CN105608510A - Traffic period automatic division method based on Fisher algorithm - Google Patents

Abstract

The present invention provides a traffic period automatic division method based on a Fisher algorithm. The method comprises the aspects of data extraction and pre-processing, segmentation algorithm design and period division optimization design. Firstly, traffic flow data is subjected to extraction, cleaning and screening and reduction repair, and the quality of the data is improved. Secondly, the diameter of a class and the loss function of the method are defined, an optimal solution is obtained by using the core recursion formula of the Fisher algorithm, finally the traffic period is divided according to the optimal solution, and different road application requirements can be satisfied. Compared with the prior art, the method has the advantages of easy realization, high accuracy and high robustness and can be used in an actual road traffic control system.

Description

A kind of method that traffic slot based on Fisher algorithm is divided automatically

Technical field

The invention belongs to intelligent traffic control system field, relate to a kind of method that traffic slot is divided automatically, particularlyA kind of method that traffic slot based on Fisher algorithm is divided automatically.

Background technology

Information technology that intelligent transportation system (IntelligentTransportationSystem, be called for short ITS) is integrated,The multiple advanced persons' such as data communication transmission technology, Electronic transducer technology, control technology and computer technology technology, can be real-time, accurateReally, apply to efficiently whole ground traffic control system. ITS can effectively utilize existing means of transportation, minimizing traffic is negativeLotus and environmental pollution, guarantee traffic safety, raising conevying efficiency, thereby, be day by day subject to the attention of various countries. From Paris head in 1994So far, existing more than 20 years of the formal proposition of ITS concept and scale exploitation, build more ripe for intelligent transportation system world conventionCountry have the U.S., Japan and European Union etc., intelligent transportation industry is just striding forward enforcement deployment phase from the technical research stage, progressivelyRealize qualitative leap. Although domestic intelligent transportation system research is started late, through effort for many years, obtain oneFixed achievement, with reference to advanced foreign technology time, is also constantly advancing every new technology that possesses independent intellectual property right.

In recent years, along with economic develop rapidly and urbanization advance fast, magnitude of traffic flow sharp increase, congested in traffic,Stop up frequently existing. Due to the otherness of the traffic capacity between intersection and section, crossing has become road traffic" bottleneck ", therefore the key of road improvement traffic is reasonably to dispatch the traffic flow of crossing, improvement and optimization signal controlling sideCase. Signal controlling is an important measure in control of traffic and road, taking three large major parameters as feature, be respectively phase place,Cycle and signal timing dial. Traditional single-point fixed cycle signal controlling is the most basic control form, but it cannot adapt to traffic flowChange larger road conditions, single timing scheme very easily causes part to block up or sky is put phenomenon. The crossing of extensive use at presentSignal controlling algorithm is multi-period timing controlled, is called for short TOD (TimeofDay) algorithm. Multi-period timing controlled is according to friendshipThe variation of prong flow was divided into several time periods 24 hours, adopted different controlling parties for different traffic slotsCase. Therefore period division is the key of TOD algorithm, is directly determining the implementation result of control program. But automatically draw about the periodThe research dividing is but often out in the cold, does not more have software to possess this function.

According to investigation, it is mainly according to experience, based on crossing traffic by experienced engineer that traditional traffic slot is dividedThe actual change of flow, to time segment structure artificially adjust, make the control decisions such as period division, fractionation, merging. But thisKind method greatly depends on engineer's professional qualities, and subjective limitation is too strong, cannot ensure to obtain optimum division result,Be difficult to meet the fast-changing demand of road traffic.

At present, period Automated Partition Method has been obtained some achievements in research. There is scholar to propose a kind of artificial immunity numberAccording to cluster algorithm, can reduce the redundancy of traffic data, but be difficult to because the adjustable parameter of needs setting is more selectReduce the robustness of division methods. Also there is scholar to utilize PAM clustering algorithm to divide, but not by the sequence spy of traffic flowLevy and include research range in, more difficultly in actual road conditions, be applied.

Summary of the invention

The technical problem to be solved in the present invention is for the deficiencies in the prior art, proposes one and designs more rationally, can operateProperty the traffic slot based on Fisher algorithm stronger, that accuracy the is higher method of automatically dividing.

The technical problem to be solved in the present invention is achieved through the following technical solutions. The present invention is a kind of based on FisherThe method that the traffic slot of algorithm is divided automatically, its feature is, comprises the steps:

Step 1, gathers the traffic flow basic parameter in any given sampling interval, obtains initial data;

Step 2, screens, processes and repair pretreatment successively to initial data, obtains preprocessed data;

Step 3, by Fisher algorithm, preprocessed data is classified, obtain optimal solution and cut-point;

Step 4, output cut-point, in conjunction with optimal classification number, divide traffic slot interval.

In the method and technology scheme that a kind of traffic slot based on Fisher algorithm of the present invention is divided automatically, further preferredTechnical scheme feature be: described step 2 realizes as follows:

Step 1: initial data is screened and differentiated, extract normal data;

Step 2: set up problem data repairing model, to disappearance class data, exception class data, mistake class in initial dataData and redundancy class data are repaired reduction, obtain repair data;

Step 3: repair data and normal data are merged, obtain described preprocessed data.

In the method and technology scheme that a kind of traffic slot based on Fisher algorithm of the present invention is divided automatically, further preferredTechnical scheme feature be: described step 3 comprises the steps:

Step 1, definition class diameter: the former sequence of establishing a certain class sample G is G_i＝{X_i1，X_i2...X_ij, define its diameter D_iFor sample dispersion quadratic sum:

$D_i=\underset{j=1}{\overset{n_i}{\Σ}}{(X_{ij}-\stackrel{\‾}{X_i})}^2$

In formula,For average, X_ijFor sample characteristics;

Step 2, suppose sample (sample number is n) to be divided into k class:

G₁＝{X₁₁，X₁₂，...，X_1j}

G₂＝{X₂₁，X₂₂，...，X_2j}

…

G_k＝{X_k1，X_k2，...，X_kj}

Wherein, n₁，n₂，...，n_kFor k cut-point, and subscript meets 1≤n₁＜n₂＜...，n_k≤n；

Step 3, objective definition function are

$L\[B(n,k)\]=\underset{i=1}{\overset{k}{\Σ}}D(i_t,i_{t+1}-1)$

Step 4, according to the core recurrence formula of Fisher algorithm:

$L\[B(n,2)\]=\underset{2\≤j\≤n}{\min }\{D(1,j-1)+D(j,n)\}$

$L\[B(n,k)\]=\underset{2\≤j\≤n}{min}\{L\[B(j-1,k-1)+D(j,n)\}$

Calculate minimum target function;

Step 5, ask for optimal solution:

If number of categories k (1 < k < is n) known, asks classification L[B (n, k)], it is issued in object function meaningLittle, ask method as follows:

First calculate non-negative slope according to object function consecutive value, the number of categories k that gets non-negative slope maximum is optimal classificationNumber; Look for the cut-point j that optimal classification number k is corresponding_k, make the formula numerical value of step G reach minimum,

L[B(n，k)]＝L[B(j_k-1，k-1)]+D(j_k，n)

Tried to achieve the optimal situation G that is divided into k class by above formula_k; Then the like, ask for j_k-1Under individual cut-pointLittle object function, obtains k-1 class G_k-1, try to achieve successively all class G_k，G_k-1，...，G₂，G₁, this is optimal solution. Optimal solutionAvatar is sample data classification situation, and which data is classified as a class, and which data is classified as other classes. Correspond to traffic flowIn amount data, what optimal classification number was corresponding is the interval number of dividing the period, and what optimal solution was corresponding is period interval division pointFacilities. The time series feature of traffic flow data, has determined the time value that data on flows is corresponding, therefore according to optimal solutionCan draw the flow value at cut-point place, can draw thus and period division points finally realize the division in period interval.

Compared with prior art, the present invention has following technique effect: traditional period division methods is changedEnter, avoided local subjectivity, solved and relied on manual research data, garbled data in the past and expend lacking of a large amount of manpower and materialsFall into; Process of data preprocessing has improved the quality of data greatly, eliminate or reduced data noise and error, increased divide canLean on property; Ordered sample based on Fisher algorithm is divided, and rapid and convenient and accuracy are high, are also final multi-period control programSetting guarantee is provided. The present invention possesses the advantages such as robustness is high, workable, the degree of accuracy is good, can put into realityRoad traffic control system in use, the division in period interval is more humane, more rationally, more convenient.

Brief description of the drawings

Fig. 1 design flow diagram of the present invention;

Fig. 2 data pretreatment process figure;

The flow chart of Fig. 3 Fisher algorithm;

The tendency chart that the object function that the algorithm that Fig. 4 the present invention adopts calculates changes with number of categories;

The traffic slot division result figure that Fig. 5 the present invention calculates.

Detailed description of the invention

Referring to accompanying drawing, further describe concrete technical scheme of the present invention, so that those skilled in the art entersThe present invention is understood on one step ground, and does not form the restriction of its power.

Embodiment 1, with reference to Fig. 1-5, first gathers the traffic data in any given sampling period, and initial data is carried outPretreatment, improves the quality of data; Secondly in former sequence, define class diameter, define objective function; Then determine best segmentsAnd calculate optimal solution, draw thus period division result and can be optimized adjustment. Its concrete steps are as follows:

Step 1, collection traffic flow data:

The collection of traffic data is the prerequisite of carrying out traffic slot division, relies on multiple detection means can collect arbitrarilyGive the traffic flow basic parameter of fixed sample interval: flow, speed, density. Flow is by certain place of road in the unit intervalVehicle number, i.e. vehicle flowrate, speed is Vehicle Speed, density is on the road of unit length, at certain flashy vehicleSum. The analysis data that the present invention adopts are data on flows. But due to the interference of many external environments, initial data exists abnormalThe situations such as value, missing values, can not be directly used in the input of traffic model, particularly in traffic control, induction, information issue etc.In real-time system, more need data to carry out pretreatment, avoid the appearance of error result.

Step 2, initial data is carried out to pretreatment:

The pretreatment of dynamic traffic data comprises three aspects, data screening, data processing and data reparation. ModelData screening model, screens and differentiates initial data, extracts normal data; Moreover set up problem data repairing model,Disappearance class data, exception class data, mistake class data and redundancy class data are repaired to reduction; Finally by the data after repairingMerge with normal data, and be saved in database.

2.1 disappearance class data processing methods: different pieces of information source size, the strategy of reply is also different. Short time data is limited adoptsWith the reconstruct in addition of spatial sequence data, or directly abandon need not. When long, the limited employing time series data of data is carried out cover,Can set up forecast model carries out perfect.

2.2 wrong class data processings: such data formatting error, is generally common in three kinds of situations: first short-term dataFormat error, can remove automatically; Its two be detector install wrong or communication failure, adjustable engineering staff carries out scene and repaiiesMultiple; It three is that serious traffic congestion causes sample data ratio to be overflowed, and adjustable technical staff carries out Field Research, improves numberAccording to discrimination model.

2.3 exception class data processings: adopt threshold method to carry out upper lower limit value identification, the person of exceeding to the feedback data of detectorMethod described in can repeating 2.2.

2.4 redundancy class data processings: common two kinds of situations, first data repeat completely, can Delete superfluous record, only guarantorDeposit a record; It two is that data are similar, can get average to traffic flow data.

Step 3, by repair after data add Fisher algorithm, determine different class diameters, ask for according to object functionOptimal solution, determines cut-point. Specifically comprise following steps:

Step 3 (1), definition class diameter: the former sequence of establishing a certain class sample G is G_i＝{X_i1，X_i2...X_ij, define itDiameter D_iFor being sample dispersion quadratic sum:

$D_i=\underset{j=1}{\overset{n_i}{\&Sigma;}}{(X_{ij}-\stackrel{\&OverBar;}{X_i})}^2$

In formula,For average, X_ijFor sample characteristics.

Step 3 (2), sample (sample number is n) to be divided into k class:

G₁＝{X₁₁，X₁₂，...，X_1j}

G₂＝{X₂₁，X₂₂，...，X_2j}

…

G_k＝{X_k1，X_k2，...，X_kj}

Wherein, n₁，n₂，...，n_kFor k cut-point, and subscript meets 1≤n₁＜n₂＜...，n_k≤n。

Step 3 (3), objective definition function are

$L\&lsqb;B(n,k)\&rsqb;=\underset{i=1}{\overset{k}{\&Sigma;}}D(i_t,i_{t+1}-1)$

When sample sequence sum n determines, when number of categories k determines, L[B (n, k)] all kinds of sum of squares of deviations of less expression is moreLittle; The optimum segmentation of Fisher algorithm is exactly in fact to seek a component cutpoint, is the diameter integrated minimums of all classification, ensuresThe difference minimum of each intersegmental part sample room, and the difference maximum of each intersegmental sample.

The core recurrence formula of step 3 (4), Fisher algorithm:

$L\&lsqb;B(n,2)\&rsqb;=\underset{2\&le;j\&le;n}{\min }\{D(1,j-1)+D(j,n)\}---\left(1\right)$

$L\&lsqb;B(n,k)\&rsqb;=\underset{2\&le;j\&le;n}{min}\{L\&lsqb;B(j-1,k-1)+D(j,n)\}---\left(2\right)$

Formula (1) is the minimum target function that sample is divided into two classes, and formula 2 is the minimum target functions that sample are divided into k class,If n sample will be divided into the optimum segmentation of k class, should be based upon j-1 sample is divided on the optimum segmentation basis of k-1 class(j=1 herein, 2,3 ..., n), analogize gradually process by formula 1 to formula 2. In algorithm design process, not only consider between class looseDegree, also considers divergence in class, increases the reliable guarantee that the period is divided.

Step 3 (5), ask for optimal solution:

If number of categories k (1 < k < is n) known, asks classification L[B (n, k)], make it be issued to minimum in object function meaningClassification situation be optimal solution. First determine optimal classification number, solve L[B (n, k)] non-negative between adjacent target functional valueSlope:

$\mathrm{\&rho;}\left(z\right)=\left|\frac{L\&lsqb;B(n,k)\&rsqb;-L\&lsqb;B(n,k-1)\}}{k-(k-1)}\right|$

When slope is larger, represent that k class is better than (k-1) class, slope value approach represent not continue classification at 0 o'clock must, generally getting slope maximum is optimal classification number.

The optimal classification being drawn by said method is counted k, tries to achieve the classification situation of the formula minimum of a value of step 3 (4) step,Obtain the cut-point j of k class_k, get final product to obtain k class G_kClassification situation; Then the like, ask for j_kUnder individual cut-pointLittle object function, obtains k-1 class G_k-1, try to achieve successively all class G_k，G_k-1，...，G₂，G₁, this is optimal solution.

Step 4, output cut-point, according to the optimal solution in step 3 (5), can show which data can be classified as a class, baseIn the sequence signature of traffic flow, the division points of data on flows can be exchanged into corresponding time value, and traffic slot is divided.

In conjunction with actual road conditions, an isolated crossing, the period divides more, and signal timing plan more can adapt to changeableTraffic flow; But between actual crossing and crossing, between section and section, between region, road surface and region, have closely and contact, noIsolated single-point, if because of the too much continuous variation that causes timing scheme of period division, can be to the even whole district of adjacent intersectionTerritory produces harmful effect. Also there is certain relation in traffic flow itself, frequent changes timing scheme is difficult to meet stronger adaptationProperty. When the general fluctuation of the change curve when traffic flow is very frequent, should increases the division number of period as far as possible, otherwise reduce. BentThe time length of line fluctuation has determined that division period length of an interval is short.

Traffic flow is the system of Discrete Stochastic, in order to describe the various complex characteristics of traffic flow, need to certain continuouslyThe characteristic parameter of observation traffic flow in time period, therefore, vital impact is selected also to play in the interval of data sampling. ConsiderTo detector precision factor, the too short sampling interval can increase detection error greatly, and that long interval cannot show is completeVariation characteristic. For traffic slot being carried out to rationally correct division, the present invention proposes the traffic signals based on Fisher algorithmPeriod division methods, flow chart as shown in Figure 1, Fisher algorithm can be realized to the cutting apart of multidimensional sample data, and the present inventionMiddle traffic flow data refers to data on flows, therefore based on be the cluster analysis of Fisher algorithm for one-dimensional data, concreteComprise the steps:

Step 1, taking conventional four branch road conditions as research object, taking 15min as the sampling interval, extract the flow number of 24 hoursAccording to (data on flows numerical value unit be/15min), as shown in table 1:

Table 1

Step 2, set up data screening model, initial data carried out to pretreatment, after question marks data cleansing reparation with justRegular data merging is saved to database again. By the investigation to all-weather traffic flow data, can grasp crossing whole day and change ruleRule, can scientifically carry out period division, flow chart as shown in Figure 2:

Step 3, the data after repairing are added in Fisher algorithm, design flow diagram as shown in Figure 3, the concrete step of implementingRapid as follows:

Step 3 (1), definition class diameter: the former sequence of establishing a certain class sample G is G_i＝{X_i1，X_i2...X_ij, define itDiameter D_iFor sample dispersion quadratic sum:

$D_i=\underset{j=1}{\overset{n_i}{\&Sigma;}}{(X_{ij}-\stackrel{\&OverBar;}{X_i})}^2$

In formula,For average, X_ijFor the traffic characteristic value of sample data. Calculate according to table 1 dataDraw class diameter data as shown in table 2, i.e. the variation matrix of classification.

Table 2

Factor data is more, a display section data, and class diameter is less, shows that this classification is more concentrated, and the data of interval class are drawnBe divided into of a sort science higher.

Step 3 (2), the data sample of 24 hours is divided into k class, sample number is n:

G₁＝{X₁₁，X₁₂，...，X_1j}

G₂＝{X₂₁，X₂₂，...，X_2j}

…

G_k＝{X_k1，X_k2，...，X_kj}

Wherein, n₁，n₂，...，n_kFor k cut-point, and subscript meets 1≤n₁＜n₂＜...，n_k≤n。

Step 3 (3), calculate the target function value in classification situation separately respectively:

$L\&lsqb;B(n,k)\&rsqb;=\underset{i=1}{\overset{k}{\&Sigma;}}D(i_t,i_{t+1}-1)$

In the time that n and k determine, L[B (n, k)] all kinds of sum of squares of deviations of less expression is less, in so-called class, takes a walkMinimum, difference minimum.

The core recurrence formula of step 3 (4), Fisher algorithm:

$L\&lsqb;B(n,k)\&rsqb;=\underset{2\&le;j\&le;n}{\min }\underset{i=1}{\overset{k}{\&Sigma;}}\{D(1,j-1)+D(j,n)\}---\left(3\right)$

$L\&lsqb;B(n,k)\&rsqb;=\underset{k\&le;j\&le;n}{\min }\underset{i=1}{\overset{k}{\&Sigma;}}\{D(j-1,k-1)+D(j,n)\}---\left(4\right)$

Formula 1 is the minimum target function formula that data is divided into two classes, and formula 2 is the minimum target letters that sample are divided into k classNumber formula. If n sample will be divided into the optimum segmentation of k class, should be based upon the optimum segmentation that j-1 sample is divided into k-1 classOn basis (j=1 herein, 2,3 ..., n), analogize gradually process by formula 1 to formula 2.

Step 3 (5), by first calculating and be divided into the object function of two classes in (3) formula of step 3 (4), draw target function valueBe shown in table 3

Step 3 (6), by calculating and be divided into three classes, four classes again in (4) formula of step 3 (4) ..., (n-1) the target letter of classNumber, result is presented in table 3.

Table 3

Step 3 of the present invention calculated respectively by 96 data be divided into 2 classes, 3 classes, 4 classes ..., 95 classes optimum segmentationObject function, result of calculation is listed in table 3, and factor data is more, and the number that the traffic slot in actual road conditions is divided can not be tooMany, therefore only show and be divided into the target function value of 2 classes to 15 classes. Target function value parenthetic numeral below, for example table 3First numerical value 180.5 (3), now j=3, k=2, this data description be the optimum point-score that j data are divided into k class, draw togetherNumeral 3 in arc can be used as cut-point, and conduct one class before 3, represents all shapes as G_i＝{X_i1，X_i2，X₁₃,Sample data, is divided into two classes, with G as wanted₁＝{X_i1，X_i2}，G₂＝{X_i3Point-score be optimal situation.

Step 3 (7) is asked for optimal solution, if can directly draw optimal classification number from data structure angle, certainlyGood, how can to know dividing data by table 3 like this, but can not determine optimal classification number in large absolutely number situations, now can doGo out L[B (n, k)] with the changing trend diagram of number of categories k, as shown in Figure 4:

The present embodiment adopts more scientific method to obtain optimal classification numerical value, by calculating the non-tiltedly negative of adjacent target functionRate value is asked for:

$\mathrm{\&rho;}\left(z\right)=\left|\frac{L\&lsqb;B(n,k)\&rsqb;-L\&lsqb;B(n,k-1)\}}{k-(k-1)}\right|$

Step 3 (8), relatively slope value, determines optimal classification number, when slope is larger, represents that k class is better than (k-1)Class, slope value approaches the necessity that represents not continue classification at 0 o'clock, and generally getting slope maximum is optimal classification number.

Step 4, according to step 3 (7) and step 3 (8) according to the classification point of optimal classification number output, carry out period districtBetween divide.

Step 4 (1), count the parenthetic data m of respective objects functional value in k and table 3 according to optimal classification, determine G_k＝{X_im，X_i(k+1)...X_ij, be same class, belong to same period interval; Remaining (m-1) individual data are again according to number in table 3According to dividing, the like, can obtain optimal classification number and be k time, the concrete classification situation of 96 sample datas.

Step 4 (2), when the period division based on optimum segmentation result, does not have in fact for the number of divided periodHave strictly and reasonably arrange in other words, and the optimal classification number that above-mentioned steps solves is desired quantity; Therefore, period number of partitions againToo much unsuitable, traffic slot number of partitions is generally 4-10. In the present embodiment, pass through to calculate, when gained cut-point is converted intoCarve, obtain final period division result as shown in Figure 5. When conventionally 24h being divided into three of morning peaks, Ping Feng, evening peakTraditional division methods of section is compared, division methods is herein more careful, and high crest segment embodies emphatically transition, peak and declineTrend, more can embody the variation tendency of traffic flow.

The final effect of the present embodiment is: technical staff is loaded into said method in whistle control system by software,The operation interface of hommization is easier to operating personnel to be understood, and operating personnel can also rely on rich experiences and actual road conditions to dividingResult is optimized improves fine setting, capable of regulating period interval, increase and decrease period. Result demonstration, the method according to this invention drawsDivision result, is science and rational, and piecewise fitting precision is high, and method is simple, and theoretical property is strong, is easy to accept, can be very bigDelay is blocked up, is reduced in ground alleviation.

Claims (3)

1. the method that the traffic slot based on Fisher algorithm is divided automatically, is characterized in that, comprises the steps:

Step 1, gathers the traffic flow basic parameter in any given sampling interval, obtains initial data;

Step 2, screens, processes and repair pretreatment successively to initial data, obtains preprocessed data;

Step 3, by Fisher algorithm, preprocessed data is classified, obtain optimal solution and cut-point;

Step 4, output cut-point, in conjunction with optimal classification number, divide traffic slot interval.

2. the method that the traffic slot based on Fisher algorithm according to claim 1 is divided automatically, is characterized in that instituteThe step 2 of stating realizes as follows:

Step 1: initial data is screened and differentiated, extract normal data;

Step 2: set up problem data repairing model, to the disappearance class data in initial data, exception class data, mistake class dataRepair reduction with redundancy class data, obtain repair data;

Step 3: repair data and normal data are merged, obtain described preprocessed data.

3. the method that the traffic slot based on Fisher algorithm according to claim 1 and 2 is divided automatically, its feature existsIn, described step 3 comprises the steps:

Step 1, definition class diameter: the former sequence of establishing a certain class sample G is G_i＝{X_i1，X_i2…X_ij, define its diameter D_iFor sampleThis sum of squares of deviations:

$D_i=\underset{j=1}{\overset{n_i}{\&Sigma;}}{(X_{ij}-\stackrel{\&OverBar;}{X_i})}^2$

In formula, For average, X_ijFor sample characteristics;

Step 2, suppose sample (sample number is n) to be divided into k class:

G₁＝{X₁₁，X₁₂，…，X_1j}

G₂＝{X₂₁，X₂₂，…，X_2j}

…

G_k＝{X_k1，X_k2，…，X_kj}

Wherein, n₁，n₂，…，n_kFor k cut-point, and subscript meets 1≤n₁＜n₂＜…，n_k≤n；

Step 3, objective definition function are

$L\&lsqb;B(n,k)\&rsqb;=\underset{i=1}{\overset{k}{\&Sigma;}}D(i_t,i_{t+1}-1)$

Step 4, according to the core recurrence formula of Fisher algorithm:

$L\&lsqb;B(n,2)\&rsqb;=\underset{2\&le;j\&le;n}{min}\{D(1,j-1)+D(j,n)\}$

$L\&lsqb;B(n,k)\&rsqb;=\underset{2\&le;j\&le;n}{min}\{L\&lsqb;B(j-1,k-1)+D(j,n)\}$

Calculate minimum target function;

Step 5, ask for optimal solution:

If number of categories k (1 < k < is n) known, asks classification L[B (n, k)], make it be issued to minimum in object function meaning, askMethod is as follows:

First calculate non-negative slope according to object function consecutive value, the number of categories k that gets non-negative slope maximum is optimal classification number; Look forThe cut-point j that optimal classification number k is corresponding_k, make the formula numerical value of step G reach minimum,

L[B(n，k)]＝L[B(j_k-1，k-1)]+D(j_k，n)

Tried to achieve the optimal situation G that is divided into k class by above formula_k; Then the like, ask for j_k-1Minimum target under individual cut-pointFunction, obtains k-1 class G_k-1, try to achieve successively all class G_k，G_k-1，…，G₂，G₁, this is optimal solution.