CN106651838A - Gel protein partitioning method based on fuzzy clustering - Google Patents

Abstract

The invention discloses a gel protein partitioning method based on fuzzy clustering. The method comprises the steps that first, images are filtered, and the contrast ratio of the images is enhanced; second, the number of clustering categories, weighted indexes, an iteration termination threshold value, the maximum number of iterations and an initial clustering center are initialized; third, a radial width value in a kernel function is calculated; fourth, a membership matrix and a clustering center are updated; fifth, whether an absolute difference value of the current new clustering center and the last clustering center is smaller than the iteration termination threshold value or whether a current value of an iteration counter is greater than the maximum number of iterations is judged through comparison, if yes, the process is stopped, a final membership matrix and a final clustering center are output, and the sixth step continues to be executed, or else the fourth step continues to be executed after the iteration counter adds one; sixth, defuzzification is performed to obtain an optimal partitioning result. Through the method, noise eliminating ability is improved, relatively weak protein spots can be separated, and consequently more protein spots are separated; moreover, the method has a good separation effect on lightly-overlapping protein spots and has high partitioning precision.

Description

Gel protein dividing method based on fuzzy clustering

Technical field

The present invention relates to two-way gel image analysis technical field, more particularly to the gel protein segmentation based on fuzzy clustering Method.

Background technology

In many method for protein isolation, two dimensional gel electrophore- sis (2-DE) technology is widely applied to proteomics In, mainly according to isoelectric points of proteins and the difference of molecular weight, by the protein in complex proteins mixture in a clotting Separated in the form of point-like on glue.Subsequently protein gel is scanned using scanning device, obtains digitizing gel images. Protein presents the different point of shape, size and gray scale on image, and each of which point represents one specifically Protein.Segmentation is the important step of graphical analysis, and the research of gel images needs to extract protein site from image, and its is main Target be find protein site position and protein site around border, determine the different shapes of their quantity and analysing protein State.

Fuzzy clustering is applied to the fields such as pattern-recognition, image procossing, water analysis.Application is specifically recognized at some In, the classification and matching such as in speech recognition, the aspect such as the foundation of object library and the new classification to target in radar target recognition Achieve preferable effect；Image segmentation, such as texture image, medical image and aviation are widely used in image procossing The segmentations such as remote sensing images aspect, efficiently solves image target area obscurity boundary, typical mixed pixel in remote sensing images The problems such as.

Image segmentation is exactly, according to features such as gray scale, color, texture and shapes, to divide the image into several specific, tools There is the region of peculiar property and propose the technology and process of interesting target.The advantage of gel protein image segmentation is exactly by image It is separated into a little and without a region, to be preferably estimated to protein, the existing dividing method for gel images has It is several below：

Based on the dividing method of rim detection, split by detecting the edge of zones of different, for edge positioning The determination on precision and border has good segmentation effect and remains the important structure attribute of image, but be highly prone to noise and The impact of image itself fog-level.

Problems of the Bi Yuhui et al. for watershed algorithm over-segmentation, it is proposed that using topological curvature and watershed algorithm phase With reference to partitioning algorithm, the method has more specific aim for gel electrophoresis images.

The gel electrophoresis images partitioning algorithm based on markov random file of the propositions such as Zhang Yanqing, is fixed according to Bayes Reason realizes the segmentation of image, is used as priori by the fuzzy clustering of a second-order logic model (MLL) during being somebody's turn to do and obtains Therefore its prior probability simultaneously obtains posterior probability, and introduce gray scale dot density weights come realize clustering and mean variance improvement Update.Faint protein site is solved to a certain extent and the detection and segmentation of protein site is overlapped, and further increases gel figure As the accuracy of segmentation.

Rashwan S et al. in 2010 on the basis of traditional FCM algorithms, in order to isolate more from different backgrounds Many protein sites introduce fuzzy relation concept, and the method shows higher performance, for relatively weak blackening point also can It is enough effectively to detect.

At present the country does not also form the further investigation to gel images segmentation, from the point of view of scanning the research situation of foreign countries, respectively The method of kind has pros and cons, so our work to be done are aiming at the characteristic of protein site in gel images, studies gel images Partitioning algorithm, protecting image information and while details, strengthening to faint protein site and overlap the identification of protein site and examine Survey.

The content of the invention

The purpose of the present invention is exactly to solve the above problems, there is provided the gel protein dividing method based on fuzzy clustering, Picture contrast is filtered and strengthens to image first by wave filter；Then fuzzy core C means clustering algorithm is passed through To sample clustering, finally using maximum membership grade principle de-fuzzy, optimum segmentation is realized, sample variance is introduced in the process To calculate gaussian kernel function radial width σ value, the method has more preferable adaptability and segmentation precision.

To achieve these goals, the present invention is adopted the following technical scheme that：

Based on the gel protein dividing method of fuzzy clustering, comprise the following steps：

Step one：Image is pre-processed, the contrast of image is filtered and strengthens to image using wave filter Degree；

Step 2：Initialization cluster classification number, Weighted Index, iteration ends threshold value, maximum iteration time and initial clustering Center；

Step 3：Calculate the radially-wide angle value in kernel function；

Step 4：Update subordinated-degree matrix and cluster centre；

Step 5：Whether relatively more current new cluster centre is less than iteration ends with the absolute difference of last cluster centre Threshold value, or whether the value of iteration count be more than maximum iteration time, and if setting up final degree of membership square is stopped and export Battle array and cluster centre, go to step 6 and continue executing with；Otherwise, iteration count adds a rear steering step 4 to continue executing with；

Step 6：De-fuzzy, obtains the segmentation result of optimum.

In the step one, with morphological method the contrast between protein site and background is strengthened.

In the step 2, optional c different pieces of information is concentrated respectively as initial cluster center from protein site sample data C initial cluster center value, 2≤c ＜ n, n refers to that cluster data concentrates the number of all data.

In the step 2, cluster classification number and pass through the different value of imparting with Weighted Index, carry out experiment test contrast effect Fruit figure is obtained.

In the step 3, by calculating protein site sample data variance the radially-wide angle value of gaussian kernel function is determined.

The computational methods of radially-wide angle value are specially：

Wherein,For the average of protein site sample data set, σ is the radially-wide angle value of gaussian kernel function；Σ is summation behaviour Make；N refers to that cluster data concentrates the number of all data；x_kRefer to k-th sample point.

In the step 4, under constraints, object function is made to seek partial derivative simultaneously to degree of membership and cluster centre respectively 0 is entered as, so as to obtain the expression formula of degree of membership and cluster centre.

The computational methods of degree of membership are：

The computational methods of cluster centre are：

Wherein, c refers to cluster classification number；M is Weighted Index；N refers to that cluster data concentrates the number of all data；Σ is summation Operation；u_ikRefer to that k-th sample point belongs to the degree of membership of the i-th class；v_iRepresent the center of the i-th class；x_kRefer to k-th sample point；K(x_k, v_i) refer to that data concentrate k-th sample point x_kWith the kernel function value of ith cluster central value in cluster centre；K(x_k,v_j) refer to data Concentrate k-th sample point x_kWith the kernel function value of j-th cluster centre value in cluster centre.

In the step 6, according to maximum membership grade principle de-fuzzy.

The concrete grammar of de-fuzzy is to calculate each sample point x using membership function_kIt is under the jurisdiction of the value of the i-th class, Sample point x is taken by comparing_kMaximum is subordinate to angle value, and as judgement sample point which kind of foundation is belonged to.

Beneficial effects of the present invention：

1st, method proposed by the present invention improves the ability for eliminating noise, can isolate relatively weak protein site, because Protein site that this is isolated is more and also has preferable separating effect to the slight protein site that overlaps, with higher segmentation essence Degree.

2nd, provide the radially-wide angle value of gaussian kernel function and determine method, it is to avoid by a large amount of in different gel protein images The trouble that experiment is manually set so that cluster has more adaptivity, it is easy to accomplish.

Description of the drawings

Fig. 1 (a) is simulation gel images, and Fig. 1 (b) is the pretreated gel images schematic diagram of simulation gel images；

Fig. 1 (c) is that the image to Fig. 1 (b) adopts FCM method segmentation results, and Fig. 1 (d) is that the image to Fig. 1 (b) is adopted KFCM method segmentation results, Fig. 1 (e) is that the image to Fig. 1 (b) is adopted based on distance variance segmentation result, and Fig. 1 (f) is to Fig. 1 B the image of () is using the inventive method to simulating the image after gel images are split；

Fig. 2 (a) is true gel images, and Fig. 2 (b) is the pretreated gel images schematic diagram of true gel images；

Fig. 2 (c) is that the image to Fig. 2 (b) adopts FCM method segmentation results, and Fig. 2 (d) is that the image to Fig. 2 (b) is adopted KFCM method segmentation results, Fig. 2 (e) is that the image to Fig. 2 (b) is adopted based on distance variance segmentation result, and Fig. 2 (f) is to Fig. 2 B the image of () is using the inventive method to simulating the image after gel images are split；

Fig. 3 simulates gel images to FCM methods, KFCM methods, distance cluster, method of the present invention several method segmentation result Com-parison and analysis.

The true gel images of Fig. 4 are to FCM methods, KFCM methods, distance cluster, method of the present invention several method segmentation knot The com-parison and analysis of fruit.

Fig. 5 is simulated and true gel images are to FCM methods, KFCM methods, distance cluster, method of the present invention several method Com-parison and analysis in terms of segmentation precision.

The overall flow schematic diagram of Fig. 6 inventions.

Specific embodiment

Below in conjunction with the accompanying drawings the invention will be further described with embodiment.

As shown in fig. 6, the gel protein dividing method based on fuzzy clustering, comprises the following steps：

Step one：Image is pre-processed, first with wave filter to image denoising process, afterwards with form Method strengthens picture contrast；

Step 2：Initialization cluster classification number 2≤c ＜ n, Weighting exponent m >=1, iteration ends threshold value is ε ＞ 0, and maximum changes Generation number is 100, concentrates optional c different pieces of information individual initial respectively as the c of initial cluster center from protein site sample data Cluster centre value, c can be chosen for 2 in the present embodiment；

Step 3：Calculate the radially-wide angle value in kernel function；

Step 4：By object function respectively to degree of membership u_ikWith cluster centre v_iPartial derivative is sought, and makes partial derivative be 0； Under constraints, degree of membership and cluster centre iteration expression formula are obtained；Update subordinated-degree matrix u_ikWith cluster centre v_i；

Step 5：Whether relatively more current new cluster centre is less than iteration ends with the absolute difference of last cluster centre Threshold value, or whether the value of iteration count be more than maximum iteration time, i.e., | | V^(l+1)-V^(l)| | ＜ ε or l ＞ M whether into Vertical, method stops and exports final subordinated-degree matrix U and cluster centre V if setting up, and continues executing with into step 6；It is no Then, make l=l+1 turn to step 4 to continue executing with, wherein l is iteration count.

Step 6：According to maximum membership grade principle de-fuzzy, the segmentation result of optimum is obtained.

In the step 2, cluster classification number and pass through the different value of imparting with Weighted Index, carry out experiment test contrast effect Fruit figure is obtained.

Low for the border of protein site in gel images and the contrast of background in the step 3, distribution presents many The characteristics of sample and skewness, gel images are split using fuzzy core C means clustering method.

Wherein, the radially-wide angle value of different kernel functions has a great impact to the segmentation result of image, at present the parameter value Not clear and definite theoretical direction and fixed method, majority is obtained by man-made chamber, but artificial coarse determination is radially-wide Angle value parameter cannot improve its precision.

Rationally determine gaussian kernel function radial width σ value by calculating protein site sample data variance in the present invention, solve The drawbacks of different images of having determined determine radially-wide angle value by artificial experience, improves the adaptivity of method.Its number for calculating Learning expression formula is：

Wherein,The average of finger protein point sample data set；Σ refers to sum operation；x_kRefer to k-th sample point.

Fuzzy core C Mean Method be by input space data by Nonlinear Mapping in higher dimensional space, the image of input Data X_i, i=1,2 ..., N is defined as Φ (X in high-dimensional feature space_j), j=1,2 ..., M, wherein Φ () is non-linear Mapping function：Φ:R^p→R^q, p ＜ ＜ q.The object function of fuzzy kernel clustering method defined in the input space is：

By definition K (x, the y)=Φ (x) of Mercer cores^TΦ (y), and | | Φ (x_k)-Φ(v_i)||²=K (x_k,x_k)+K (v_i,v_i)-2K(x_k,v_i).Generally we select gaussian kernel functionWherein σ is gaussian kernel function Radial width, exp is index operation, and K (x, x)=1.Thus object function can be rewritten as：

Wherein, kernel function isΣ is sum operation；C refers to cluster classification number；N refers to poly- All data amount checks in class data set；M is Weighted Index, controls the fog-level between class；V refers to c cluster centre set；u_ik (i=1,2 ..., c；K=1,2 ... n) refer to that k-th sample point is under the jurisdiction of the degree of the i-th class, and meetAnd 0≤ u_ik≤1；v_i(i=1,2 ..., c) represent the center of the i-th class.

By realizing minimizing object function, object function is minimized using Lagrangian method, construct letter Number is as follows：

Wherein, λ=(λ₁,λ₂,...λ_n) it is Lagrange multiplier, c refers to cluster classification number；It is all that n refers to that cluster data is concentrated The number of data；Σ refers to sum operation；M refers to Weighted Index；V refers to c cluster centre set；u_ikRefer to that k-th sample point is under the jurisdiction of The degree of the i-th class；v_iRepresent the center of the i-th class；K(x_k,v_i) refer to that data concentrate k-th sample point x_kWith i-th in cluster centre The kernel function value of cluster centre value.

Object function is made to ask degree of membership partial derivative to be equal to 0, i.e.,Can obtain：

Object function is made to λ_kPartial derivative is asked to be equal to 0, i.e.,Can obtain：

And (4) are substituted into (5) Shi Ke get：

Again (6) substitution (4) formula can be obtained into degree of membership expression formula：

Wherein, c refers to cluster classification number；Σ is sum operation；M is Weighted Index；u_ikRefer to that k-th sample point is under the jurisdiction of i-th The degree of class；v_iRepresent the center of the i-th class；K(x_k,v_i) refer to that data concentrate k-th sample point x_kIt is poly- with i-th in cluster centre The kernel function value of class central value；K(x_k,v_j) refer to that data concentrate k-th sample point x_kWith j-th cluster centre value in cluster centre Kernel function value.

Object function is made to ask cluster centre partial derivative to be equal to 0, i.e.,Cluster centre expression formula can be obtained：

Wherein, Σ is sum operation；N refers to that cluster data concentrates the number of all data；M is Weighted Index；v_iRepresent i-th The center of class；u_ikRefer to that k-th sample point is under the jurisdiction of the degree of the i-th class；K(x_k,v_i) refer to that data concentrate k-th data x_kWith cluster The kernel function value of ith cluster central value in center；x_kRefer to k-th sample point.

In the step 6, maximum membership grade principle is to calculate each sample point x using membership function_kIt is under the jurisdiction of The value of the i-th class, by comparing sample point x is taken_kMaximum is subordinate to angle value, and as judgement sample point which kind of foundation is belonged to.

Usually said kernel function radial width σ is mainly the separation degree of judgement sample data.For gel protein figure As for, if dispersion is compared in the distribution of protein site on image, then the membership function for obtaining will be fuzzyyer, causes The possibility that a certain albuminoid point is under the jurisdiction of a certain class is lower；Conversely, the membership function for obtaining will be more clear, protein site category It is higher in the possibility of a certain class, it is easier to which that cluster separation is carried out to protein site.Because sample variance describes sample set " distribution degree ", when sample data distribution compare concentration when, the sample variance for obtaining is less, and the compactness in class is higher；Conversely, Compactness in class is lower.Therefore, we reasonably determine radially-wide angle value by sample data variance, so as to be subordinate to The distribution situation of degree function.

The protein site sample data set that hypothesis is obtained is X=(x₁,x₂,...,x_n), first protein site is obtained by formula (9) The average of sample data set：

Then, the radial width σ value of gaussian kernel function is reasonably determined using protein site sample variance：

Wherein, Σ is sum operation；N refers to that cluster data concentrates the number of all data；x_kRefer to k-th sample point.

Fig. 1 (a)-Fig. 1 (b) simulates gel images and pretreated image comparison schematic diagram.

Fig. 1 (c)-Fig. 1 (f) is different clustering methods and the inventive method to simulating the image comparison after gel images are split Schematic diagram, contrast finds that different clustering methods have certain difference to the protein site quantity for splitting.

The true gel images of Fig. 2 (a)-Fig. 2 (b) and pretreated gel images schematic diagram, are found by contrasting, pre- place Gel images after reason are more clear than original image.

Fig. 2 (c)-Fig. 2 (f) is for different clustering methods and the inventive method to simulating the image pair after gel images are split Than schematic diagram, from the point of view of experimental result, there is difference in different clustering methods to the result for splitting.

Fig. 3-Fig. 5 is respectively the objective analysis ratio in simulation and true gel images to above-mentioned several method segmentation result Compared with wherein division factor is bigger, and segmentation entropy gets over hour, cluster segmentation best results, but this and nonabsoluteness, with reference to segmentation essence Degree, on the whole from the point of view of, the protein site that the inventive method splits is more, improves the segmentation precision of method.

Although the above-mentioned accompanying drawing that combines is described to the specific embodiment of the present invention, not to present invention protection model The restriction enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme those skilled in the art are not Need the various modifications made by paying creative work or deformation still within protection scope of the present invention.

Claims (10)

1. the gel protein dividing method based on fuzzy clustering, is characterized in that, comprise the following steps：

Step one：Image is pre-processed, the contrast of image is filtered and strengthens to image using wave filter；

Step 2：Initialization cluster classification number, Weighted Index, iteration ends threshold value, maximum iteration time and initial cluster center；

Step 3：Calculate the radially-wide angle value in kernel function；

Step 4：Update subordinated-degree matrix and cluster centre；

Step 5：Whether relatively more current new cluster centre is less than iteration ends threshold with the absolute difference of last cluster centre It is worth, or whether the value of iteration count is more than maximum iteration time, and if setting up final subordinated-degree matrix is stopped and export And cluster centre, go to step 6 and continue executing with；Otherwise, iteration count adds a rear steering step 4 to continue executing with；

Step 6：De-fuzzy, obtains the segmentation result of optimum.

2. gel protein dividing method as claimed in claim 1 based on fuzzy clustering, is characterized in that, in the step one, fortune Strengthen the contrast between protein site and background with morphological method.

3. gel protein dividing method as claimed in claim 1 based on fuzzy clustering, is characterized in that, in the step 2, from Protein site sample data concentrates optional c different pieces of information respectively as c initial cluster center value of initial cluster center, 2≤c ＜ n, n refer to that cluster data concentrates the number of all data.

4. gel protein dividing method as claimed in claim 1 based on fuzzy clustering, is characterized in that, in the step 2, gather Class classification number passes through the different value of imparting with Weighted Index, carries out the acquisition of experiment test contrast effect figure.

5. gel protein dividing method as claimed in claim 1 based on fuzzy clustering, is characterized in that, in the step 3, lead to Cross calculating protein site sample data variance to determine the radially-wide angle value of gaussian kernel function.

6. gel protein dividing method as claimed in claim 5 based on fuzzy clustering, is characterized in that, the calculating of radially-wide angle value Method is specially：

$\mathrm{\σ}=\frac{\underset{k=1}{\overset{n}{\Σ}}\left|\right|x_k-\stackrel{\‾}{x}|{|}^2}{n-1},\stackrel{\‾}{x}=\frac{\underset{k=1}{\overset{n}{\Σ}}{x}_k}{n}$

Wherein,For the average of protein site sample data set, σ is the radially-wide angle value of gaussian kernel function；Σ is sum operation；N refers to Cluster data concentrates the number of all data；x_kRefer to k-th sample point.

7. gel protein dividing method as claimed in claim 1 based on fuzzy clustering, is characterized in that, in the step 4, Under constraints, make object function seek partial derivative to degree of membership and cluster centre respectively and be entered as 0, so as to obtain degree of membership and The expression formula of cluster centre.

8. gel protein dividing method as claimed in claim 7 based on fuzzy clustering, is characterized in that,

The computational methods of degree of membership are：

The computational methods of cluster centre are：

Wherein, c refers to cluster classification number；M is Weighted Index；N refers to that cluster data concentrates the number of all data；Σ is summation behaviour Make；u_ikRefer to that k-th sample point belongs to the degree of membership of the i-th class；v_iRepresent the center of the i-th class；x_kRefer to k-th sample point；K(x_k,v_i) Refer to that data concentrate the kernel function value of k-th sample point xk and ith cluster central value in cluster centre；K(x_k,v_j) refer to data set In k-th sample point x_kWith the kernel function value of j-th cluster centre value in cluster centre.

9. gel protein dividing method as claimed in claim 1 based on fuzzy clustering, is characterized in that, in the step 6, root According to maximum membership grade principle de-fuzzy.

10. gel protein dividing method as claimed in claim 9 based on fuzzy clustering, is characterized in that, de-fuzzy it is concrete Method is to calculate each sample point x using membership function_kIt is under the jurisdiction of the value of the i-th class, by comparing sample point x is taken_kIt is maximum Be subordinate to angle value, as judge sample point belong to which kind of foundation.