C4.5 algorithm - Revision history

Trulyy: Added image

2024-06-23T20:39:51Z

Added image

← Previous revision		Revision as of 20:39, 23 June 2024
Line 1:		Line 1:
	{{Short description\|Algorithm for making decision trees}}		{{Short description\|Algorithm for making decision trees}}
	{{More footnotes\|date=July 2008}}		{{More footnotes\|date=July 2008}}
			[[File:Diagramm_beispiel_sarah_geht_segeln.png \| thumb \| right]]
	'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>		'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>

LucasBrown: Adding local short description: "Algorithm for making decision trees", overriding Wikidata description "decision trees algorithm"

2024-05-15T11:08:27Z

Adding local short description: "Algorithm for making decision trees", overriding Wikidata description "decision trees algorithm"

← Previous revision		Revision as of 11:08, 15 May 2024
Line 1:		Line 1:
			{{Short description\|Algorithm for making decision trees}}
	{{More footnotes\|date=July 2008}}		{{More footnotes\|date=July 2008}}
	'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>		'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>

Revanchist317: /* Algorithm */

2024-01-05T21:05:59Z

Algorithm

← Previous revision		Revision as of 21:05, 5 January 2024
Line 7:		Line 7:
	C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.		C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.

	At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information gain in decision trees\|information gain]] (difference in ~~[[Entropy (information theory)\|~~entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.		At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information gain in decision trees\|information gain]] (difference in entropy). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.

	This algorithm has a few [[Base case (recursion)\|base cases]].		This algorithm has a few [[Base case (recursion)\|base cases]].

Frap at 13:38, 25 January 2023

2023-01-25T13:38:01Z

← Previous revision		Revision as of 13:38, 25 January 2023
Line 27:		Line 27:
	'''J48''' is an [[open source]] [[Java (programming language)\|Java]] implementation of the C4.5 algorithm in the [[Weka (machine learning)\|Weka]] [[data mining]] tool.		'''J48''' is an [[open source]] [[Java (programming language)\|Java]] implementation of the C4.5 algorithm in the [[Weka (machine learning)\|Weka]] [[data mining]] tool.

	==Improvements from ~~ID.3~~ algorithm==		==Improvements from ID3 algorithm==

	C4.5 made a number of improvements to ID3. Some of these are:		C4.5 made a number of improvements to ID3. Some of these are:
Line 48:		Line 48:
	* Winnowing - a C5.0 option automatically [[Winnow (algorithm)\|winnow]]s the attributes to remove those that may be unhelpful.		* Winnowing - a C5.0 option automatically [[Winnow (algorithm)\|winnow]]s the attributes to remove those that may be unhelpful.

	Source for a single-threaded Linux version of C5.0 is available under the GPL.		Source for a single-threaded Linux version of C5.0 is available under the [[GNU General Public License]] (GPL).

	== See also ==		== See also ==

Clog Wolf: /* Algorithm */fix, typo(s) fixed: ously- → ously

2022-02-10T10:08:20Z

Algorithm: fix, typo(s) fixed: ously- → ously

← Previous revision		Revision as of 10:08, 10 February 2022
Line 7:		Line 7:
	C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.		C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.

	At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[~~Information_gain_in_decision_trees~~\|information gain]] (difference in [[Entropy (information theory)\|entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.		At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information gain in decision trees\|information gain]] (difference in [[Entropy (information theory)\|entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.

	This algorithm has a few [[Base case (recursion)\|base cases]].		This algorithm has a few [[Base case (recursion)\|base cases]].
	*All the samples in the list belong to the same class. When this happens, it simply creates a leaf node for the decision tree saying to choose that class.		*All the samples in the list belong to the same class. When this happens, it simply creates a leaf node for the decision tree saying to choose that class.
	*None of the features provide any information gain. In this case, C4.5 creates a decision node higher up the tree using the expected value of the class.		*None of the features provide any information gain. In this case, C4.5 creates a decision node higher up the tree using the expected value of the class.
	*Instance of previously-unseen class encountered. Again, C4.5 creates a decision node higher up the tree using the expected value.		*Instance of previously unseen class encountered. Again, C4.5 creates a decision node higher up the tree using the expected value.

	===Pseudocode===		===Pseudocode===

Kotskokos: /* Algorithm */ removed excess spaces

2021-04-20T19:20:25Z

Algorithm: removed excess spaces

← Previous revision		Revision as of 19:20, 20 April 2021
Line 7:		Line 7:
	C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.		C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.

	At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information_gain_in_decision_trees\|information gain]] (difference in [[Entropy (information theory)\|entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.		At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information_gain_in_decision_trees\|information gain]] (difference in [[Entropy (information theory)\|entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.

	This algorithm has a few [[Base case (recursion)\|base cases]].		This algorithm has a few [[Base case (recursion)\|base cases]].

MrOllie: Restored revision 943211739 by Brendon.eric.lucas (talk): WP:EL

2021-02-24T13:16:17Z

Restored revision 943211739 by Brendon.eric.lucas (talk): WP:EL

← Previous revision		Revision as of 13:16, 24 February 2021
Line 61:		Line 61:
	* Original implementation on Ross Quinlan's homepage: [http://www.rulequest.com/Personal/ http://www.rulequest.com/Personal/]		* Original implementation on Ross Quinlan's homepage: [http://www.rulequest.com/Personal/ http://www.rulequest.com/Personal/]
	* [http://www.rulequest.com/see5-info.html See5 and C5.0]		* [http://www.rulequest.com/see5-info.html See5 and C5.0]
	* [https://github.com/serengil/chefboost An implementation of C4.5 in Python]

	{{DEFAULTSORT:C4.5 Algorithm}}		{{DEFAULTSORT:C4.5 Algorithm}}

Johncasey: python implementation

2021-02-24T08:44:14Z

python implementation

← Previous revision		Revision as of 08:44, 24 February 2021
Line 61:		Line 61:
	* Original implementation on Ross Quinlan's homepage: [http://www.rulequest.com/Personal/ http://www.rulequest.com/Personal/]		* Original implementation on Ross Quinlan's homepage: [http://www.rulequest.com/Personal/ http://www.rulequest.com/Personal/]
	* [http://www.rulequest.com/see5-info.html See5 and C5.0]		* [http://www.rulequest.com/see5-info.html See5 and C5.0]
			* [https://github.com/serengil/chefboost An implementation of C4.5 in Python]

	{{DEFAULTSORT:C4.5 Algorithm}}		{{DEFAULTSORT:C4.5 Algorithm}}

Brendon.eric.lucas: Changed "recur" to "recurse" in pseudocode description of algorithm. This was likely a typo, as "recurse" is the verb form of "recursion", and the standard implementation of the DT algorithm is in fact recursive.

2020-02-29T15:21:51Z

Changed "recur" to "recurse" in pseudocode description of algorithm. This was likely a typo, as "recurse" is the verb form of "recursion", and the standard implementation of the DT algorithm is in fact recursive.

← Previous revision		Revision as of 15:21, 29 February 2020
Line 22:		Line 22:
	#Let ''a_best'' be the attribute with the highest normalized information gain.		#Let ''a_best'' be the attribute with the highest normalized information gain.
	#Create a decision ''node'' that splits on ''a_best''.		#Create a decision ''node'' that splits on ''a_best''.
	#~~Recur~~ on the sublists obtained by splitting on ''a_best'', and add those nodes as children of ''node''.		#Recurse on the sublists obtained by splitting on ''a_best'', and add those nodes as children of ''node''.

	==Implementations==		==Implementations==

Frap: /* pseudocode */ MOS:HEAD

2020-02-21T14:53:33Z

pseudocode: MOS:HEAD

← Previous revision		Revision as of 14:53, 21 February 2020
Line 14:		Line 14:
	*Instance of previously-unseen class encountered. Again, C4.5 creates a decision node higher up the tree using the expected value.		*Instance of previously-unseen class encountered. Again, C4.5 creates a decision node higher up the tree using the expected value.

	===~~pseudocode~~===		===Pseudocode===

	In [[pseudocode]], the general algorithm for building decision trees is:<ref>S.B. Kotsiantis, "Supervised Machine Learning: A Review of Classification Techniques", ''Informatica'' 31(2007) 249-268, 2007</ref>		In [[pseudocode]], the general algorithm for building decision trees is:<ref>S.B. Kotsiantis, "Supervised Machine Learning: A Review of Classification Techniques", ''Informatica'' 31(2007) 249-268, 2007</ref>

← Previous revision		Revision as of 20:39, 23 June 2024
Line 1:		Line 1:
	{{Short description\|Algorithm for making decision trees}}		{{Short description\|Algorithm for making decision trees}}
	{{More footnotes\|date=July 2008}}		{{More footnotes\|date=July 2008}}
			[[File:Diagramm_beispiel_sarah_geht_segeln.png \| thumb \| right]]
	'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>		'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>

← Previous revision		Revision as of 11:08, 15 May 2024
Line 1:		Line 1:
			{{Short description\|Algorithm for making decision trees}}
	{{More footnotes\|date=July 2008}}		{{More footnotes\|date=July 2008}}
	'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>		'''C4.5''' is an algorithm used to generate a [[decision tree]] developed by [[Ross Quinlan]].<ref>Quinlan, J. R. C4.5: ''Programs for Machine Learning''. Morgan Kaufmann Publishers, 1993.</ref> C4.5 is an extension of Quinlan's earlier [[ID3 algorithm]]. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a [[Statistical classification\|statistical classifier]]. In 2011, authors of the [[Weka (machine learning)\|Weka]] machine learning software described the C4.5 algorithm as "a landmark decision tree program that is probably the machine learning workhorse most widely used in practice to date".<ref>{{cite web \|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html \|title=Data Mining: Practical machine learning tools and techniques, 3rd Edition \|author=Ian H. Witten \|author2=Eibe Frank \|author3=Mark A. Hall \|year=2011 \|publisher=Morgan Kaufmann, San Francisco \| page=191 }}</ref>

← Previous revision		Revision as of 21:05, 5 January 2024
Line 7:		Line 7:
	C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.		C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.

	At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information gain in decision trees\|information gain]] (difference in ~~[[Entropy (information theory)\|~~entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.		At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information gain in decision trees\|information gain]] (difference in entropy). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.

	This algorithm has a few [[Base case (recursion)\|base cases]].		This algorithm has a few [[Base case (recursion)\|base cases]].

← Previous revision		Revision as of 19:20, 20 April 2021
Line 7:		Line 7:
	C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.		C4.5 builds decision trees from a set of training data in the same way as [[ID3 algorithm\|ID3]], using the concept of [[Entropy (information theory)\|information entropy]]. The training data is a set <math>S = {s_1, s_2, ...}</math> of already classified samples. Each sample <math> s_i</math> consists of a p-dimensional vector <math>(x_{1,i}, x_{2,i}, ...,x_{p,i}) </math>, where the <math> x_j </math> represent attribute values or [[Feature (machine learning)\|features]] of the sample, as well as the class in which <math> s_i </math> falls.

	At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information_gain_in_decision_trees\|information gain]] (difference in [[Entropy (information theory)\|entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.		At each node of the tree, C4.5 chooses the attribute of the data that most effectively splits its set of samples into subsets enriched in one class or the other. The splitting criterion is the normalized [[Information_gain_in_decision_trees\|information gain]] (difference in [[Entropy (information theory)\|entropy]]). The attribute with the highest normalized information gain is chosen to make the decision. The C4.5 algorithm then [[Recursion (computer science)\|recurses]] on the [[Partition of a set\|partitioned]] sublists.

	This algorithm has a few [[Base case (recursion)\|base cases]].		This algorithm has a few [[Base case (recursion)\|base cases]].