CN110334770A - Figure clustering method based on the sparse study of robust order constraint - Google Patents

Abstract

The invention discloses a kind of figure clustering method based on the sparse study of robust order constraint, the technical issues of for solving existing figure clustering method poor robustness.Technical solution is by sparse representation method learning data similar diagram S, in conjunction with L_2,1Norm obtains initial target function；Initial graph is constructed adjacent to method using k, constrains required similar diagram S in the neighborhood of initial graph；In addition Laplce's order constraint, makes order be equal to data point number and subtracts the similar diagram connected region number, obtain final objective function.Using augmented vector approach, objective function is transformed into unconstrained optimization problem from constrained optimization problem；For the variable alternative optimization for including in objective function；In each iteration finally, being updated to the parameter that augmented vector approach includes；After iteration reaches termination condition, according to the solution acquired, similarity matrix is decomposed, obtains final cluster result.The present invention utilizes L by structure figures in high quality_2,1Norm improves the robustness of method.

Description

Figure clustering method based on the sparse study of robust order constraint

Technical field

The present invention relates to a kind of figure clustering method, in particular to a kind of figure cluster side based on the sparse study of robust order constraint Method.

Background technique

With the development of Information technology, people touch the growth that geometry grade is presented with information to be treated daily, In face of such large-scale information resources, how they are effectively organized and are utilized, become one it is in the urgent need to address The problem of.In this context, largely not labeled data are greatly promoted in the field of data mining one and important grind Study carefully the development in direction --- cluster.Cluster stems primarily from taxology, it is to be based on similitude for physical object or abstract object It is grouped into the process of multiple classes.The process is using the feature of sample as classification foundation, to ensure the individual tool in same category There is homogeney as high as possible, and there is heterogeneity as far as possible between classification.Cluster is the representative of " unsupervised learning ", cluster When do not need artificial input data tag, do not need priori knowledge, can be by data click and sweep by the operation in finite time It is divided into different classifications.Cluster can be used as the tool of independent analysis data, immediately arrive at analysis as a result, can also be in data volume When larger, as the pretreatment to data, the presence of cluster is frequently accompanied by " big data " this concept.

In numerous clustering techniques, figure cluster possesses relatively advanced performance, and can be with the immanent structure of mining data. Figure cluster is a kind of clustering algorithm by digital simulation for spatial point, i.e. the distance building data according to data in space are similar Figure, then post-processes data similar diagram to complete cluster task.J.Huang et al. is in document " J.Huang, F.Nie, and H.Huang,A new simplex sparse learning model to measure data similarity for clustering,in Proc.IEEE Conf.Twenty-Fourth International Joint Conference On Artificial Intelligence, 2015, " in propose simplex sparse table diagram clustering method, this method is dilute It dredges on the basis of indicating, the constrained rarefaction representation of tool can be used to calculate the similarity between sample point in proposition, achieves Preferable Clustering Effect.F.Nie et al. is in document " F.Nie, X.Wang, M.I.Jordan, and H.Huang, The constrained laplacian rank algorithm for graph-based clustering,in Proc.IEEE Conf.Thirtieth AAAI Conference on Artificial Intelligence, 2016, " in propose La Pu Lars order constraint figure clustering method, this method directly learn datagram on the basis of order constraint, in this way can basis Connected relation of the data point in similar diagram directly obtains cluster result, improves the speed and accuracy of cluster.

Both methods all has limitation.First, the similar diagram to learn can not accurately reflect the relationship between data. Second, the error of each data point is squared in objective function, these methods are easy to be influenced by exceptional value and noise, Shandong Stick is poor.

Summary of the invention

In order to overcome the shortcomings of that existing figure clustering method poor robustness, the present invention provide a kind of sparse based on robust order constraint The figure clustering method of study.This method is by sparse representation method learning data similar diagram S, in combination with L_2,1Norm obtains just Beginning objective function；Initial graph is constructed adjacent to method using k, constrains required similar diagram S in the neighborhood of initial graph；In addition Laplce Order constraint makes order be equal to data point number and subtracts the similar diagram connected region number；It is added together after above-mentioned three additions coefficient, Obtain final objective function.Using augmented vector approach, objective function is transformed into nothing from constrained optimization problem Constrained optimization problem；It for the variable for including in objective function, is initialized first, then in each iteration, fixes it His three variables are constant, a certain variable of alternative optimization；In each iteration finally, the ginseng for including to augmented vector approach Number is updated；After iteration reaches termination condition, according to the solution acquired, similarity matrix is decomposed, is obtained final Cluster result.The present invention utilizes L by structure figures in high quality_2,1Norm improves the robustness of method.

The technical solution adopted by the present invention to solve the technical problems: a kind of figure based on the sparse study of robust order constraint is poly- Class method, its main feature is that the following steps are included:

Step 1: by sparse representation method learning data similar diagram S, in combination with L_2,1Norm, X are data, initial mesh Scalar functions are as follows:

Step 2: constructing initial graph adjacent to method using k, pass through regularization termRequired similar diagram S is constrained first Begin in the neighborhood of figure B；

Step 3: to the Laplacian Matrix L of S_sOrder use restraint, make order be equal to data point number subtract the similar diagram Connected region number directly obtains cluster result according to connected relation of the data point in similar diagram, specifically, passes throughIt is constrained；

Step 4: obtaining final objective function for being added together after above-mentioned three additions coefficient:

Step 5: enabling E=X-XZ, Z=S using augmented vector approach, objective function is converted are as follows:

Step 6: being initialized first for E, Z, S, F wherein included, then in each iteration, other are fixed Three variables are constant, a certain variable of alternative optimization；

Step 7: in each iteration finally, being updated to the parameter that augmented vector approach includes, by having Time iteration is limited, optimal solution is gradually acquired.

Step 8: decomposing according to the optimal solution acquired to S, final cluster result is obtained.

The beneficial effects of the present invention are: this method passes through sparse representation method learning data similar diagram S, in combination with L_2,1 Norm obtains initial target function；Initial graph is constructed adjacent to method using k, constrains required similar diagram S in the neighborhood of initial graph； In addition Laplce's order constraint, makes order be equal to data point number and subtracts the similar diagram connected region number；Above-mentioned three additions system It is added together after number, obtains final objective function.Using augmented vector approach, by objective function from constrained optimization Problem is transformed into unconstrained optimization problem；It for the variable for including in objective function, is initialized, is then being changed every time first Dai Zhong, it is constant to fix other three variables, a certain variable of alternative optimization；In each iteration finally, multiplying to augmentation Lagrange The parameter that sub- method includes is updated；After iteration reaches termination condition, according to the solution acquired, similarity matrix is divided Solution, obtains final cluster result.The present invention utilizes L by structure figures in high quality_2,1Norm improves the robust of method Property.

It elaborates with reference to the accompanying drawings and detailed description to the present invention.

Detailed description of the invention

Fig. 1 is that the present invention is based on the flow charts of the figure clustering method of the sparse study of robust order constraint.

Specific embodiment

Referring to Fig.1.The present invention is based on the figure clustering method of the sparse study of robust order constraint, specific step is as follows:

Step 1: by sparse representation method learning data similar diagram S, in combination with L_2,1Norm improves figure with this Building quality and the influence for reducing data noise and exceptional value.Specifically, X is data, initial target function are as follows:

Step 2: constructing initial graph adjacent to method using k, pass through regularization termRequired similar diagram S is constrained first Begin in the neighborhood of figure B, so that the similar diagram acquired can accurately reflect the relationship between data；

Step 3: adding Laplce's order constraint, i.e., to the Laplacian Matrix L of S_sOrder use restraint, be equal to order Data point number subtracts the similar diagram connected region number, thus can be straight according to connected relation of the data point in similar diagram It connects to obtain cluster result, without operating after subsequent execution, improves the quality and efficiency of cluster.Specifically, pass throughIt is constrained；

Step 4: obtaining final objective function for being added together after above-mentioned three additions coefficient:

Step 5: enabling E=X-XZ, Z=S using augmented vector approach, objective function is converted are as follows:

Step 6: being initialized first for E, Z, S, F wherein included, then in each iteration, other are fixed Three variables are constant, a certain variable of alternative optimization；

Step 7: being passed through in this way in each iteration finally, be updated to the parameter that augmented vector approach includes Limited times iteration is crossed, optimal solution can be gradually acquired.

Step 8: decomposing according to the solution acquired to S, final cluster result is obtained.

Effect of the invention is described further by following emulation experiment.

1. simulated conditions.

The present invention is to be in central processing unitI5-3470 3.2GHz CPU, memory 4G, WINDOWS 7 operation system On system, with the emulation of MATLAB software progress.

COIL20 data set is from D.Cai et al. in document " D.Cai, X.He, J.Han, and used in experiment T.S.Huang,Graph regularized nonnegative matrix factorization for data representation,IEEE transactions on pattern analysis and machine It is proposed in intelligence, vol.33, no.8, pp.1548-1560,2010. ", includes 1440 groups of data, there is 20 classifications, Corresponding one 32 × 32 picture of every group of data.2. emulation content.

Cluster experiment is carried out to data set.In order to compare effectiveness of the invention, F.Nie et al. is had chosen in document " F.Nie,X.Wang,M.I.Jordan,and H.Huang,The constrained laplacian rank algorithm for graph-based clustering,in Proc.IEEE Conf.Thirtieth AAAI Conference on Artificial Intelligence, 2016, " in the Laplce's order constraint figure clustering method (CLR) and J.Huang mentioned Et al. in document " J.Huang, F.Nie, and H.Huang, A new simplex sparse learning model to measure data similarity for clustering,in Proc.IEEE Conf.Twenty-Fourth International Joint Conference on Artificial Intelligence, 2015, " in propose it is simple Shape sparse table diagram clustering method and some other basic clustering method.Adjustment parameter calculates accuracy (ACC), normalization Mutual information (NMI) and degree of purity (Purity).Comparing result is as shown in table 1.

The comparison of 1 experimental result of table

Method	K-means	NMF	NCut	CAN	CLR	SSR	This method
								ACC	0.55	0.47	0.49	0.82	0.83	0.69	0.88
NMI	0.72	0.60	0.66	0.90	0.91	0.80	0.93
								Purity	0.60	0.50	0.56	0.86	0.87	0.75	0.89

As seen from Table 1, the clustering performance of this method is better than other control methods.This can be verified by the above emulation experiment The validity of invention.

Claims (1)

1. a kind of figure clustering method based on the sparse study of robust order constraint, it is characterised in that the following steps are included:

Step 1: by sparse representation method learning data similar diagram S, in combination with L_2,1Norm, X are data, initial target letter Number are as follows:

Step 2: constructing initial graph adjacent to method using k, pass through regularization termRequired similar diagram S is constrained in initial graph B Neighborhood in；

Step 3: to the Laplacian Matrix L of S_sOrder use restraint, make order be equal to data point number subtract the similar diagram connection Areal directly obtains cluster result according to connected relation of the data point in similar diagram, specifically, passes throughIt is constrained；

Step 4: obtaining final objective function for being added together after above-mentioned three additions coefficient:

Step 5: enabling E=X-XZ, Z=S using augmented vector approach, objective function is converted are as follows:

Step 6: being initialized first for E, Z, S, F wherein included, then in each iteration, other three are fixed Variable is constant, a certain variable of alternative optimization；

Step 7: in each iteration finally, being updated to the parameter that augmented vector approach includes, by limited times Iteration gradually acquires optimal solution；

Step 8: decomposing according to the optimal solution acquired to S, final cluster result is obtained.