1-\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[\frac{1}{2}\&times;(w_i+w_{i-1})\&times;\frac{1}{N}]}{\frac{1}{2}}=1-\frac{1}{N}\&times;\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_i+w_{i+1})$

The concrete reasoning process of Gini coefficient is exemplified below:

During application Gini coefficient of deriving estimates user interest pattern, three are first simulated Know the user of type, provide its Gini coefficient and calculate process.

As shown in table 1, a user being named as " rich " is had to be denoted as user A, can from table 1 It is that every field is all preferred with the feature finding out him intuitively；Another one user is " specialized personnel one ", is denoted as user B, and it is only concerned physical culture, finance and economics and military field, never reads Cross the news of other field；Also have a user " specialized personnel two ", be denoted as user C, user's C base Originally fashion, healthy and education sector are only focused on.Numerical value in table 1 is that it reads association area literary composition The number of chapter, as it was previously stated, the number of the read news of user is equal to user to this field Interest-degree.

1 three typical user's interest-degree distribution situations of table

After carrying out user interest modeling according to vector space model, the interest of three users can be distinguished It is expressed as by vector form:

U_A={ 5,3,4,7,6,2,8,4}

U_B={ 8,10,0,3,0,0,0,0}

U_C={ 0,0,1,0,0,5,12,7}

The difference of three user interest pattern can be found out according to these three vector intuitively, it is clear that The interest-degree distribution of user A is more average than user B, C.Next Gini coefficient is used Carry out the interest mode of quantitative measurement user, and qualitative observation can be carried out by lorenz curve.

The calculating process of user interest pattern Gini coefficient is:

The first step: A, B after being sorted successively by each user interest degree ascending sort and The vector model of user C:

$U_A^{\mathrm{Sorted}}=\left\{\mathrm{2,3,4,4,5,6,7,8}\right\}$

$U_B^{\mathrm{Sorted}}=\left\{\mathrm{0,0,0,0,0,3,8,10}\right\}$

$U_C^{\mathrm{Sorted}}=\{\mathrm{0,0,0,0},\mathrm{1,5,7,12}\}$

Second step: the interest-degree chemical conversion in vector in the first step is taken family total interest degree own Percentage, it is clear that after percentage, in each user vector, numerical value sum is 100%, That is:

$U_A^{\%}=\{5.2\%,7.7\%,10.3\%,10.3\%,12.8\%,15.4\%,17.9\%,20.5\%\}$

$U_B^{\%}=\{\mathrm{0,0,0,0,0,14.3}\%,30.1\%,55.6\%\}$

$U_C^{\%}=\{\mathrm{0,0,0,0,4}\%,20\%,28\%,48\%\}$

3rd step: for calculating Gini coefficient, also need to calculate each user's according to second step Being used to generate the vector of lorenz curve, n represents field Sum (n=8 herein), w_i, (1≤i≤n) i.e.:

$U_A^{\mathrm{Gini}}=\{5.2\%,12.9\%,23.1\%,33.4\%,46.2\%,61.6\%,79.5\%,100\%\}$

$U_B^{\mathrm{Gini}}=\{\mathrm{0,0,0,0,0,14.3}\%,44.4\%,100\%\}$

$U_C^{\mathrm{Gini}}=\{\mathrm{0,0,0,0,4}\%,24\%\%,52\%\%,100\%\}$

Then with vector U^GiniValue be ordinate, with all fields as abscissa, described point generates Curve be exactly user A, B and the lorenz curve of user C.As it is shown on figure 3, near " absolutely To fair line " some bar line be the lorenz curve of user A, dotted lines is the long-range navigation of user B Thatch curve, the stripline runs between user A, B is the lorenz curve of user C.Herein should be special Not it is noted that for these three user, the field of abscissa is by unique user fancy grade Height arrangement, is incremented by from left to right successively, might not be identical for different user specific field, Such as in Fig. 3 abscissa field 8, only represents the favorite field of unique user, for user A From the point of view of field 8 be its favorite health, and for user B from the point of view of, field 8 is that it likes best Finance and economics, for the two user, the particular content in field 8 is simultaneously different, but identical Being healthy and finance and economics is the favorite field of user A, B respectively, field 8 is liked by i.e. two users Ranking in all spectra for the good degree is identical.

For calculating the Gini coefficient of three users, as a example by user A.As shown in Figure 4, user A Lorenz curve and absolute average line between area be defined as S_A, with abscissa and absolutely not fair The area being formed between line is S_B, can obtain according to formula (1), the Gini coefficient of user A is Formula (2):

$G_A=\frac{S_A}{S_A+S_B}=\frac{(S_A+S_B)-S_B}{S_A+S_B}=1-\frac{S_B}{S_A+S_B}---\left(2\right)$

In abscissa, interest worlds totally takes 100%, it is clear that S_A+S_BArea be equal to 0.5.

Calculating S_BWhen, owing to actual lorenz curve is the line of a bending, it is impossible to directly Reference area, can only use certain methods to approximate.As shown in Figure 4, herein by S_BClosely Like for n with the width in field total shared by field between i-th group and the i-th-1 group as the end, with i-th The accumulative interest-degree w of group_iAdd up interest-degree w with the i-th-1 group_i-1Trapezoidal face for upper bottom Long-pending sum.The hypothesis general at this has n field,

For user: $U_{\mathrm{User}}^{\mathrm{Gini}}=\{w_1,w_2,...,w_i,...,w_n\}(1\&le;i\&le;n;w_0=0),$ Its Gini coefficient meter Calculating formula is:

$G_{\mathrm{User}}=1-\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}[\frac{1}{2}\&times;(w_i+w_{i-1})\&times;\frac{1}{N}]}{\frac{1}{2}}=1-\frac{1}{N}\&times;\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(w_i+w_{i+1})---\left(3\right)$

User A, B can be calculated according to formula (3) to be respectively as follows: with the Gini coefficient of user C G_A=0.22, G_B=0.73, G_C=0.69.

It it can thus be seen that the interest Gini coefficient of user A " rich " is 0.22, is similar to 0.2, Gini coefficient smaller explanation this user interest distribution is relatively uniform, belongs to hobby An extensive class people；And the Gini coefficient of user B " specialized personnel one " is 0.73, numeric ratio is relatively big, Illustrate that this user distributes and uneven, belong to the single-minded narrow class people of hobby；User C Interest distribution is also uneven, also belongs to the narrow crowd of hobby.Long-range navigation thatch from Fig. 3 Can also find out intuitively on curve, the lorenz curve of user A is than user B and user C more Near " absolute average line ", illustrate user A in distribution in all fields for the interest than use Family B is more uniform.And the lorenz curve of user B and user C is closely, show that it has phase As interest mode.

To the checking of the method experiment simulation of the present invention, it was demonstrated that feasibility, detailed process and Simulation result is as follows:

For effect in measure user interest mode for the actual verification Gini coefficient, have chosen Movielens data set carries out experimental verification.Movielens data set be Grouplens tissue from User's film score data that movielens website gathers.The data set using includes 943 100,000 scoring (1～5 point) to 1682 films for the user, each user is at least to 20 Film had scoring.

It is (comedy, dynamic that every film on Movielens data set all belongs to 18 fields Make piece, romance movie etc.) in a class or a few class, emerging for user with the type of this 18 kinds of films Interest field overall space, investigates the distribution situation that user interest is liked at this 18 type film. For the calculating of user interest degree, use and the scoring seen a film is added to by user this film institute The field belonging to, tries to achieve the interest-degree to this 18 class film for the user respectively.

Actual experiment finds, when investigating user preferences distribution with this whole 18 types, several The Gini coefficient of all users is all near 0.8, and discrimination is very low, and this shows almost do not have Having user all interested in the film of 18 types, this is also consistent with real daily life, because one As the class dabbled of the extensive people of interest also seldom can cover all.

Solve the overall quantity in Gini coefficient field for this according to 80/20 principle determination.Assume to use It is 80% that the main interest at family all accounts for its interest-degree population proportion, before then obtaining 943 users Shared by the main interest place relevant of 80%, the mean value of relevant is 7.14, therefore exists User is only investigated the highest to its interest when seeking lorenz curve and calculate user interest Gini coefficient The hobby situation of front 7 type films.Fig. 5 is the long-range navigation thatch of 943 users drawing accordingly Curve (abscissa is similar to Fig. 3, and the rightmost side is the field that user is most interested in, from left to right, Level of interest is incremented by successively), Fig. 6 is corresponding user's Gini coefficient frequency disribution.

The frequency disribution of 943 user's Gini coefficients substantially matching normal distribution in Fig. 6.In order to more Add the implication understanding these numerical value accurately, provide the Gini coefficient of 5 reference user as ginseng According to.Assuming that the interest distribution in 7 kinds of most interested fields for the user meets 80/20 principle, user feels The field of interest takies the 80% of family total interest, and remaining field accounts for 20% altogether.For example for One double Interests User, this user only has two main interests, and user is to the two field interest Degree accounts for the half of total amount 80% proportion respectively, and i.e. 40%, remain five fields of loseing interest in and divide equally The interest-degree of residue 20%, i.e. 4%.

So can respectively obtain following five class reference user and corresponding fancy grade distribution feelings thereof Condition, as shown in table 2:

Table 2 five class reference user interest-degree distribution situation and Gini coefficient

Reference user	Interest-degree is distributed	Gini coefficient
			Single Interests User	33%, 33%, 33%, 33%, 33%, 33%, 80%}	014
Double Interests User	4%, 4%, 4%, 4%, 4%, 40%, 40%}	024
			Three Interests User	5%, 5%, 5%, 5%, 266%, 266%, 266%}	038
Four Interests User	66%, 66%, 66%, 20%, 20%, 20%, 20%}	052
			Five Interests User	10%, 10%, 16%, 16%, 16%, 16%, 16%}	063

By user's Gini coefficient frequency in Fig. 6 respectively according to above five class reference user standards again Dividing, statistics draws user's Gini coefficient distribution situation, as shown in Figure 7.

It can be seen that Gini coefficient is very effective to the division result of user interest pattern, In 943 users being investigated, most is about 44.5% user have 3 to 4 interest necks Territory；The user of 24.4% has 4 to 5 main interests, and the user of 22.6% has 2 to 4 interest, The user of 6.5% only has 1 to 2 main interests；The artificial absolute single interest mode class of 1.2% Type, the only people of only a few 0.8% are liked interest worlds and are reached more than 5.

Above experimental data shows, application Gini coefficient measure user interest mode has well Discrimination, can be observed qualitatively by lorenz curve, and it is fixed also to be carried out by Gini coefficient Quantitative analysis.

Embodiment of above is merely to illustrate the present invention, and not limitation of the present invention, relevant The those of ordinary skill of technical field, without departing from the spirit and scope of the present invention, Can also make a variety of changes and modification, therefore all equivalent technical schemes fall within the present invention Category, the scope of patent protection of the present invention should be defined by the claims.

Claims (1)

1. the user interest pattern division methods estimated based on Gini coefficient, its feature exists In comprising the following steps:

S1: based on vector space model framework user interest model, user interest field Collect and be combined into T={ interest 1, interest 2 ..., interest N}, for any one user, its user Interest model can be expressed as U={<interest 1, interest-degree 1>...,<interest N, interest-degree N>}；

S2: user interest model is ranked up according to user interest degree ascending order, after being sorted User interest degree be:

$U_{User}^{Sorted}=\{w_1^{sorted},w_2^{sorted},...,w_N^{Sorted}\};$

S3: by step S2Interest-degreeChange into that to take family itself totally emerging The percentage of interest degree:

$U_{User}^{\%}=\{w_1^{\%},w_2^{\%},...,w_N^{\%}\};$

S4: according toCalculate each user's Make a living Become the vector of lorenz curve, wherein:

$w_i=\underset{j=1}{\overset{i}{\&Sigma;}}{w}_j^{\%},1\&le;i\&le;N;$

S5: withValue be ordinate, be arranged as horizontal seat from low to high with the interest-degree in field Mark, draws the lorenz curve of user interest pattern, and calculates Gini coefficient, by Gini coefficient Divide the interest mode of user；

It in described step S5, is calculated as follows Gini coefficient:

$G_{User}=1-\frac{\underset{i=1}{\overset{N}{\&Sigma;}}\&lsqb;\frac{1}{2}\&times;(w_i+w_{i-1})\&times;\frac{1}{N}\&rsqb;}{\frac{1}{2}}=1-\frac{1}{N}\&times;\underset{i=1}{\overset{N}{\&Sigma;}}(w_i+w_{i-1});$

The less user of described Gini coefficient difference, interest mode is more similar.