CN103093239B - A kind of merged point to neighborhood information build drawing method - Google Patents

Abstract

The present invention discloses a kind of point that merged to the drawing method of building with neighborhood information, and step is: the data set X obtaining n composition of sample, obtains the proper vector after dimension-reduction treatment, and they represent with node in figure G; The k nearest neighbor of all elements in data set X is found based on Euclidean distance; Set up the Optimized model merging sample neighborhood of a point and put right information; Solving-optimizing model, to each sample and k nearest neighbor thereof, determines five intermediate variables, obtains n the vector be made up of limit weights; The weight vector of acquisition is arranged in the adjacency matrix of figure G, thus obtains graph model.The present invention merged in the process of building figure simultaneously sample neighborhood of a point and point to information, thus can represent the tightness degree contacted between sample more exactly, foundation be a quadratic programming model, can solve easily and quickly.The present invention can obtain more rationally, effective graph model, can obtain higher accuracy rate in classification.

Description

A kind of merged point to neighborhood information build drawing method

Technical field

The invention belongs to machine learning and area of pattern recognition, particularly, relate to a kind of merged point to neighborhood information build drawing method.

Background technology

In machine learning field, the use of graph model is very widely.At numerous areas such as semi-supervised learning (Semi-supervisedLearning), spectral clustering (SpectralClustering), scale learning (MetricLearning), manifold learning (ManifoldLearning), markov random file (MarkovRandomFields), condition random fields (ConditionalRandomFields), graph model has all played very important effect.Graph model most clearly can represent the contact between sample point, has intuitively, feature fast and efficiently, is thus subject to the attention of more and more people.

At machine learning and area of pattern recognition, set up an accurate and effective graph model, commercial Application tool is had very great significance, such as: (1) can improve the discrimination of handwriting digital, thus offers help for the postcode identification of mail Automated Sorting System; (2) field of face identification can be applied to, for face is checked card examination or suspect searches and provides support; (3) can be applied in the expert system of medical diagnosis on disease, thus for disease automated intelligent diagnosis provide auxiliary; (4) can field of bioinformatics be applied to, improve identification and the mark accuracy rate of kinds of protein.Etc..

A complete graph model comprises node and two, limit key element usually, it can use G=<V, E> is represented, wherein G represents whole figure (Graph), V representation node collection (Vertexset), the set (Edgeset) that the limit that E representative connects these nodes is formed.Fig. 1 gives typical graph model and represents.

The basic task of machine learning and pattern-recognition is at function space find function set up sampling feature vectors to the mapping of label y, namely suppose there is the data set X={ (x that n sample point is formed ₁, y ₁), (x ₂, y ₂) ..., (x _n, y _n), in order to realize, to the classification of wherein sample, commonly using these samples of node on behalf when building figure, and go the similarity that represents between sample with limit, two points be simultaneously connected by a limit are referred to as " put to ".Based on this framework, existing drawing method of building is summarized as follows at present:

1. full map interlinking (FullyConnectedGraph).It is right that every two sample standard deviations be meant in figure form a point, and be connected by a limit, namely all sample standard deviations are directly related.

2. k nearest neighbor figure (KNNGraph).Each sample is only related with its K neighbour, namely only has between sample and its neighbour and has limit to be connected.

3. mutual k nearest neighbor figure (MutualKNNGraph).Be 2. without part, when only having the k nearest neighbor as two samples the other side each other, they are connected by ability limit.

4. ε neighbour figure (ε NNGraph).Euclidean distance x between two samples ₁-x ₂|| during≤ε, will with limit

They are connected, and wherein ε is the threshold value preset in advance.

Build drawing method for all above, also can define the weights omega on limit further to weigh the tightness degree contacted between sample.Main method has:

1. 0-1 weights (0-1Weight).As long as there is limit to be connected between two samples, then weights are just 1, otherwise are 0.This method thinks that the contact tightness degree between all-pair is all the same.

2. gaussian kernel (GaussianKernel).Point between contact tightness degree relevant with the similarity between them.The following gaussian kernel function of concrete employing describes:

${\mathrm{\&omega;}}_{12}=\exp (-\frac{{\left|\right|x_1-x_j\left|\right|}^2}{2{\mathrm{\&sigma;}}^2}).---\left(1\right)$

3. linear reconstruction power (LinearReconstructionWeights).The method thinks that each sample by its K neighbour's sample linear reconstruction, thus can set up the relation between sample and its neighbour.

Existing main stream approach can be classified as above a few class.Publication number is the Chinese invention patent application of 102024153A, utilizes linear reconstruction to weigh the classification solving high-spectrum remote sensing; Publication number is the Chinese invention patent application of 102637199A, utilizes k nearest neighbor figure (K=1) to devise a kind of new image labeling method; Publication number is the Chinese invention patent application of 101295360A, utilizes the k nearest neighbor figure with gaussian kernel to propose a kind of semi-supervision image classification method; Publication number is that the Chinese invention patent application of 101694521A utilizes 0-1 weights figure to propose target predicting and tracking algorithm; Publication number is the Chinese invention patent application of 102750385A, utilizes the full map interlinking of gaussian kernel to devise quality-ordered image search method; Publication number is the Chinese invention patent application of 102622756A, proposes spectral clustering image partition method by the full map interlinking containing gaussian kernel.

The result of quality on above method that graph model is set up has important impact.Such as Images Classification problem, good figure can represent the relation between sample point more accurately, thus obtains higher classification pregroup rate.But it should be noted that, the various method before enumerated or the neighborhood information that only make use of sample, or only pay close attention to the information that point is right, namely the decision of limit weights omega is only relevant with two samples that this limit connects, thus the result accuracy rate of these methods has much room for improvement, thus when being specifically applied in above-mentioned industry, or not ideal enough.

Summary of the invention

For defect of the prior art, the object of this invention is to provide and a kind ofly more accurate and effective build drawing method, for a specific sample point, the present invention not only considers the information that its point is right, also contemplate the relation between it and all neighbours, can obtain more accurate and effective graph model like this, thus improve the accuracy rate of application result, this is of great significance concrete commercial Application tool.

Suppose the data set X={ (x of n composition of sample ₁, y ₁), (x ₂, y ₂) ..., (x _n, y _n), wherein x ₁~ x _nfor the proper vector of d dimension, y ₁~ y _nfor the label of corresponding sample generic.The acquisition methods of proper vector has a lot, such as image, can adopt RGB color histogram feature, histogram of gradients (HOG) feature, scale invariant feature conversion (SIFT); Concerning text, word frequency-reverse document-frequency feature (TF-IDF) etc. can be adopted.The original dimension of these proper vectors is general all higher, can pass through principal component analysis (PCA) (PCA), linearly distinguish the dimension reduction methods such as analysis (LDA) and carry out Dimensionality Reduction.After proper vector after these dimensionality reductions obtains all, graph model G be set up and go to characterize these samples and the association between them or similarity.

The invention provides a kind of point that merged to the drawing method of building with neighborhood information, the method comprises the steps:

The first step, obtains the data set X of n composition of sample, obtains the proper vector x after dimension-reduction treatment ₁, x ₂..., x _n, they represent with node in figure G;

Second step, finds the k nearest neighbor of all sample elements in data set X based on Euclidean distance;

3rd step, sets up the Optimized model merging sample neighborhood of a point and put right information;

Suppose for a sample x _i, its K neighbour x _i1, x _i2..., x _iK, corresponding weight vectors ω _i=(ω _i1, ω _i2..., ω _iK), x _itwo neighbour x _ij, x _ik, 1≤i≤n, k≤K, then described Optimized model is as follows:

$\underset{{\mathrm{\&omega;}}_i=({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&omega;}}_{\mathrm{iK}})}{\min }{\mathrm{\&epsiv;}}_i={\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2+\mathrm{\&gamma;}\underset{j=1}{\overset{K-1}{\mathrm{\&Sigma;}}}\underset{k=j+1}{\overset{K}{\mathrm{\&Sigma;}}}{\left({\mathrm{\&omega;}}_{\mathrm{ij}}\right||x_i-x_{\mathrm{ij}}||-{\mathrm{\&omega;}}_{\mathrm{ik}}||x_i-x_{\mathrm{ik}}|\left|\right)}^2---\left(3\right)$

Order and x _ithe all limits be connected are weighed and are 1, and these weights are all non-negative, then:

$\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{ij}}=1,{\mathrm{\&omega;}}_{\mathrm{ij}}\&GreaterEqual;0---\left(4\right)$

Wherein: γ >0 is the weight coefficient between two, || || the l-2 norm of representation vector, the Section 1 of above-mentioned model represents a certain sample point x _iwith the relation of its neighborhood, Section 2 then represent to put between neighbour between relation.

Regulate the γ parameter in above-mentioned model, this parameter to represent in modeling process the relative attention degree to information to neighborhood information or point, and it regulates according to the actual demand of user and application background and determines.Such as, if user thinks a little important to its Application comparison to information, then γ parameter should correspondingly be tuned up; Otherwise, if user needs to utilize neighborhood information more, then should suitably reduce γ parameter.

Samples all in data set X is operated according to formula (3) and (9), just can obtain the connection weight on all limits in figure G.

4th step, solves the Optimized model of the 3rd step, to each sample x _iand k nearest neighbor, determine following H, p, A, b and q five intermediate variables, obtain n the vectorial ω be made up of limit weights _i, 1≤i≤n;

For solving above-mentioned Optimized model, formula (8) and (9) are rewritten as more succinct matrix form:

$\underset{{\mathrm{\&omega;}}_i={({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&omega;}}_{\mathrm{iK}})}^T}{\min }\mathrm{\&epsiv;}\left({\mathrm{\&omega;}}_i\right)=\frac{1}{2}{{\mathrm{\&omega;}}_i}^{T}H{\mathrm{\&omega;}}_i+p^T{\mathrm{\&omega;}}_i+q,---\left(2\right)$

s.t.Aω _i=b,ω _i≥0

Wherein H is the matrix of a symmetrical K × K:

To each sample x _iand k nearest neighbor, determine H according to (11) ~ (14) formula, p, A, b and q five intermediate variables, these five variablees determine the form of a quadratic programming uniquely;

$H_{j,k}=\left\{\begin{array}{cc}2({\left|\right|x_{\mathrm{ij}}\left|\right|}^2+\mathrm{\&gamma;}(K-1){\left|\right|x_i-x_{\mathrm{ij}}\left|\right|}^2)& j=k\\ 2(x_{\mathrm{ij}}^T{x}_{\mathrm{ik}}-\mathrm{\&gamma;}||x_i-x_{\mathrm{ij}}|\left|\right||x_i-x_{\mathrm{ik}}|\left|\right)& j\&NotEqual;k\end{array}\right.---\left(3\right)$

$p={(-2x_i^T{x}_{i1}\&CenterDot;\&CenterDot;\&CenterDot;-2x_i^T{x}_{\mathrm{ik}}\&CenterDot;\&CenterDot;\&CenterDot;-2x_i^T{x}_{\mathrm{iK}})}^T,---\left(4\right)$

q=||x _i|| ²，(5)

5th step, by the weight vector ω obtained ₁~ ω _nbe arranged in the adjacency matrix of figure G, thus obtain graph model.

Compared with prior art, the present invention has following beneficial effect:

The present invention has been merged sample neighborhood of a point simultaneously and has been put information in the process of building figure, thus can represent the tightness degree contacted between sample more exactly; What set up is quadratic programming (QP) model, can be solved easily and quickly by existing method.Experiment proof compares to existing method, and the present invention can obtain more rationally, effective graph model, can obtain higher accuracy rate, and can be successfully applied in the industry such as Handwritten Digital Recognition, make application result more accurate in Images Classification etc.

Accompanying drawing explanation

By reading the detailed description done non-limiting example with reference to the following drawings, other features, objects and advantages of the present invention will become more obvious:

Fig. 1 is typical graph model schematic diagram.

Fig. 2 is the design sketch of the present invention on DoubleMoon data set.

Fig. 3 is the design sketch of the present invention on DoubleRing data set.

Fig. 4 is the present invention and existing methods accuracy rate correlation curve on Iris data set.

Fig. 5 is the present invention and existing methods accuracy rate correlation curve on Wine data set.

Fig. 6 is the sample of some handwriting digitals.

Fig. 7 is the present invention and existing methods accuracy rate correlation curve in Handwritten Digital Recognition.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in detail.Following examples will contribute to those skilled in the art and understand the present invention further, but not limit the present invention in any form.It should be pointed out that to those skilled in the art, without departing from the inventive concept of the premise, some distortion and improvement can also be made.These all belong to protection scope of the present invention.

The invention provides a kind of method for building up of graph model, the method have employed sample neighborhood of a point simultaneously and some the information of two aspects to be determined to the weight on each limit in figure, use the point of sample to have employed the new method being different from prior art during information, namely by the function served as bridge of central sample, indirectly determine the relation between its neighbour, thus avoid the manual adjustments of gaussian kernel width in classic method, better can improve accuracy, the validity of Commercial application.

Suppose a total n sample, be expressed as x by the proper vector of d dimension ₁, x ₂..., x _n, they represent with node in figure G.For one of them sample x _i, (1≤i≤n), first needs to use k nearest neighbor algorithm to obtain its K neighbour x _i1, x _i2..., x _iK, and final purpose to obtain its corresponding weight vectors ω _i=(ω _i1, ω _i2..., ω _iK).Choosing of K should be moderate, and generally speaking, if data centralization sample Relatively centralized, it is less that K can get, otherwise then should suitably tune up.

In order to incorporate a little to information, (1) formula of can applying simply expresses x _iwith the relation of its each neighbour.But the method that in noticing (1), the adjustment of parameter σ there is no at present in the world, its determination can only lean on experience.In order to avoid this problem, the present invention allows x _isimultaneously and its two neighbour x _ij, x _ik, (1≤i, k≤K) is related.See intuitively, x _iwith which neighbour from obtaining (namely more similar) more, so corresponding weights also just should be larger, so can be written as following optimization problem:

$\underset{{\mathrm{\&omega;}}_i=({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&omega;}}_{\mathrm{iK}})}{\min }\underset{j=1}{\overset{K-1}{\mathrm{\&Sigma;}}}\underset{k=j+1}{\overset{K}{\mathrm{\&Sigma;}}}{\left({\mathrm{\&omega;}}_{\mathrm{ij}}\right||x_i-x_{\mathrm{ij}}||-{\mathrm{\&omega;}}_{\mathrm{ik}}||x_i-x_{\mathrm{ik}})\left|\right|}^2---\left(7\right)$

Wherein || || the l-2 norm of representation vector.Pass through x like this _ifunction served as bridge, just establish x _ijand x _ikbetween relation, avoid simultaneously introduce parameter σ.

In addition, x is further considered _iuse for reference the thought of linear neighborhood transmission (LNP) with the relation of its all neighbour, can obtain final objective function is

$\underset{{\mathrm{\&omega;}}_i=({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&omega;}}_{\mathrm{iK}})}{\min }{\mathrm{\&epsiv;}}_i={\left|\right|x_i-\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{ij}}{x}_{\mathrm{ij}}\left|\right|}^2+\mathrm{\&gamma;}\underset{j=1}{\overset{K-1}{\mathrm{\&Sigma;}}}\underset{k=j+1}{\overset{K}{\mathrm{\&Sigma;}}}{\left({\mathrm{\&omega;}}_{\mathrm{ij}}\right||x_i-x_{\mathrm{ij}}||-{\mathrm{\&omega;}}_{\mathrm{ik}}||x_i-x_{\mathrm{ik}}|\left|\right)}^2,---\left(8\right)$

Wherein γ >0 is the weight coefficient between two.(8) Section 1 illustrates x _iwith the relation of its neighborhood, Section 2 then illustrate to put between neighbour between relation.Here x is conveyed _ithe all limits power be connected and be 1, and these weights obviously should be all non-negative, thus give further (8) impose restriction into

$\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{\mathrm{ij}}=1,{\mathrm{\&omega;}}_{\mathrm{ij}}\&GreaterEqual;0.---\left(9\right)$

Samples all in data set X is operated according to (8) and (9), just can obtain the connection weight on all limits in figure G.In order to solve this optimization problem, (8) and (9) can be written as more succinct matrix form:

$\underset{{\mathrm{\&omega;}}_i={({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},\&CenterDot;\&CenterDot;\&CenterDot;{\mathrm{\&omega;}}_{\mathrm{iK}})}^T}{\min }\mathrm{\&epsiv;}\left({\mathrm{\&omega;}}_i\right)=\frac{1}{2}{{\mathrm{\&omega;}}_i}^{T}H{\mathrm{\&omega;}}_i+p^T{\mathrm{\&omega;}}_i+q,---\left(10\right)$

s.t.Aω _i=b,ω _i≥0

Wherein H is the matrix of a symmetrical K × K:

$H_{j,k}=\left\{\begin{array}{cc}2({\left|\right|x_{\mathrm{ij}}\left|\right|}^2+\mathrm{\&gamma;}(K-1){\left|\right|x_i-x_{\mathrm{ij}}\left|\right|}^2)& j=k\\ 2(x_{\mathrm{ij}}^T{x}_{\mathrm{ik}}-\mathrm{\&gamma;}||x_i-x_{\mathrm{ij}}|\left|\right||x_i-x_{\mathrm{ik}}|\left|\right)& j\&NotEqual;k\end{array}\right.---\left(11\right)$

$p={(-2x_i^T{x}_{i1}\&CenterDot;\&CenterDot;\&CenterDot;-2x_i^T{x}_{\mathrm{ik}}\&CenterDot;\&CenterDot;\&CenterDot;-2x_i^T{x}_{\mathrm{iK}})}^T,---\left(12\right)$

q=||x _i|| ²，(13)

(10) formula of noticing is actually quadratic programming (QP) problem.By solving n shape as the optimization problem of (10) formula, just vectorial ω can be tried to achieve ₁, ω ₂..., ω _nso the weight on all limits is tried to achieve all, and then the adjacency matrix of figure G can be designated as

W=(ω ₁ω ₂…ω _n) ^T.(15)

Note W _ijfor (i, j) individual element of matrix W.If definition diagonal matrix D=diag is (d ₁, d ₂..., d _n), wherein d _ifor sample x _idegree (degree), namely so according to the method that the present invention proposes, the Laplacian Matrix (GraphLaplacian) of figure G is

L＝D-W.(16)

In the present invention, parameter K and γ needs to be adjusted to a desired value in advance, and the Optimized model that the present invention proposes can use the quadprog function carried in Mathworks company MatlabR2011a software to solve.The input value of this function is H, p, A, b and q five intermediate variables, and rreturn value is exactly required x _iweight vectors ω _i.

In order to verify the method that the present invention proposes, DoubleMoon and DoubleRing data set is adopted to carry out testing (see Fig. 2, Fig. 3).Obviously, in these two data centralizations, all samples are all 2 dimensions, and the sample in them can be divided into two classes.Wherein, DoubleMoon data set is made up of upper and lower two semicircles, and each semicircle is a class, and each semicircle is containing 200 data points.The center of circle of two semicircles is respectively (0,0) and (10,0).DoubleRing data set is made up of two concentric rings, and the sample in each ring is a class.Their center of circle is (0,0), the radius of its outer-loop is 1.5, the radius of inner ring is the method that 0.5. proposes according to the present invention, first finds the k nearest neighbor of all sample points in figure, then calculates the H belonging to each sample, p, A, b and q, finally recycle (10) formula and can obtain result.In figs. 2 and 3, be connected if wired between two samples, then illustrate and build drawing method according to of the present invention, these two samples are relevant, otherwise then illustrate and directly do not contact between two samples.As can be seen from the figure the present invention builds drawing method and can will contact similar sample well, distinguishes foreign peoples's sample, and excavates the geometric properties be hidden in sample point exactly.

In addition, the drawing method of building proposed also is used for semi-supervised learning by the present invention, and tests on public data collection Iris and Wine in machine learning field, and classification results is shown in that Fig. 4, Fig. 5 .Iris data set comprises 3 class samples respectively, each class is containing 50 samples, and each sample is 4 dimensions.Wine data set also comprises 3 class samples, has 59,71 and 48 samples respectively, and each sample is 13 dimensions.In order to reach classifying quality, the method establishment graph model that can first adopt the present invention to propose, then adopt existing label transmission method (labelpropagation) by figure the label of marker samples each limit in figure be passed to a large amount of unmarked samples, the sample in final figure representated by each node can obtain the pseudo-label within the scope of a real number.And then the generic of each sample just can be determined according to these pseudo-labels.

Consider that point more contributes to promoting classifying quality to neighborhood information to prove to build in figure process, the present invention uses the method for linear neighborhood transmission (being abbreviated as LNP) to contrast simultaneously.Linear neighborhood TRANSFER METHOD only considers x _ithe one-sided information of neighborhood, and have ignored a little to information, be therefore unfavorable for the Accurate classification of sample.And method of the present invention is owing to considering the information of above two aspects, so be not difficult to find out that the effect obtained on two data sets obviously will be better than existing linear neighborhood TRANSFER METHOD.It can also be seen that in addition, along with the continuous increase of marker samples number, classification accuracy of the present invention also can promote with speed faster.When marker samples number reaches some, classification accuracy can reach about 95%.This also describes the validity of building drawing method that the present invention proposes from another aspect.

The present invention is also helpful for solution Handwritten Digital Recognition.The sample of some handwriting digitals is shown in Fig. 6.Here namely each digital picture is a sample, has 8 × 8=64 pixel.The present invention directly adopts the gray-scale value of these 64 pixels as feature, so the proper vector of each sample has 64 dimensions.Characterize each sample and mutual relationship thereof with the drawing method of building that the present invention proposes equally, re-use label transmission method and carry out numeral identification, gratifying discrimination can be reached.The method propose the present invention and linear neighbour's TRANSFER METHOD contrast, and the classification accuracy curve of acquisition as shown in Figure 7.Can find out, effect of the present invention is better than existing method.And (be about 6) when marker samples number is little, discrimination has just exceeded 90%, this illustrates that the drawing method of building that the present invention proposes truly, accurately reflects similarity (or otherness) between sample point, for correctly discriminating digit provides good foundation.

Above specific embodiments of the invention are described.It is to be appreciated that the present invention is not limited to above-mentioned particular implementation, those skilled in the art can make various distortion or amendment within the scope of the claims, and this does not affect flesh and blood of the present invention.

Claims (5)

1. merged point to the drawing method of building with neighborhood information, it is characterized in that, comprise the steps:

The first step, obtains the data set X of n composition of sample, obtains the proper vector x after dimension-reduction treatment ₁, x ₂..., x _n, they represent with node in figure G;

Second step, finds the k nearest neighbor of all sample elements in data set X based on Euclidean distance;

3rd step, sets up the Optimized model merging sample neighborhood of a point and put right information;

Suppose for a sample x _i, its K neighbour x _i1, x _i2..., x _iK, corresponding weight vectors ω _i=(ω _i1, ω _i2..., ω _iK), x _itwo neighbour x _ij, x _ik, 1≤i≤n, k≤K, then Optimized model is as follows:

$\underset{{\mathrm{\&omega;}}_i=({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},...,{\mathrm{\&omega;}}_{iK})}{min}{\mathrm{\&epsiv;}}_i=\left|\right|x_i-\underset{j=1}{\overset{K}{\&Sigma;}}{\mathrm{\&omega;}}_{ij}{x}_{ij}|{|}^2+\mathrm{\&gamma;}\underset{j=1}{\overset{K-1}{\&Sigma;}}\underset{k=j+1}{\overset{K}{\&Sigma;}}{\left({\mathrm{\&omega;}}_{ij}\right||x_i-x_{ij}||-{\mathrm{\&omega;}}_{ik}||x_i-x_{ik}|\left|\right)}^2$

Order and x _ithe all limits be connected are weighed and are 1, and these weights are all non-negative, then:

$\underset{j=1}{\overset{K}{\&Sigma;}}{\mathrm{\&omega;}}_{ij}=1,{\mathrm{\&omega;}}_{ij}\&GreaterEqual;0$

Wherein: γ > 0 is the weight coefficient between two, || || the l-2 norm of representation vector, the Section 1 of above-mentioned model represents a certain sample point x _iwith the relation of its neighborhood, Section 2 then represent to put between neighbour between relation;

4th step, solves the Optimized model of the 3rd step, to each sample x _iand k nearest neighbor, determine following H, p, A, b and q five intermediate variables, obtain n the vectorial ω be made up of limit weights _i, 1≤i≤n;

For solving above-mentioned Optimized model, be rewritten as more succinct matrix form:

$\underset{{\mathrm{\&omega;}}_i={({\mathrm{\&omega;}}_{i1},{\mathrm{\&omega;}}_{i2},...,{\mathrm{\&omega;}}_{iK})}^T}{min}\mathrm{\&epsiv;}\left({\mathrm{\&omega;}}_i\right)=\frac{1}{2}{{\mathrm{\&omega;}}_i}^T{\mathrm{H\&omega;}}_i+p^T{\mathrm{\&omega;}}_i+q,$

s.t.Aω _i＝b,ω _i≥0

The wherein transposition of subscript T representation vector, H is the matrix of a symmetrical K × K

To each sample x _iand k nearest neighbor, determine H according to following formula, p, A, b and q five intermediate variables, these five variablees determine the form of a quadratic programming uniquely:

$H_{j,k}=\left\{\begin{array}{cc}2\left(\right|\left|x_{ij}\right|{|}^2+\mathrm{\&gamma;}(K-1)\left|\right|x_i-x_{ij}\left|{|}^2\right)& j=k\\ 2(x_{ij}^T{x}_{ik}-\mathrm{\&gamma;}||x_i-x_{ij}|\left|\right||x_i-x_{ik}|\left|\right)& j\&NotEqual;k\end{array}\right.$

$p={\left(\begin{array}{ccccc}-2x_i^T{x}_{i1}& \mathrm{...}& -2x_i^T{x}_{ik}& \mathrm{...}& -2x_i^T{x}_{iK}\end{array}\right)}^T,$

q＝||x _i|| ²，

5th step, by the weight vector ω obtained ₁~ ω _nbe arranged in the adjacency matrix of figure G, thus obtain graph model.

2. the point that merged according to claim 1 is to the drawing method of building with neighborhood information, it is characterized in that in described Optimized model, regulate γ parameter wherein, this parameter to represent in modeling process the relative attention degree to information to neighborhood information or point, its adjustment is determined according to the actual demand of user and application background, if user thinks a little important to its application to information, then correspondingly tune up γ parameter; Otherwise, if user needs to utilize neighborhood information more, then reduce γ parameter.

3. the point that merged according to claim 1 is to the drawing method of building with neighborhood information, and it is characterized in that in described second step, the selection principle of K: if data centralization sample Relatively centralized, K gets little, otherwise then should tune up.

4. the point that merged according to claim 1 is to the drawing method of building with neighborhood information, and it is characterized in that described 5th step, the weight on all limits has been tried to achieve all, and the adjacency matrix of figure G is designated as

W＝(ω ₁ω ₂…ω _n) ^T

Note W _ijfor (i, j) individual element of matrix W, if definition diagonal matrix D=diag is (d ₁, d ₂..., d _n), wherein d _ifor sample x _idegree (degree), namely 1≤i≤n, so the Laplacian Matrix of figure G is

L＝D-W。

5. fusion according to any one of claim 1-4 point, to the drawing method of building with neighborhood information, is characterized in that described Optimized model uses the quadprog function carried in Mathworks company MatlabR2011a software to solve.