CN107992895A - A kind of Boosting support vector machines learning method - Google Patents
A kind of Boosting support vector machines learning method Download PDFInfo
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Abstract
The invention discloses a kind of Boosting support vector machines learning method, it is related to field of artificial intelligence, the present invention comprises the following steps：Step 1：Data processing, carries out initial support vector machine classifier the selection of parameter γ；Step 2：Weights are initialized, choose n training sample composition total data set, initialize the weights of each training sample；Step 3：Into loop iteration, the weights of all training samples are updated；Step 4：Pass through T circulation, obtain final classification device H (x), the thought of combination supporting vector machine of the present invention and Adaboost algorithm, improve the study precision of the resampling technique of classifier design in pattern-recognition and ensure stable learning ability, optimize classifying quality so that classification accurate rate greatly promotes.
Description
Technical field
The present invention relates to field of artificial intelligence, more particularly to support vector machines study and integrated learning approach, have more
Body is to be related to a kind of Boosting support vector machines learning method.
Background technology
By the propositions such as Corinna Cortes and Vapnik support vector machines (Support Vector Machine,
SVM it is) a kind of machine learning method based on Statistical Learning Theory, as a kind of new general-purpose machinery learning method, it has
Succinct mathematical form, standard efficiently training method and good Generalization Capability, be successfully applied at present pattern-recognition,
The various fields such as regression estimates and Multilayer networks.However, more learner learning method researchs at present on SVM are very few,
And more learner study can effectively improve the generalization ability of study.Therefore, the more learner learning methods for studying SVM have weight
The theory significance wanted and direct application value.
A kind of extensive energy that can effectively improve machine learning of the integrated study technology as more learner learning methods
Power, its research start from nineteen nineties, and theoretical to integrated study at present and algorithm research is as machine learning
Integrated study is classified as first of the research greatly of machine learning four by one hot spot, internal authority Dietterich.Integrated study technology shows
The multiple fields of machine learning are successfully applied to, such as：Recognition of face, optical character identification, accurate image analysis, medical analysis
With seismic signal classification etc..
In the evolution of integrated study, there is the impetus that two important process play it key：Firstth,
Hansen and
Salamon solved the problems, such as using one group of neutral net, they are attempted all neutral net knots by the method for voting
Altogether, experiment generates interesting phenomenon, i.e., the integrated result of this group neutral net is not more a little than best individual difference, than
Worst is individual quite a lot of, but not worse than the performance of best individual neutral net.This makes integrated out of the result of intuition
Practise and cause the attention of many scholars, early period nineteen nineties integrated study technology be widely applied to multiple fields simultaneously
It is subject to good effect.Second, Schapire with Boosting algorithms to the weak learning algorithm that Kearns and Valiant are proposed with
The equivalence question of strong learning algorithm has carried out constructive proof, because the requirement of Boosting algorithms knows learning algorithm in advance
Generalization ability lower bound, and this lower bound is difficult to obtain, so real problems can not be solved.Freund and Schapire into
One step proposes AdaBoost algorithms, which is no longer required for knowing extensive lower bound in advance, can very easily be applied to reality
The problem of in.Breiman proposes the technology similar to Boosting Bagging one by one, further promotes integrated study
Development.
Integrated study be one develop rapidly in research field, from its appearance up to the present, the short more than ten years when
Between, it oneself through being widely used in the various fields such as language identification, text filtering, remote sensing information process, medical diagnosis on disease, especially
After Zhou in 2001 et al. proposes " selective ensemble " concept, very big repercussion is at home and abroad caused, integrated study band
A brand-new developing stage is entered so that people are expanded into one integrated study from deeper level, more vast field
The research of step.
Effective integrated model key is that each base grader of construction should be accurate and discrepant.Otherness requires base
Grader is mutually independent, if in fact, being negatively correlated between base grader, more preferable generalization can be obtained by integrating
Energy.Some researchs show that integrated study overcomes following three problems to a certain extent so that Generalization Capability is improved：
1), statistical problem.When obtainable training sample number is abundant, some algorithms can find optimal really
Habit machine.But actually training sample is limited, learning algorithm is only able to find the equal learning machine of many precision of predictions, although can
Therefrom to select most simple complexity in other words minimum, but existing risk is prediction essence of the learning machine for unknown sample
Degree is but very low.This risk can be reduced by being combined using several learning machines.
2), computational problem.It is too big to find the learning machine calculation amount best to training data fitting, thus needs using inspiration
Formula searching method, but usually there are certain distance with target for the result of its study.Integrated study be to these and it is faulty
A kind of compensation of searching method.
3), problem is described.When learning algorithm descriptive power is limited, search range is too small, so that not including object function
Or the preferable approximating function on object function, its learning outcome are also just unsatisfactory.Although many learning algorithms
With Uniform Approximation, when data are limited, progressive nature is no longer set up, and the search space of learning algorithm is can to obtain trained number
According to function, the hypothesis space that is considered under progressive situation may be much smaller than.Integrated study can expand function space, so as to obtain
Object function must more accurately be approached.
Boosting algorithms are that a series of learning machines are successively produced in training, and training set used in each learning machine is all
It is a subset put forward from total training set, whether each sample appears in the study for depending on producing before this in the subset
The performance of machine, existing learning machine judge that the sample of error will be appeared in new training subset with larger probability.This causes it
The learning machine produced afterwards focus more on processing have learning machine to oneself for more difficult sample distinguish problem.
Integrated study is a kind of new machine learning normal form, it solved the problems, such as using multiple learners it is same, can
The generalization ability of learning system is significantly increased, therefore since the 1990s, integrated study has been increasingly becoming engineering
One new hot spot in habit field.In actual classification problem, in order to reduce the probability of loss and error, often to classification side
Method is put forward higher requirements, and reaches classification accurate rate as high as possible, for example, planetary detection, seismic wave analysis, Web believe
Breath filtering, living things feature recognition, computer-aided medical diagnosis etc. some need the actual items of precise classification.But integrated
Learning method is currently not met by such high-precision requirement.Based on the consideration of such realistic problem, invention is a kind of high-precision
Integrated learning approach is extremely necessary.
The content of the invention
It is an object of the invention to：It is not high enough in order to solve existing integrated learning approach precision, it is impossible to meet high precision
The problem of requirement of rate project, the present invention provide a kind of Boosting support vector machines learning method, combination supporting vector machine with
The thought of Boosting algorithms, proposes lifting algorithm of support vector machine, improves the resampling skill of classifier design in pattern-recognition
The study precision of art and ensure stable learning ability, Optimum Classification effect so that classification accurate rate greatly promotes.
The present invention specifically uses following technical scheme to achieve these goals：
A kind of Boosting support vector machines learning method, it is characterised in that comprise the following steps：
Step 1：Data processing, carries out initial support vector machine classifier the selection of parameter γ；
Step 2：Weights are initialized, choose n training sample composition total data set [(x1,y1),…,(xn,yn)], wherein
xi∈X,yi∈ Y={ -1 ,+1 } (X x1,...,xnSet), initialize the weights D of each training sample1(i)
=1/n；
Step 3：K sample is arbitrarily chosen in the n training sample from step 2, first run data set is formed and combines step
Parameter γ in rapid 1 is trained, and obtains training dataset, and into loop iteration, loop iteration total degree is T, previous cycle
Iterations is t；
Step 4：Grader h is drawn according to training dataset and SVM learning algorithmst:X→{-1,+1}；
Step 5：By grader htApplied to total data set, total data set is predicted, respectively to grader htClassification is just
Really it is marked with wrong training sample, and error ε is determined according to the training sample of classification errort, calculate grader htPoint
Class error alphat, calculation formula is：
Step 6：The error in classification α drawn according to step 5tUpdate the weights D that training data concentrates all training samplest+1
(i), calculation formula is：
Dt+1(i)=Dt(i)exp(-αtyiht(xi))/Zt
In formula, ZtFor Dt+1The normalized function of distribution；
Step 7：T values are updated, make t=t+1, as t≤T, return to step 4, continues next round loop iteration；Work as t>During T,
End loop；
Step 8：By T circulation, final classification device H (x) is just obtained, calculation formula is：
In above-mentioned technical proposal, the data processing in the step 1 specifically includes following steps：
Step 1.1：By practical problem digitization, the manageable data formats of SVM are changed into；
Step 1.2：Normalized is carried out to the data in step 1.1 Jing Guo conversion processing.
In above-mentioned technical proposal, the step 1 makes choice parameter γ using gridding method, when parameter γ is SVM training
The kernel function of use, additionally relates to another parameter C (penalty factor), parameter γ and parameter C composition parameters to (γ, C),
Grid search is carried out to parameter first, i.e., various possible parameters is attempted to value using the method for exhaustion, then carries out cross validation, look for
The highest parameter pair of cross validation accuracy of sening as an envoy to, the target of parameter selection is the parameter pair found so that grader can
Calculate to a nicety unknown data.
In Boosting algorithms, in iteration each time according to current sample distribution weights ωi,jLearnt, root
Concentrated according to the principle of minimum from Weak Classifier and choose most effective Weak Classifier εi,j=∑iωi,j|hj(xi)-yi|.Weak training
Sample by misclassification, then aggravates distribution weights in current iteration.Conversely, then reduce weights.It can so utilize and aggravate mistake point
The weights of class sample force algorithm these mistakes of selective learning in ensuing iteration to divide sample.In general, change when each
When the training error for the Weak Classifier that generation selects is less than 50%, the training error of strong classifier can be as iterations be with index
Form declines and is intended to zero.Whole process is as follows：
(1) first pass through the study to N number of training data and obtain first Weak Classifier h1；
(2) data of h1 misclassifications and other new datas are formed into a new sample for having N number of training data together, led to
Cross the study to this sample and obtain second Weak Classifier h2；
(3) data by h1 and h2 all misclassifications, which add other new datas and form another, new has N number of training data
Sample, the 3rd Weak Classifier h3 is obtained by the study to this sample；
(4) the strong classifier h of lifting is finally obtainedfinal=MajorityVote (h1,h2,h3), i.e., some data is divided into
Which kind of will pass through h1,h2,h3Majority voting.
Boosting algorithms can strengthen the generalization ability of given algorithm, but also there are two shortcomings:This method needs
Know the lower limit of weak learning machine study accuracy, and this is difficult to accomplish in practical problem；Secondly, this method may be led
Cause later learning machine to concentrate too much on a small number of especially difficult samples, cause to show unstable, and calculated for Boosting
For the realization of method, also there are two difficulties：
(1) how adjusting training collection so that on training set training Weak Classifier carried out.
(2) how obtained each Weak Classifier will be trained to jointly form strong classifier.
For two above problem, Adaboost algorithm is adjusted：
(1) training data randomly selected is replaced using the training data chosen after weighting, so by trained focus collection
In on more difficult point of training data.
(2) when Weak Classifier is joined together, average voting mechanism is replaced using the voting mechanism of weighting.Allow classifying quality
Good Weak Classifier has a larger weight, and the poor grader of classifying quality has less weight.
Unlike Boosting algorithms, Adaboost algorithm need not be known a priori by weak learning algorithm study accuracy
Lower limit, that is, Weak Classifier error, and the nicety of grading of the strong classifier finally obtained dependent on all Weak Classifiers point
Class precision, so can deeply excavate the potentiality of Weak Classifier algorithm.
Different training sets is realized by adjusting each sample corresponding weight in Adaboost algorithm.Start
When, the corresponding weights of each sample are identical, i.e. Ui(i)=1/n (i=1 ..., n), wherein n is number of samples, in this sample
One's duty, which plants, trains a Weak Classifier h1.For the sample of h1 classification errors, its corresponding weight is increased；And for classifying just
True sample, reduces its weight, and the sample of such misclassification is just projected, so as to obtain a new sample distribution Ui.
Under new sample distribution, Weak Classifier is trained again, obtains Weak Classifier h2.And so on, by T circulation, obtain
To T Weak Classifier, this T Weak Classifier is got up by certain weighted superposition, the strong classifier finally wanted.
Support vector machines is established on the basis of the VC of Statistical Learning Theory ties up concept and structural risk minimization principle, we
Using finite sample information is in model complexity (the study precision i.e. to specific training sample) and learning ability is (i.e. without error
Identify arbitrary sample ability) between seek to trade off, with the generalization ability obtained.
Support vector machines seeks the optimal solution under existing information, rather than sample tends to be infinite specifically for finite sample
Optimal solution when big.By the way that the Construct question of optimal separating hyper plane is converted into quadratic form optimization problem, so as to obtain the overall situation
Optimum point, solves the unavoidable local extremum problem in neural net method.The solution of optimization problem be one group of support to
Amount, it is determined that the structure of support vector machines, determines the boundary between classification, and other samples do not play any work in classification
With unlike neutral net scheduling algorithm would generally use whole or numerical example mostly statistical information.Due to sample in a model
Occur only in the form of dot product, therefore be easy to be generalized to nonlinear model from linear model.By nonlinear function by data
High-dimensional feature space is mapped to, then constructs linear discriminant function in this space, realizes the nonlinear discriminant in luv space
Function.The explicit construction of mapping function is dexterously avoided, without knowing its concrete form.Support vector machines has clearly several
What meaning, can be according to its geometric properties come preference pattern structure, learning of structure method.
Beneficial effects of the present invention are as follows：
1st, present invention incorporates the thought of support vector machines and Adaboost methods, it is proposed that lifting support vector machines this
New sorting technique, support vector machines are avoided from the conventional procedure concluded to deduction, be enormously simplify common classification and are returned
The problems such as returning, and Adaboost methods, it is easy to implement, Generalization error rate, the method for the invention by support vector machines can be reduced
Adaboost methods are incorporated, greatly reduce Generalization error rate, improve study precision, and the method for the present invention can not only answer
Classify for two classes, it may also be used for multicategory classification task, has excellent learning performance, can reach the classifying quality of higher.
2nd, the present invention proposes lifting algorithm of support vector machine, combines the thought of SVM and Adaboost, wherein, SVM has
Fairly perfect theoretical foundation, preferable learning classification performance, particularly on compared with small data set, can also reach good point
Class effect, and as integrated study Adaboost methods have the advantages that to realize it is simple, flexibly, should be readily appreciated that, it is contemplated that shadow
The often a few sample of classification accuracy is rung, and lifts the sample that algorithm of support vector machine is the classification of selective analysis mistake, is made
The sample of classification error can obtain multiple study, so that model more adapts to the sample that these are easily classified by mistake,
Reach more efficient classifying quality, improve the generalization ability of learning machine.
3rd, basic classification device of the present invention using SVM as Adaboost, SVM have very outstanding classification in Weak Classifier
Effect, and Weak Classifier can be combined into a strong classifier by Adaboost, the method for combination is the one of weighted majority voting
Side, that is, increase the weights of the small Weak Classifier of error in classification rate, it is served in voting larger, and it is big to reduce error in classification rate
Weak Classifier weights, it is served in voting less, by the combination of SVM and Adaboost, just can reach
More excellent classifying quality, improves classification accuracy.
Brief description of the drawings
Fig. 1 is the flow chart that the present invention is applied to two classification problems.
Fig. 2 is the flow chart that the present invention is applied to more classification problems.
Embodiment
In order to which those skilled in the art are better understood from the present invention, below in conjunction with the accompanying drawings with following embodiments to the present invention
It is described in further detail.
Embodiment 1
As shown in Figure 1, the present embodiment proposes a kind of Boosting support vector machines learning method, comprise the following steps：
Step 1：Data processing, carries out initial support vector machine classifier using gridding method the selection of parameter γ；
Specifically, the data processing in step 1 specifically includes following two steps：
Step 1.1：By practical problem digitization, the manageable data formats of SVM are changed into；
Step 1.2：Normalized is carried out to the data in step 1.1 Jing Guo conversion processing；
Step 2：Weights are initialized, choose n training sample composition total data set [(x1,y1),…,(xn,yn)], wherein xi
∈X,yi∈ Y={ -1 ,+1 } (X x1,...,xnSet), initialize the weights D of each training sample1(i)=1/n；
Step 3：K sample is arbitrarily chosen in the n training sample from step 2, first run data set is formed and combines step
Parameter γ in rapid 1 is trained, and obtains training dataset, and into loop iteration, loop iteration total degree is T, previous cycle
Iterations is t；
Step 4：Grader h is drawn according to training dataset and SVM learning algorithmst:X→{-1,+1}；
Step 5：By grader htApplied to total data set, total data set is predicted, respectively to grader htClassification is just
Really it is marked with wrong training sample, and error ε is determined according to the training sample of classification errort, calculate grader htPoint
Class error alphat, calculation formula is：
Step 6：The error in classification α drawn according to step 5tUpdate the weights D that training data concentrates all training samplest+1
(i), calculation formula is：
Dt+1(i)=Dt(i)exp(-αtyiht(xi))/Zt
In formula, ZtFor Dt+1The normalized function of distribution；
Step 7：T values are updated, make t=t+1, as t≤T, return to step 4, continues next round loop iteration；Work as t>During T,
End loop；
Step 8：By T circulation, final classification device H (x) is just obtained, calculation formula is：
In the present embodiment, parameter γ is made choice using gridding method, parameter γ is the kernel function used during SVM training,
Another parameter C (penalty factor), parameter γ and parameter C composition parameters are additionally related to (γ, C), first to parameter into
Row grid search, i.e., attempt various possible parameters to value using the method for exhaustion, since the target of parameter selection is the ginseng that has found
It is several right so that grader can calculate to a nicety unknown data, therefore carry out cross validation to value to parameter, obtain making intersection
Verify the highest parameter pair of accuracy.
Basic classification device of the present embodiment using SVM as Adaboost, SVM have very outstanding classification in Weak Classifier
Effect, and Weak Classifier can be combined into a strong classifier by Adaboost, the method for combination is the one of weighted majority voting
Side, that is, increase the weights of the small Weak Classifier of error in classification rate, it is served in voting larger, and it is big to reduce error in classification rate
Weak Classifier weights, it is served in voting less, by the combination of SVM and Adaboost, just can reach
More excellent classifying quality, greatly reduces Generalization error rate, improves study precision.
Embodiment 2
Solved as shown in Fig. 2, the present embodiment proposes on the basis of embodiment 1 using lifting support vector machine method
The method of more classification problems, initial SVM are to solve two class classification problems, it is impossible to are directly used in multicategory classification, but can have
Effect ground is generalized to multicategory classification problem, these algorithms are referred to as " multi-class support vector machine ", can be roughly divided into two major classes:
(1) a series of binary classifier is constructed by certain mode and is combined to them to realize multiclass point
Class；
(2) parametric solution of multiple classifying faces is merged into an optimization problem, by solving the optimization problem
" disposable " realize multicategory classification.
Second class method is while it appear that succinct, but the variable during duty Optimization is far more than first
Class method, training speed are not also dominant not as good as first kind method in nicety of grading, when number of training is very big,
This problem is more prominent, and just because of this, first kind method is more commonly used, and the method applied in the present invention, using circulation
Iterative operation, after selecting k number according to sample, according to one-against-one method, k (k-1) a SVM is drawn by multiple training data
Learning machine, is then predicted all samples with this k (k-1) a grader.
The above, is only presently preferred embodiments of the present invention, is not intended to limit the invention, patent protection model of the invention
Enclose and be subject to claims, the equivalent structure change that every specification and accompanying drawing content with the present invention is made, similarly
It should include within the scope of the present invention.
Claims (3)
1. a kind of Boosting support vector machines learning method, it is characterised in that comprise the following steps：
Step 1：Data processing, carries out initial support vector machine classifier the selection of parameter γ；
Step 2：Weights are initialized, choose n training sample composition total data set [(x1,y1),…,(xn,yn)], wherein xi∈X,
yi∈ Y={ -1 ,+1 }, initialize the weights D of each training sample1(i)=1/n；
Step 3：K sample is arbitrarily chosen in the n training sample from step 2, first run data set is formed and combines in step 1
Parameter γ be trained, obtain training dataset, carry out loop iteration, loop iteration total degree be T, and previous cycle iteration is secondary
Number is t；
Step 4：Grader h is drawn according to training dataset and SVM learning algorithmst:X→{-1,+1}；
Step 5：By grader htApplied to total data set, total data set is predicted, respectively to grader htClassification correctly and
The training sample of mistake is marked, and determines error ε according to the training sample of classification errort, calculate grader htClassification miss
Poor αt, calculation formula is：
Step 6：The error in classification α drawn according to step 5tUpdate the weights D that training data concentrates all training samplest+1(i), count
Calculating formula is：
Dt+1(i)=Dt(i)exp(-αtyiht(xi))/Zt
In formula, ZtFor Dt+1The normalized function of distribution；
Step 7：T values are updated, make t=t+1, as t≤T, return to step 4, continues next round loop iteration；Work as t>During T, terminate
Circulation；
Step 8：By T circulation, final classification device H (x) is just obtained, calculation formula is：
A kind of 2. Boosting support vector machines learning method according to claim 1, it is characterised in that the step 1
In data processing specifically include following steps：
Step 1.1：By practical problem digitization, the manageable data formats of SVM are changed into；
Step 1.2：Normalized is carried out to the data in step 1.1 Jing Guo conversion processing.
A kind of 3. Boosting support vector machines learning method according to claim 1 or 2, it is characterised in that the step
Rapid 1 makes choice parameter γ using gridding method.
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