Algorithm::DecisionTree - A Perl module for constructing a decision tree from multidimensional training data and for using the decision tree thus constructed for classifying new data.
# FOR CONSTRUCTING A DECISION TREE AND FOR CLASSIFYING A SAMPLE: # If your training data includes numeric features (a feature is numeric if it can # take any floating point value over an interval), you are expected to supply your # training data through a CSV file and your call for constructing a decision tree # will look like: my $training_datafile = "stage3cancer.csv"; my $dt = Algorithm::DecisionTree->new( training_datafile => $training_datafile, csv_class_column_index => 2, csv_columns_for_features => [3,4,5,6,7,8], entropy_threshold => 0.01, max_depth_desired => 8, symbolic_to_numeric_cardinality_threshold => 10, ); # The constructor option `csv_class_column_index' informs the module as to which # column of your CSV file contains the class label. THE COLUMN INDEXING IS ZERO # BASED. The constructor option `csv_columns_for_features' specifies which columns # are to be used for feature values. The first row of the CSV file must specify # the names of the features. See examples of CSV files in the `examples' # subdirectory. # The option `symbolic_to_numeric_cardinality_threshold' is also important. For # the example shown above, if an ostensibly numeric feature takes on only 10 or # fewer different values in your training datafile, it will be treated like a # symbolic features. The option `entropy_threshold' determines the granularity # with which the entropies are sampled for the purpose of calculating entropy gain # with a particular choice of decision threshold for a numeric feature or a feature # value for a symbolic feature. # After you have constructed an instance of the DecisionTree module, you read in # the training data file and initialize the probability cache by calling: $dt->get_training_data(); $dt->calculate_first_order_probabilities(); $dt->calculate_class_priors(); # Now you are ready to construct a decision tree for your training data by calling: $root_node = $dt->construct_decision_tree_classifier(); # where $root_node is an instance of DTNode class that is also defined in the # module file. Now you are ready to classify a data record. Let's say that your # data record looks like: my @test_sample = qw / g2=4.2 grade=2.3 gleason=4 eet=1.7 age=55.0 ploidy=diploid /; # You can classify it by calling: my $classification = $dt->classify($root_node, \@test_sample); # The call to `classify()' returns a reference to a hash whose keys are the class # names and the values the associated classification probabilities. This hash also # includes another key-value pair for the solution path from the root node to the # leaf node at which the final classification was carried out. # FOR THE CASE OF PURELY SYMBOLIC FEATURES: # If your features are purely symbolic, you can continue to use the same # constructor syntax that was used in the older versions of this module. However, # your old `.dat' training files will not work with the new version. The good news # is that with just a small fix, you can continue to use them. The fix and why it # was needed is described in the file README_for_dat_files in the `examples' # directory.
Version 2.2 makes it easier to write code for classifying in one go all of your test data samples in a CSV file. The bulk classifications obtained can be written out to either a CSV file or to a regular text file. See the script
classify_test_data_in_a_file_numeric.pl in the
examples directory for how to classify all of your test data records in a CSV file. This version also includes improved code for generating synthetic numeric/symbolic training and test data records for experimenting with the decision tree classifier.
Version 2.1 allows you to test the quality of your training data by running a 10-fold cross-validation test on the data. This test divides all of the training data into ten parts, with nine parts used for training a decision tree and one part used for testing its ability to classify correctly. This selection of nine parts for training and one part for testing is carried out in all of the ten different ways that are possible. This testing functionality in Version 2.1 can also be used to find the best values to use for the constructor parameters
Version 2.0 is a major rewrite of this module. Now you can use both numeric and symbolic features for constructing a decision tree. A feature is numeric if it can take any floating-point value over an interval.
Version 1.71 fixes a bug in the code that was triggered by 0 being declared as one of the features values in the training datafile. Version 1.71 also include an additional safety feature that is useful for training datafiles that contain a very large number of features. The new version makes sure that the number of values you declare for each sample record matches the number of features declared at the beginning of the training datafile.
Version 1.7 includes safety checks on the consistency of the data you place in your training datafile. When a training file contains thousands of samples, it is difficult to manually check that you used the same class names in your sample records that you declared at top of your training file or that the values you have for your features are legal vis-a-vis the earlier declarations of the values in the training file. Another safety feature incorporated in this version is the non-consideration of classes that are declared at the top of the training file but that have no sample records in the file.
Version 1.6 uses probability caching much more extensively compared to the previous versions. This should result in faster construction of large decision trees. Another new feature in Version 1.6 is the use of a decision tree for interactive classification. In this mode, after you have constructed a decision tree from the training data, the user is prompted for answers to the questions pertaining to the feature tests at the nodes of the tree.
Some key elements of the documentation were cleaned up and made more readable in Version 1.41. The implementation code remains unchanged from Version 1.4.
Version 1.4 should make things faster (and easier) for folks who want to use this module with training data that creates very large decision trees (that is, trees with tens of thousands or more decision nodes). The speedup in Version 1.4 has been achieved by eliminating duplicate calculation of probabilities as the tree grows. In addition, this version provides an additional constructor parameter,
max_depth_desired for controlling the size of the decision tree. This is in addition to the tree size control achieved by the parameter
entropy_threshold that was introduced in Version 1.3. Since large decision trees can take a long time to create, you may find yourself wishing you could store the tree you just created in a disk file and that, subsequently, you could use the stored tree for classification work. The
examples directory contains two scripts,
classify_from_disk_stored_dt.pl, that show how you can do exactly that with the help of Perl's
Version 1.3 addresses the issue that arises when the header of a training datafile declares a certain possible value for a feature but that (feature,value) pair does NOT show up anywhere in the training data. Version 1.3 also makes it possible for a user to control the size of the decision tree by changing the value of the parameter
entropy_threshold. Additionally, Version 1.3 includes a method called
determine_data_condition() that displays useful information regarding the size and some other attributes of the training data. It also warns the user if the training data might result in a decision tree that would simply be much too large --- unless the user controls the size with the entropy_threshold parameter.
In addition to the removal of a couple of serious bugs, version 1.2 incorporates a number of enhancements: (1) Version 1.2 includes checks on the names of the features and values used in test data --- this is the data you want to classify with the decision tree classifier constructed by this module. (2) Version 1.2 includes a separate constructor for generating test data. To make it easier to generate test data whose probabilistic parameters may not be identical to that used for the training data, I have used separate routines for generating the test data. (3) Version 1.2 also includes in its examples directory a script that classifies the test data in a file and outputs the class labels into another file. This is for folks who do not wish to write their own scripts using this module. (4) Version 1.2 also includes addition to the documentation regarding the issue of numeric values for features.
For those transitioning from versions older than 2.0 of this module, if your training data consists of numeric features, or has a combination of numeric and symbolic features, you MUST use a CSV file to supply your data to the module. Additionally, this CSV file must satisfy certain formatting constraints. See
README_for_CSV_files in the
examples directory for what these formatting restrictions are. And, even if your training data is purely symbolic, your old-style `
.dat' training files will not work with the new module. See
README_for_dat_files in the
examples directory for the formatting related to the new `
Algorithm::DecisionTree is a perl5 module for constructing a decision tree from a training datafile containing multidimensional data. In one form or another, decision trees have been around for about fifty years. From a statistical perspective, they are closely related to classification and regression by recursive partitioning of multidimensional data. Early work that demonstrated the usefulness of recursive partitioning of data can be traced, in the statistics community, to the contributions by Terry Therneau in the early 1980's and, in the machine learning community, to the work of Ross Quinlan in the mid 1990's.
For those not familiar with decision tree ideas, the traditional way to classify multidimensional data is to start with a feature space whose dimensionality is the same as that of the data. Each feature in this space corresponds to the attribute that each dimension of the data measures. You then use the training data to carve up the feature space into different regions, each corresponding to a different class. Subsequently, when you try to classify a new data sample, you locate it in the feature space and find the class label of the region to which it belongs. One can also give the new data point the same class label as that of the nearest training sample. This is referred to as the nearest neighbor classification.
A decision tree classifier works differently. When you construct a decision tree, you select for the root node a feature test that partitions the training data in a way that causes maximal disambiguation of the class labels associated with the data. In terms of information content as measured by entropy, such a feature test would cause maximum reduction in class entropy in going from all of the training data taken together to the data as partitioned by the feature test. You then drop from the root node a set of child nodes, one for each partition of the training data created by the feature test at the root node. When your features are purely symbolic, you'll have one child node for each value of the feature chosen for the feature test at the root. When the test at the root involves a numeric feature, you find the decision threshold for the feature that best bipartitions the data and you drop from the root node two child nodes, one for each partition. Now at each child node you pose the same question that you posed when you found the best feature to use at the root: Which feature at the child node in question would maximally disambiguate the class labels associated with the training data corresponding to that child node?
As the reader would expect, the two key steps in any approach to decision-tree based classification are the construction of the decision tree itself from a file containing the training data, and then using the decision tree thus obtained for classifying new data.
What is cool about decision tree classification is that it gives you soft classification, meaning it may associate more than one class label with a given data vector. When this happens, it may mean that your classes are indeed overlapping in the underlying feature space. It could also mean that you simply have not supplied sufficient training data to the decision tree classifier. For a tutorial introduction to how a decision tree is constructed and used, visit https://engineering.purdue.edu/kak/Tutorials/DecisionTreeClassifiers.pdf
This module also allows you to generate your own synthetic training and test data. Generating your own training data, using it for constructing a decision-tree classifier, and subsequently testing the classifier on a synthetically generated test set of data is a good way to develop greater proficiency with decision trees.
If you are new to the concept of a decision tree, their practical utility is best understood with an example that only involves symbolic features. However, as mentioned earlier, versions of the module higher than 2.0 allow you to use both symbolic and numeric features.
Consider the following scenario: Let's say you are running a small investment company that employs a team of stockbrokers who make buy/sell decisions for the customers of your company. Assume that your company has asked the traders to make each investment decision on the basis of the following four criteria:
price_to_earnings_ratio (P_to_E) price_to_sales_ratio (P_to_S) return_on_equity (R_on_E) market_share (MS)
Since you are the boss, you keep track of the buy/sell decisions made by the individual traders. But one unfortunate day, all of your traders decide to quit because you did not pay them enough. So what do you do? If you had a module like the one here, you could still run your company and do so in such a way that, on the average, would do better than any of the individual traders who worked for your company. This is what you do: You pool together the individual trader buy/sell decisions you have accumulated during the last one year. This pooled information is likely to look like:
example buy/sell P_to_E P_to_S R_on_E MS ============================================================+= example_1 buy high low medium low example_2 buy medium medium low low example_3 sell low medium low high .... ....
This data would constitute your training file. You could feed this file into the module by calling:
my $dt = Algorithm::DecisionTree->new( training_datafile => $training_datafile, ); $dt->get_training_data(); $dt->calculate_first_order_probabilities(); $dt->calculate_class_priors();
Subsequently, you would construct a decision tree by calling:
my $root_node = $dt->construct_decision_tree_classifier();
Now you and your company (with practically no employees) are ready to service the customers again. Suppose your computer needs to make a buy/sell decision about an investment prospect that is best described by:
price_to_earnings_ratio = low price_to_sales_ratio = very_low return_on_equity = none market_share = medium
All that your computer would need to do would be to construct a data vector like
my @data = qw / P_to_E=low P_to_S=very_low R_on_E=none MS=medium /;
and call the decision tree classifier you just constructed by
The answer returned will be 'buy' and 'sell', along with the associated probabilities. So if the probability of 'buy' is considerably greater than the probability of 'sell', that's what you should instruct your computer to do.
The chances are that, on the average, this approach would beat the performance of any of your individual traders who worked for you previously since the buy/sell decisions made by the computer would be based on the collective wisdom of all your previous traders. DISCLAIMER: There is obviously a lot more to good investing than what is captured by the silly little example here. However, it does nicely the convey the sense in which the current module could be used.
A feature is symbolic when its values are compared using string comparison operators. By the same token, a feature is numeric when its values are compared using numeric comparison operators. Having said that, features that take only a small number of numeric values in the training data can be treated symbolically provided you are careful about handling their values in the test data. At the least, you have to set the test data value for such a feature to its closest value in the training data. The module does that automatically for you for those numeric features for which the number different numeric values is less than a user-specified threshold.
The constructor parameter
symbolic_to_numeric_cardinality_threshold let's you tell the module when to consider an otherwise numeric feature symbolically. Suppose you set this parameter to 10, that means that all numeric looking features that take 10 or fewer different values in the training datafile will be considered to be symbolic features by the module. See the tutorial at https://engineering.purdue.edu/kak/Tutorials/DecisionTreeClassifiers.pdf for further information on the implementation issues related to the symbolic and numeric features.
Version 2.1 includes a new class named
EvalTrainingData, derived from the main class
DecisionTree, that runs a 10-fold cross-validation test on your training data to test its ability to discriminate between the classes mentioned in the training file.
The 10-fold cross-validation test divides all of the training data into ten parts, with nine parts used for training a decision tree and one part used for testing its ability to classify correctly. This selection of nine parts for training and one part for testing is carried out in all of the ten different possible ways.
The following code fragment illustrates how you invoke the testing function of the EvalTrainingData class:
my $training_datafile = "training.csv"; my $eval_data = EvalTrainingData->new( training_datafile => $training_datafile, csv_class_column_index => 1, csv_columns_for_features => [2,3], entropy_threshold => 0.01, max_depth_desired => 3, symbolic_to_numeric_cardinality_threshold => 10, ); $eval_data->get_training_data(); $eval_data->evaluate_training_data()
The last statement above prints out a Confusion Matrix and the value of Training Data Quality Index on a scale of 0 to 100, with 100 designating perfect training data. The Confusion Matrix shows how the different classes were mis-labeled in the 10-fold cross-validation test.
This testing functionality can also be used to find the best values to use for the constructor parameters
The following two scripts in the
examples directory illustrate the use of the
EvalTrainingData class for testing the quality of your data:
The module provides the following methods for constructing a decision tree from training data in a disk file and for classifying new data records with the decision tree thus constructed:
my $dt = Algorithm::DecisionTree->new( training_datafile => $training_datafile, csv_class_column_index => 2, csv_columns_for_features => [3,4,5,6,7,8], entropy_threshold => 0.01, max_depth_desired => 8, symbolic_to_numeric_cardinality_threshold => 10, );
A call to
new() constructs a new instance of the
Algorithm::DecisionTree class. For this call to make sense, the training data in the training datafile must be according to a certain format. For the format, see the files
training.dat in the
examples directory. If your training data includes numeric features, you must use a CSV file for supplying the data to the module. The previous versions of this module used `
.dat' files for the training data. You can still use your old `
.dat' files provided you modify them a little bit. See
README_for_dat_files in the
examples directory for how to modify your old
.dat files. Note that column indexing is zero-based. With the index set to 2 as shown above, the class labels are in the third column for the above case.
This parameter supplies the name of the file that contains the training data. This must be a CSV file if your training data includes both numeric and symbolic features. If your data is purely symbolic, you can use the old-style `.dat' file.
When using a CSV file for your training data, this parameter supplies the zero-based column index for the column that contains the class label for each data record in the training file.
When using a CSV file for your training data, this parameter supplies a list of columns corresponding to the features you wish to use for decision tree construction. Each column is specified by its zero-based index.
This parameter sets the granularity with which the entropies are sampled by the module. For example, a feature test at a node in the decision tree is acceptable if the entropy gain achieved by the test exceeds this threshold. The larger the value you choose for this parameter, the smaller the tree. Its default value is 0.001.
This parameter sets the maximum depth of the decision tree. For obvious reasons, the smaller the value you choose for this parameter, the smaller the tree.
This parameter allows the module to treat an otherwise numeric feature symbolically if the number of different values the feature takes in the training data file does not exceed the value of this parameter.
You can choose the best values to use for the last three constructor parameters by running a 10-fold cross-validation test on your training data through the class
EvalTrainingData that comes with Version 2.1 of this module. See the section "TESTING THE QUALITY OF YOUR TRAINING DATA" of this document page.
After you have constructed a new instance of the
Algorithm::DecisionTree class, you must now read in the training data that is the file named in the call to the constructor. This you do by:
IMPORTANT: The training datafile must be in a format that makes sense to the decision tree constructor. See the files
README_for_dat_files in the
examples directory for these formats. Also see the files
training.dat for examples of such files.
If you wish to see the training data that was just digested by the module, call
After the module has read the training data file, it needs to initialize the probability cache. This you do by invoking:
With the probability cache initialized, it is time to construct a decision tree classifier. This you do by
my $root_node = $dt->construct_decision_tree_classifier();
This call returns an instance of type
DTNode class is defined within the main package file. So, don't forget, that
$root_node in the above example call will be instantiated to an object of type
This will display the decision tree in your terminal window by using a recursively determined offset for each node as the display routine descends down the tree.
I have intentionally left the syntax fragment
$root_node in the above call to remind the reader that
display_decision_tree() is NOT called on the instance of the
DecisionTree we constructed earlier, but on the
DTNode instance returned by the call to
Let's say you want to classify the following data record:
my @test_sample = qw / g2=4.2 grade=2.3 gleason=4 eet=1.7 age=55.0 ploidy=diploid /;
you'd make the following call:
my $classification = $dt->classify($root_node, \@test_sample);
$root_node is an instance of type
DTNode returned by the call to
construct_decision_tree_classifier(). The variable
$classification holds a reference to a hash whose keys are the class names and whose values the associated probabilities. The hash that is returned by the above call also includes a special key-value pair for a key named
solution_path. The value associated with this key is an anonymous array that holds the path, in the form of a list of nodes, from the root node to the leaf node in the decision tree where the final classification was made.
This method allows you to use a decision-tree based classifier in an interactive mode. In this mode, a user is prompted for answers to the questions pertaining to the feature tests at the nodes of the tree. The syntax for invoking this method is:
my $classification = $dt->classify_by_asking_questions($root_node);
$dt is an instance of the
Algorithm::DecisionTree class returned by a call to
$root_node the root node of the decision tree returned by a call to
The module file contains the following additional classes: (1)
TrainingAndTestDataGeneratorNumeric, and (2)
TrainingAndTestDataGeneratorSymbolic for generating synthetic training and test data.
TrainingAndTestDataGeneratorNumeric outputs one CSV file for the training data and another one for the test data for experimenting with numeric features. The numeric values are generated using a multivariate Gaussian distribution whose mean and covariance are specified in a parameter file. See the file
param_numeric.txt in the
examples directory for an example of such a parameter file. Note that the dimensionality of the data is inferred from the information you place in the parameter file.
TrainingAndTestDataGeneratorSymbolic generates synthetic training and test data for the purely symbolic case. The relative frequencies of the different possible values for the features is controlled by the biasing information you place in a parameter file. See
param_symbolic.txt for an example of such a file.
It depends on whether you apply the classifier at once to all the data samples in a file, or whether you feed one data sample at a time into the classifier.
In general, the classifier returns soft classification for a test data vector. What that means is that, in general, the classifier will list all the classes to which a given data vector could belong and the probability of each such class label for the data vector. Run the examples scripts in the Examples directory to see how the output of classification can be displayed.
For large test datasets, you would obviously want to process an entire file of test data samples in one go. As to how you can do that, see the following two scripts in the
the first for the case of numeric/symbolic data placed in a CSV file and the second case of purely symbolic data placed in a `.dat' file. These script requires three command-line arguments, the first argument names the training datafile, the second the test datafile, and the third in which the classification results will be deposited. The test data files for both the numeric/symbolic and the purely symbolic cases must look like the training data files. If the test data files do not mention the class labels --- as will be the case for real-world test data --- you must still have a column for the class labels with the entries set to the empty string
"". The test datafile for the purely symbolic case must mention the order in which the features values are presented. For an example, see the file
testdata.dat in the
A special feature of the script
classify_test_data_in_a_file_numeric.pl is that its last command-line argument (meaning the 3rd argument) can be either a
.csv filename or a
.txt filename. As you'd expect, the output classifications are displayed in a CSV format for the former case. For the latter case, the results are shown with white-space separation between the different class names and their probabilities. Additionally, for the latter case, you can the tell the script either to show you only the most probable class for each data sample or all the classes. You control this choice by setting the variable
$show_hard_classifications in the script. When this variable is set, you'll only be shown the most probable class for each sample when the output is to a
With regard to the soft classifications returned by this classifier, if the probability distributions for the different classes overlap in the underlying feature space, you would want the classifier to return all of the applicable class labels for a data vector along with the corresponding class probabilities. Another reason for why the decision tree classifier may associate significant probabilities with multiple class labels is that you used inadequate number of training samples to induce the decision tree. The good thing is that the classifier does not lie to you (unlike, say, a hard classification rule that would return a single class label corresponding to the partitioning of the underlying feature space). The decision tree classifier give you the best classification that can be made given the training data you fed into it.
examples directory in the distribution for how to construct a decision tree, and how to then classify new data using the decision tree. To become more familiar with the module, run the scripts
construct_dt_and_classify_one_sample_case1.pl construct_dt_and_classify_one_sample_case2.pl construct_dt_and_classify_one_sample_case3.pl construct_dt_and_classify_one_sample_case4.pl
The first script is for the purely symbolic case, the second for the case that involves both numeric and symbolic features, the third for the case of purely numeric features, and the last for the case when the training data is synthetically generated by the script
Next run the following scripts just as you find them:
classify_test_data_in_a_file_numeric.pl training4.csv test4.csv out4.csv classify_test_data_in_a_file_symbolic.pl training4.dat test4.dat out4.dat
and examine the contents of the output files
out4.dat. Each of above two scripts first constructs a decision tree using the training data in the training file supplied by the first command-line argument. The script then calculates the class label for each data record in the test data file supplied through the second command-line argument. The estimated class labels are written out to the output file named by the third argument.
In general, for the two calls shown above, the test data files should look identical to the training data files. Of course, for real-world test data, you will not have the class labels for the test samples. For real-world test data, you are still required to reserve a column for the class label, which now must be just the empty string
"" for each data record. For example, the test data records supplied in the following two calls through the files
test4_no_class_labels.dat do not mention class labels:
classify_test_data_in_a_file_numeric.pl training4.csv test4_no_class_labels.csv out4.csv classify_test_data_in_a_file_symbolic.pl training4.dat test4_no_class_labels.dat out4.dat
For bulk classification, the output file can also be a
.txt file. In that case, you will see white-space separate results in the output file. When you mention a
.txt file for the output, you can control the extent of information placed in the output file by setting the variable
$show_hard_classifications in the scripts. If this variable is set, the output will show only the most probable class for each test data record.
The following script in the
shows how you can use a decision-tree classifier interactively. In this mode, you first construct the decision tree from the training data and then the user is prompted for answers to the feature tests at the nodes of the tree.
examples directory also contains the following scripts:
that show how you can use the module to generate synthetic training and test data. Synthetic training and test data are generated according to the specifications laid out in a parameter file. There are constraints on how the information is laid out in a parameter file. See the files
param_symbolic.txt in the
examples directory for how to structure these files.
examples directory of Version 2.1 and above of the
DecisionTree module also contains the following two scripts:
that illustrate how the Perl class
EvalTrainingData can be used to evaluate the quality of your training data (as long as it resides in a `
.csv' file.) This new class is a subclass of the
DecisionTree class in the module file. See the README in the
examples directory for further information regarding these two scripts.
None by design.
Please notify the author if you encounter any bugs. When sending email, please place the string 'DecisionTree' in the subject line.
perl Makefile.PL make make test make install
if you have root access. If not,
perl Makefile.PL prefix=/some/other/directory/ make make test make install
I wish to thank many users of this module for their feedback. Many of the improvements I have made to the module over the years are a result of the feedback received.
Avinash Kak, email@example.com
If you send email, please place the string "DecisionTree" in your subject line to get past my spam filter.
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
Copyright 2014 Avinash Kak