CN107301513A - Bloom prealarming method and apparatus based on CART decision trees - Google Patents
Bloom prealarming method and apparatus based on CART decision trees Download PDFInfo
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Abstract
The invention provides a kind of bloom prealarming method and apparatus based on CART decision trees, the factor of influence of K influence wawter bloom is chosen, the coefficient correlation between the K factor of influence and default decision attribute is calculated respectively；T factor of influence is chosen as the conditional attribute of influence wawter bloom, wherein T is the integer more than 0 and less than or equal to K；Based on Fayyad boundary point cor-responding identified theorems, the corresponding GINI coefficients of each conditional attribute in data set are obtained；The data set refers to：The data acquisition system that the parameter detected from different water body environments is constituted；The cut-point of each conditional attribute is determined according to the GINI coefficients；Decision tree is built according to the cut-point and coefficient correlation recurrence；Bloom prealarming is carried out to water body based on the decision tree.Method in the present invention solves traditional CART decision-tree models and there are problems that run time is longer and precision of prediction, and wawter bloom that can be effectively to water body is predicted, and forecasting efficiency is high.
Description
Technical field
The present invention relates to water environment protection technical field, in particular it relates to the bloom prealarming method based on CART decision trees
And device.
Background technology
Because a large amount of town sewages and industrial and agricultural wastewater flow into the water bodys such as river, river, lake so that the pollutional load of water body is not
Disconnected increase, causes wawter bloom event to take place frequently.In order to which preferably the water body of eutrophication is monitored and managed, many researchers carry
Go out and be predicted by setting up bloom prealarming model come the wawter bloom to water body.
Decision tree (Classification And Regression Tree, CART) be 1984 by Breiman,
The algorithm that Friedman, Olshen, Stone are proposed.CART algorithms use a kind of technology of two points of recursive subdivisions, and based on information
The algorithm of entropy is different, and division of the CART algorithms to each sample set calculates GINI coefficients, wherein, GINI coefficients are metric datas point
Area's either sample set E impure degree, GINI coefficients are smaller, divide more reasonable.CART algorithms are always by current sample set point
It is segmented into two sub- sample sets so that each non-leaf node of the decision tree of generation only has two branches.Therefore CART algorithms life
Into decision tree be binary tree simple for structure.CART decision trees both can may also be used for doing regression tree for doing classification tree.
But, the problem of traditional CART algorithms have computationally intensive and long operational time.
The content of the invention
For defect of the prior art, it is an object of the invention to provide a kind of bloom prealarming side based on CART decision trees
Method and device.
In a first aspect, the present invention provides a kind of bloom prealarming method based on CART decision trees, including：
The factor of influence of K influence wawter bloom is chosen, the K factor of influence and default decision attribute (leaf are calculated respectively
Green plain a concentration) between coefficient correlation；Wherein, K is the integer more than 0；
T factor of influence is chosen from K factor of influence according to the value of the coefficient correlation, the T factor of influence is made
To influence the conditional attribute of wawter bloom, wherein T is the integer more than 0 and less than or equal to K；
Based on Fayyad boundary point cor-responding identified theorems, the corresponding GINI coefficients of each conditional attribute in data set are obtained；Wherein,
The data set refers to：The data acquisition system that the parameter detected from different water body environments is constituted；
The cut-point of each conditional attribute is determined according to the GINI coefficients；
Decision tree is built according to the cut-point and coefficient correlation recurrence；
Bloom prealarming is carried out to water body based on the decision tree.
Alternatively, the calculation formula of the coefficient correlation between the K factor of influence and default decision attribute is as follows：
In formula：Represent i-th of conditional attribute AiWith the coefficient correlation between default decision attribute B, AiRepresent i-th
Conditional attribute, i is the integer more than or equal to 1 and less than or equal to K, and B represents default decision attribute, Cov (Ai, B) and represent AiWith B
Covariance, D (Ai) represent AiVariance, D (B) represent B variance.
Alternatively, it is described to be based on Fayyad boundary point cor-responding identified theorems, obtain each conditional attribute in data set corresponding
GINI coefficients, including：
Assuming that the data set E is divided into two subset E according to either condition attribute A1And E2, then the conditional attribute A
The calculation formula of corresponding data collection E GINI coefficients is as follows：
Wherein：
In formula：GINIA(E) gini indexs of the E under A attributes is represented,Represent subset E1Ratio in set E,
GINI(E1) represent E1Gini index,Represent subset E2Ratio in set E, GINI (E2) represent E2Geordie refer to
Number, GINI (E) represents E gini index, piTuple belongs to the probability of decision attribute final classification result in expression E, and m represents to determine
The number of plan attribute data collection classification.
Alternatively, the cut-point that each conditional attribute is determined according to the GINI coefficients, including：
Cut-point is obtained for each conditional attribute according to GINI coefficients minimum principle, the GINI coefficients minimum principle is
Refer to when based on either condition attribute by the Segmentation of Data Set into two subsets when so that the conditional attribute is on the data
The GINI coefficients of collection are minimum；
Using cut-point of GINI coefficients when minimum as the conditional attribute cut-point.
Alternatively, it is described that decision tree is built according to the cut-point and coefficient correlation recurrence, including：
A1：The maximum conditional attribute of coefficient correlation in data set is chosen as the 1st layer of node；The conditional attribute is made
For root node；
A2：The initial value for making N is 1；
A3：Data subset positioned at N+1 layers, institute are determined according to the corresponding cut-point of the conditional attribute of the N node layers
The maximum conditional attribute of coefficient correlation in N+1 layers of data subset is stated as N+1 layers of node；
A4：The data subset judged positioned at N+1 layers whether there is alienable conditional attribute, if there is alienable bar
Part attribute, then make N value from increasing 1, return and perform A3, if in the absence of alienable conditional attribute, performing A5；
A5：Decision tree is generated, terminates flow.
Alternatively, in addition to：Beta pruning is carried out to the decision tree using cost complexity pruning algorithms, what is be simplified determines
Plan tree.
Alternatively, in addition to：Decision tree based on the simplification carries out bloom prealarming to water body.
Second aspect, the present invention provides a kind of bloom prealarming device based on CART decision trees, including：First chooses mould
Block, second choose module, acquisition module, cut-point determining module, decision tree and build module and warning module；
It is described first choose module, for choose K influence wawter bloom factor of influence, calculate respectively it is described K influence because
The sub coefficient correlation between default decision attribute；Wherein, K is the integer more than 0；
It is described second choose module, for chosen according to the value of the coefficient correlation from K factor of influence T influence because
Son, the T factor of influence is as the conditional attribute of influence wawter bloom, and wherein T is the integer more than 0 and less than or equal to K；
The acquisition module, for based on Fayyad boundary point cor-responding identified theorems, obtaining each conditional attribute pair in data set
The GINI coefficients answered；Wherein, the data set refers to：The data set that the parameter detected from different water body environments is constituted
Close；
The cut-point determining module, the cut-point for determining each conditional attribute according to the GINI coefficients；
The decision tree builds module, for building decision tree according to the cut-point and coefficient correlation recurrence；
The warning module, for carrying out bloom prealarming to water body based on the decision tree.
Alternatively, the cut-point determining module, specifically for：
Cut-point is obtained for each conditional attribute according to GINI coefficients minimum principle, the GINI coefficients minimum principle is
Refer to when based on either condition attribute by the Segmentation of Data Set into two subsets when so that the conditional attribute is on the data
The GINI coefficients of collection are minimum；
Using cut-point of GINI coefficients when minimum as the conditional attribute cut-point.
Alternatively, in addition to：Pruning module, the pruning module, for utilizing cost complexity pruning algorithms to described
Decision tree carries out beta pruning, the decision tree being simplified.
Compared with prior art, the present invention has following beneficial effect：
The bloom prealarming method and apparatus based on CART decision trees that the present invention is provided, the influence of wawter bloom is influenceed by calculating
The factor selects conditional attribute with the coefficient correlation of default decision attribute；And obtained based on Fayyad boundary points cor-responding identified theorems
The GINI coefficients of each conditional attribute are taken, the cut-point that the minimum cut-point of GINI coefficients is the conditional attribute is chosen, according to
The cut-point of each conditional attribute and the raw decision tree of coefficient correlation recurrence, using decision tree come early warning water bloom of water body, it is of the invention in
Method solve traditional CART decision-tree models and there are problems that run time is longer and precision of prediction, can be effective
Ground is predicted to the wawter bloom of water body, and forecasting efficiency is high.
Brief description of the drawings
By reading the detailed description made with reference to the following drawings to non-limiting example, further feature of the invention,
Objects and advantages will become more apparent upon：
Fig. 1 is the bloom prealarming method flow diagram based on CART decision trees that the embodiment of the present invention one is provided；
The generation method flow chart for the CART decision trees that Fig. 2 provides for the present invention.
Embodiment
With reference to specific embodiment, the present invention is described in detail.Following examples will be helpful to the technology of this area
Personnel further understand the present invention, but the invention is not limited in any way.It should be pointed out that to the ordinary skill of this area
For personnel, without departing from the inventive concept of the premise, some changes and improvements can also be made.These belong to the present invention
Protection domain.
Fig. 1 is the bloom prealarming method based on CART decision trees that the embodiment of the present invention one is provided, as shown in figure 1, this reality
Applying the method in example can include：
S101, the factor of influence for choosing K influence wawter bloom, calculate the K factor of influence and belong to default decision-making respectively
Coefficient correlation between property；Wherein, K is the integer more than 0.
In the present embodiment, the factor of influence of the influence wawter bloom includes：Chlorophyll a (Chl-a), water temperature (T), PH, chemistry
Oxygen demand (COD), total nitrogen (TN), total phosphorus (TP), dissolved oxygen (DO), water quality, the meteorological factor such as illumination (E)；The default bar
Part attribute includes：Total phosphorus (TP), total nitrogen (TN), temperature (T), COD (COD), PH.
S102, choose T factor of influence from K factor of influence according to the value of the coefficient correlation, the T influence because
Son is as the conditional attribute of influence wawter bloom, and wherein T is the integer more than 0 and less than or equal to K.
In the present embodiment, T factor of influence is chosen from K factor of influence according to the size of coefficient correlation, for example, can be with
The factor of influence for selecting coefficient correlation big.
S103, based on Fayyad boundary point cor-responding identified theorems, obtain the corresponding GINI coefficients of each conditional attribute in data set；
Wherein, the data set refers to：The data acquisition system that the parameter detected from different water body environments is constituted.
In the present embodiment, the GINI coefficients of each conditional attribute, GINI systems are obtained by Fayyad boundary points cor-responding identified theorems
Number is metric data subregion either sample set E impure degree, and GINI coefficients are smaller, divide more reasonable.
S104, the cut-point for determining according to the GINI coefficients each conditional attribute.
In the present embodiment, the corresponding cut-point of each conditional attribute is chosen by the size of GINI coefficients, for example can be with
The cut-point at GINI coefficients minimum is chosen as the cut-point of the conditional attribute.
S105, decision tree built according to the cut-point and coefficient correlation recurrence.
In the present embodiment, root node can be used as by choosing the maximum conditional attribute of coefficient correlation, described section is obtained
The cut-point of point, obtains next layer of Sub Data Set, by judging in the Sub Data Set to belong to the presence or absence of alienable condition
Property gradually divide Sub Data Set, until without alienable conditional attribute again, generating decision tree, institute in the Sub Data Set of the bottom
Decision tree is stated for binary tree.
S106, based on the decision tree to water body carry out bloom prealarming.
Alternatively, the calculation formula of the coefficient correlation between the K factor of influence and default decision attribute is as follows：
In formula：Represent i-th of conditional attribute AiWith the coefficient correlation between default decision attribute B, AiRepresent i-th
Conditional attribute, i is the integer more than or equal to 1 and less than or equal to K, and B represents default decision attribute, Cov (Ai, B) and represent AiWith B
Covariance, D (Ai) represent AiVariance, D (B) represent B variance.
Alternatively, it is described to be based on Fayyad boundary point cor-responding identified theorems, obtain each conditional attribute in data set corresponding
GINI coefficients, including：
Assuming that the data set E is divided into two subset E according to either condition attribute A1And E2, then the conditional attribute A
The calculation formula of corresponding data collection E GINI coefficients is as follows：
Wherein：
In formula：GINIA(E) gini indexs of the E under A attributes is represented,Represent subset E1Ratio in set E,
GINI(E1) represent E1Gini index,Represent subset E2Ratio in set E, GINI (E2) represent E2Geordie refer to
Number, GINI (E) represents E gini index, piTuple belongs to the probability of decision attribute final classification result in expression E, and m represents to determine
The number of plan attribute data collection classification.
Alternatively, the cut-point that each conditional attribute is determined according to the GINI coefficients, including：
Cut-point is obtained for each conditional attribute according to GINI coefficients minimum principle, the GINI coefficients minimum principle is
Refer to when based on either condition attribute by the Segmentation of Data Set into two subsets when so that the conditional attribute is on the data
The GINI coefficients of collection are minimum；
Using cut-point of GINI coefficients when minimum as the conditional attribute cut-point.
The present embodiment, influences the factor of influence of wawter bloom to be selected with the coefficient correlation of default decision attribute by calculating
Conditional attribute；And obtain the GINI coefficients of each conditional attribute based on Fayyad boundary points cor-responding identified theorems, choose GINI coefficients
Minimum cut-point is the cut-point of the conditional attribute, is determined according to the cut-point of each conditional attribute and the life of coefficient correlation recurrence
Plan tree, using decision tree come early warning water bloom of water body, the method in the present invention solves traditional CART decision-tree models and there is fortune
The problems such as row time is longer and precision of prediction is inadequate, wawter bloom that can be effectively to water body is predicted, and forecasting efficiency is high.
The generation method flow chart for the CART decision trees that Fig. 2 provides for the present invention, as shown in Fig. 2 dividing described in the basis
Cutpoint and coefficient correlation recurrence build decision tree, including：
A1：The maximum conditional attribute of coefficient correlation in data set is chosen as the 1st layer of node；The conditional attribute is made
For root node；
A2：The initial value for making N is 1；
A3：Data subset positioned at N+1 layers, institute are determined according to the corresponding cut-point of the conditional attribute of the N node layers
The maximum conditional attribute of coefficient correlation in N+1 layers of data subset is stated as N+1 layers of node；
A4：The data subset judged positioned at N+1 layers whether there is alienable conditional attribute, if there is alienable bar
Part attribute, then make N value from increasing 1, return and perform A3, if in the absence of alienable conditional attribute, performing A5；
A5：Decision tree is generated, terminates flow.
Alternatively, method shown in above-mentioned Fig. 1, can also include：Using cost complexity pruning algorithms to the decision tree
Carry out beta pruning, the decision tree being simplified.
Alternatively, method shown in above-mentioned Fig. 1, can also include：Decision tree based on the simplification carries out wawter bloom to water body
Early warning.
With reference to specific embodiment, more detailed explanation is done to the technical scheme in the present invention.
The factor of influence of multiple influence wawter blooms is chosen first, and calculates the phase relation between the factor of influence and conditional attribute
Number, it is specific as shown in table 1.
The correlation coefficient charts of table 1
In table 1, TN represents total nitrogen, and TP represents total phosphorus, and PH represents hydrogen ionexponent, and DO represents dissolved oxygen, and COD is represented
COD, T represents temperature, and E represents illumination, TN:TP represents N/P ratio, wherein, conditional attribute is total phosphorus (TP), total nitrogen
(TN), temperature (T), COD (COD), PH.
Secondly, five factors of influence of TN, TP, PH, COD, T are selected from table 1 as conditional attribute.
With reference to Fayyad boundary point cor-responding identified theorems, the GINI coefficients of each attribute in data set are calculated, each attribute is selected
Minimum GINI coefficients are used as the attribute cut-point at middle cut-point.
GINI coefficients are metric data subregion either sample set E impure degree.It is defined as follows：
Wherein, classification collection is { C1, C2 ... Cn }, | Ci | to belong to Ci sample size, pi=in E | Ci |/| E | in E
Sample belong to classification Ci probability.
When only sample set is divided into two, training sample set E is divided into two subsets E1 and E2 by attribute A, then is divided
E GINI coefficients are afterwards
Wherein, | Ek|/| E | belong to the probability of kth (k=1,2) individual subset for sample in sample set.
The optimal threshold point (cut-point) for the conditional attribute selected by the above method, as shown in table 2.
The attribute optimal threshold table of table 2
Result and coefficient correlation recursive generation decision tree in table 2.
It is possible to further carry out beta pruning to the decision tree of the generation by cost complexity pruning algorithms, letter is formed
Clean decision tree.
The embodiment of the present invention additionally provides a kind of bloom prealarming device based on CART decision trees, and first chooses module, the
Two, which choose module, acquisition module, cut-point determining module, decision tree, builds module and warning module；
It is described first choose module, for choose K influence wawter bloom factor of influence, calculate respectively it is described K influence because
The sub coefficient correlation between default decision attribute；Wherein, K is the integer more than 0；
It is described second choose module, for chosen according to the value of the coefficient correlation from K factor of influence T influence because
Son, the T factor of influence is as the conditional attribute of influence wawter bloom, and wherein T is the integer more than 0 and less than or equal to K；
The acquisition module, for based on Fayyad boundary point cor-responding identified theorems, obtaining each conditional attribute pair in data set
The GINI coefficients answered；Wherein, the data set refers to：The data set that the parameter detected from different water body environments is constituted
Close.
The cut-point determining module, the cut-point for determining each conditional attribute according to the GINI coefficients；
The decision tree builds module, for building decision tree according to the cut-point and coefficient correlation recurrence；
The warning module, for carrying out bloom prealarming to water body based on the decision tree.
Alternatively, the cut-point determining module, specifically for：
Cut-point is obtained for each conditional attribute according to GINI coefficients minimum principle, the GINI coefficients minimum principle is
Refer to when based on it is any certainly conditionity by the Segmentation of Data Set into two subsets when so that the conditional attribute is on the data
The GINI coefficients of collection are minimum；
Using cut-point of GINI coefficients when minimum as the conditional attribute cut-point.
Further, in addition to：Pruning module, the pruning module, for utilizing cost complexity pruning algorithms to institute
State decision tree and carry out beta pruning, the decision tree being simplified.
It should be noted that the step in the bloom prealarming method based on CART decision trees that the present invention is provided, can
To be achieved using corresponding module, unit in the bloom prealarming device based on CART decision trees etc., art technology
The technical scheme that personnel are referred to the system realizes the step flow of methods described, i.e. the embodiment in the system can
It is interpreted as realizing the preference of methods described, will not be described here.
One skilled in the art will appreciate that except realizing the system that the present invention is provided in pure computer readable program code mode
And its beyond each device, can be caused completely by the way that method and step is carried out into programming in logic the system that provides of the present invention and its
Each device is in the form of gate, switch, application specific integrated circuit, programmable logic controller (PLC) and embedded microcontroller etc.
To realize identical function.So, the system and its every device that the present invention is provided are considered a kind of hardware component, and right
The device for realizing various functions included in it can also be considered as the structure in hardware component；It will can also be used to realize respectively
The device of kind of function, which is considered as, not only can be the software module of implementation method but also can be the structure in hardware component.
The specific embodiment of the present invention is described above.It is to be appreciated that the invention is not limited in above-mentioned
Particular implementation, those skilled in the art can make a variety of changes or change within the scope of the claims, this not shadow
Ring the substantive content of the present invention.In the case where not conflicting, feature in embodiments herein and embodiment can any phase
Mutually combination.
Claims (10)
1. a kind of bloom prealarming method based on CART decision trees, it is characterised in that including：
The factor of influence of K influence wawter bloom is chosen, the phase between the K factor of influence and default decision attribute is calculated respectively
Relation number；Wherein, K is the integer more than 0；
T factor of influence is chosen from K factor of influence according to the value of the coefficient correlation, the T factor of influence is used as shadow
The conditional attribute of China of Xiangshui County, wherein T is the integer more than 0 and less than or equal to K；
Based on Fayyad boundary point cor-responding identified theorems, the corresponding GINI coefficients of each conditional attribute in data set are obtained；Wherein, it is described
Data set refers to：The data acquisition system that the parameter detected from different water body environments is constituted；
The cut-point of each conditional attribute is determined according to the GINI coefficients；
Decision tree is built according to the cut-point and coefficient correlation recurrence；
Bloom prealarming is carried out to water body based on the decision tree.
2. the bloom prealarming method according to claim 1 based on CART decision trees, it is characterised in that the K influence
The calculation formula of coefficient correlation between the factor and default decision attribute is as follows：
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In formula：Represent i-th of conditional attribute AiWith the coefficient correlation between default decision attribute B, AiRepresent i-th of condition
Attribute, i is the integer more than or equal to 1 and less than or equal to K, and B represents default decision attribute, Cov (Ai, B) and represent AiWith B association
Variance, D (Ai) represent AiVariance, D (B) represent B variance.
3. the bloom prealarming method according to claim 1 based on CART decision trees, it is characterised in that described to be based on
Fayyad boundary point cor-responding identified theorems, obtain the corresponding GINI coefficients of each conditional attribute in data set, including：
Assuming that the data set E is divided into two subset E according to either condition attribute A1And E2, then the conditional attribute A is corresponding
The calculation formula of data set E GINI coefficients is as follows：
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Wherein：
In formula：GINIA(E) gini indexs of the E under A attributes is represented,Represent subset E1Ratio in set E, GINI
(E1) represent E1Gini index,Represent subset E2Ratio in set E, GINI (E2) represent E2Gini index,
GINI (E) represents E gini index, piTuple belongs to the probability of decision attribute final classification result in expression E, and m represents decision-making
The number of attribute data collection classification.
4. the bloom prealarming method according to claim 1 based on CART decision trees, it is characterised in that described in the basis
GINI coefficients determine the cut-point of each conditional attribute, including：
Cut-point is obtained for each conditional attribute according to GINI coefficients minimum principle, the GINI coefficients minimum principle refers to work as
Based on either condition attribute by the Segmentation of Data Set into two subsets when so that the conditional attribute is on the data set
GINI coefficients are minimum；
Using cut-point of GINI coefficients when minimum as the conditional attribute cut-point.
5. the bloom prealarming method based on CART decision trees according to any one in claim 1-4, it is characterised in that
It is described that decision tree is built according to the cut-point and coefficient correlation recurrence, including：
A1：The maximum conditional attribute of coefficient correlation in data set is chosen as the 1st layer of node；It regard the conditional attribute as root
Node；
A2：The initial value for making N is 1；
A3：Data subset positioned at N+1 layers, the N+1 are determined according to the corresponding cut-point of the conditional attribute of the N node layers
The maximum conditional attribute of coefficient correlation is used as N+1 layers of node in the data subset of layer；
A4：The data subset judged positioned at N+1 layers whether there is alienable conditional attribute, if there is alienable condition category
Property, then N value is made from increasing 1, returns and performs A3, if in the absence of alienable conditional attribute, performing A5；
A5：Decision tree is generated, terminates flow.
6. the bloom prealarming method according to claim 1 based on CART decision trees, it is characterised in that also include：Utilize
Cost complexity pruning algorithms carry out beta pruning, the decision tree being simplified to the decision tree.
7. the bloom prealarming method according to claim 6 based on CART decision trees, it is characterised in that also include：It is based on
The decision tree of the simplification carries out bloom prealarming to water body.
8. a kind of bloom prealarming device based on CART decision trees, it is characterised in that including：First chooses module, the second selection
Module, acquisition module, cut-point determining module, decision tree build module and warning module；
It is described first choose module, for choose K influence wawter bloom factor of influence, calculate respectively the K factor of influence and
Coefficient correlation between default decision attribute；Wherein, K is the integer more than 0；
Described second chooses module, for choosing T factor of influence from K factor of influence according to the value of the coefficient correlation,
The T factor of influence is as the conditional attribute of influence wawter bloom, and wherein T is the integer more than 0 and less than or equal to K；
The acquisition module, it is corresponding for based on Fayyad boundary point cor-responding identified theorems, obtaining each conditional attribute in data set
GINI coefficients；Wherein, the data set refers to：The data acquisition system that the parameter detected from different water body environments is constituted；
The cut-point determining module, the cut-point for determining each conditional attribute according to the GINI coefficients；
The decision tree builds module, for building decision tree according to the cut-point and coefficient correlation recurrence；
The warning module, for carrying out bloom prealarming to water body based on the decision tree.
9. the bloom prealarming device according to claim 8 based on CART decision trees, it is characterised in that the cut-point is true
Cover half block, specifically for：
Cut-point is obtained for each conditional attribute according to GINI coefficients minimum principle, the GINI coefficients minimum principle refers to work as
Based on either condition attribute by the Segmentation of Data Set into two subsets when so that the conditional attribute is on the data set
GINI coefficients are minimum；
Using cut-point of GINI coefficients when minimum as the conditional attribute cut-point.
10. the bloom prealarming device according to claim 8 based on CART decision trees, it is characterised in that also include：Beta pruning
Module, the pruning module, for carrying out beta pruning to the decision tree using cost complexity pruning algorithms, what is be simplified determines
Plan tree.
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