Algorithm::DecisionTree - A pure-Perl implementation for constructing a decision tree from multidimensional training data and for using the decision tree thus induced for classifying data.

- SYNOPSIS
- CHANGES
- DESCRIPTION
- WHAT PRACTICAL PROBLEM IS SOLVED BY THIS MODULE
- WHAT HAPPENS If I HAVE "TOO MANY" FEATURES AND/OR "TOO MANY" POSSIBLE VALUES FOR THE FEATURES
- WHAT HAPPENS WHEN THE FEATURE VALUES ARE NUMERIC
- METHODS
- HOW THE CLASSIFICATION RESULTS ARE DISPLAYED
- EXAMPLES
- EXPORT
- BUGS
- INSTALLATION
- AUTHOR
- COPYRIGHT

Algorithm::DecisionTree - A pure-Perl implementation for constructing a decision tree from multidimensional training data and for using the decision tree thus induced for classifying data.

# SYNOPSIS

      # FOR CONSTRUCTING A DECISION TREE AND FOR CLASSIFYING A SAMPLE:

          my $training_datafile = "training.dat";
          my $dt = Algorithm::DecisionTree->new(
                                   training_datafile => $training_datafile,
                                   entropy_threshold => 0.05,
                                   debug1 => 1,
          );
          $dt->get_training_data();
          $dt->show_training_data();
          my $root_node = $dt->construct_decision_tree_classifier();
          $root_node->display_decision_tree("   ");
          my @test_sample = qw /exercising=>never
                                smoking=>heavy
                                fatIntake=>heavy
                                videoAddiction=>heavy /;
          $dt->classify($root_node, @test_sample);

      # For the above calls to work, the format in which the training data is made
      # available to the decision-tree constructor new() must meet certain
      # assumptions.  (See the training.dat file in the examples directory.)  The
      # training datafile must declare the class names, the feature names and the
      # names of the different possible values for the features.  The rest of the
      # training datafile is expected to contain the training samples in the form of
      # a multi-column table.

      # HIGHLY RECOMMENDED: Always use the "debug1" option in the constructor call
      # above when working with a dataset for the first time.

      # FOR GENERATING TRAINING DATA:

          use Algorithm::DecisionTree;
          my $parameter_file = "param.txt";
          my $output_data_file = "training.dat";
          my $training_data_gen = Algorithm::DecisionTree->training_data_generator(
                                      output_datafile => $output_data_file,
                                      parameter_file    => $parameter_file,
                                      number_of_training_samples => 35,
          );
          $training_data_gen->read_parameter_file();
          $training_data_gen->gen_training_data();
          $training_data_gen->write_training_data_to_file();

      # For the above calls to work, the parameter file must obey certain
      # assumptions.  (See the param.txt file in the examples directory.) The
      # parameter file must declare the class names, the class priors, the
      # feature names and the different possible values for the features.
      # The parameter file is also expected to present information on how
      # you want the data vectors to be biased for the different classes.

      # FOR GENERATING TEST DATA:

          use Algorithm::DecisionTree;
          my $parameter_file = "param.txt";
          my $output_test_datafile = "testdata.dat";
          my $output_class_label_file = "test_data_class_labels.dat";
          my $test_data_gen = Algorithm::DecisionTree->test_data_generator(
                       output_test_datafile    => $output_test_datafile,
                       output_class_label_file => $output_class_label_file,
                       parameter_file          => $parameter_file,
                       write_to_file           => 1,
                       number_of_test_samples  => 10,
                       debug1                  => 1,
          );
          $test_data_gen->read_parameter_file();
          $test_data_gen->gen_test_data();
          $test_data_gen->write_test_data_to_file();

      # The test data is deposited without the class labels in the file named for
      # the parameter output_test_datafile.  The class labels are deposited
      # in a separate file named for the parameter output_class_label_file.  The
      # class names, the feature names, the feature values, and the probabilistic
      # bias used for the test data are according to the information placed in
      # the parameter file.

# CHANGES

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.

With Version 1.1, a call to `classify()` now returns a hash of the class labels and their associated probabilities. (Previously, these results were just printed out in the terminal window.) Now you should be able to write your own script that reads in the test data from a file and outputs the classification results for each data vector. This version also includes some additional documentation and a general cleanup of the code.

# DESCRIPTION

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. But their popularity during the last decade is owing to the entropy-based method proposed by Ross Quinlan for their construction. Fundamental to Quinlan's approach is the notion that a decision node in a tree should be split only if the entropy at the ensuing child nodes will be less than the entropy at the node in question. The implementation presented here is based on the same idea.

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 would correspond 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 are trying 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 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 can be expected to maximally disambiguate the class labels that could be associated with the data you are trying to classify. You then attach to the root node a set of child nodes, one for each value of the feature you chose at the root node. Now at each child node you pose the same question that you posed when you found the best feature to use at the root node: What feature at the child node in question would maximally disambiguate the class labels to be associated with a given data vector assuming that the data vector passed the root node on the branch that corresponds to the child node in question. The feature that is best at each node is the one that causes the maximal reduction in class entropy at that 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 the data.

In addition to the above two key steps, the implementation presented here also allows you to generate your own training data. Generating your own training data, using it for constructing a decision-tree classifier and subsequently testing the classifier on a test set of data is a good way to develop greater proficiency with decision trees.

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, please visit http://cobweb.ecn.purdue.edu/~kak/DecisionTreeClassifiers.pdf

# WHAT PRACTICAL PROBLEM IS SOLVED BY THIS MODULE

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();

and then 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

        $dt->classify($root_node, @data);

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 the convey the sense in which the current module could be used.

# WHAT HAPPENS If I HAVE "TOO MANY" FEATURES AND/OR "TOO MANY" POSSIBLE VALUES FOR THE FEATURES

If n is the number of features and m the largest number for the possible values for any of the features, then, in the worst case, the algorithm would want to construct m to the power of n nodes. In other words, the size of the decision tree grows exponentially as you increase either the number of features or the number of possible values for the features. That is the bad news. The good news is that you can control the actual number of nodes created by increasing the value of the parameter entropy_threshold in the call to the decision tree constructor. The default value for this parameter is 0.001.

It is always a good idea to keep the debug1 option set anytime you are experimenting with a new datafile --- especially if your training has the potential to create an inordinately large decision tree.

# WHAT HAPPENS WHEN THE FEATURE VALUES ARE NUMERIC

The current module will treat a numeric value for a feature as just a string. In that sense, there is no difference between a string value for a feature and a numeric value. This would obviously make the module unsuitable for applications in which a feature may take on a numeric value from a very large set of such values and you want feature values to be compared using numeric comparison predicates as opposed to string comparison predicates. (Consider, for example, using color as an object feature in a computer vision application.) The decision trees for applications in which the feature values are primarily numerical in nature are constructed differently, as explained in the tutorial at http://cobweb.ecn.purdue.edu/~kak/DecisionTreeClassifiers.pdf

# METHODS

The module provides the following methods for decision-tree induction from training data in a diskfile, for data classification with the decision tree, and for generating your own training data:

new():

          my $dt = Algorithm::DecisionTree->new(
                                                training_datafile => $training_datafile,
                                               );

  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 that is shown below. (Also see the file training.dat in the examples directory.)

get_training_data():

  After you have constructed a new instance of the Algorithm::DecisionTree class, you must now read in the training data that is contained in the file named above. This you do by:

          $dt->get_training_data();

  IMPORTANT: The training data file must in a format that makes sense to the decision tree constructor. The information in this file should look like

          Class names: malignant benign

          Feature names and their values:
              videoAddiction => none low medium heavy
              exercising => never occasionally regularly
              smoking => heavy medium light never
              fatIntake => low medium heavy

          Training Data:

          sample     class      videoAddiction   exercising    smoking   fatIntake
          ==========================================================================

          sample_0   benign     medium           occasionally  heavy     low
          sample_1   malignant  none             occasionally  heavy     medium
          sample_2   benign     low              occasionally  light     heavy
          sample_3   malignant  medium           occasionally  heavy     heavy
          ....
          ....

  IMPORTANT: Note that the class names, the number of classes, the feature names, and the possible values for the features can be anything that your data requires them to be. The training data file that is generated by the data generation part of the module will be in the format shown above. More on that later.

show_training_data():

  If you wish to see the training data that was just digested by the module, call

          $dt->show_training_data();

construct_decision_tree_classifier():

  After the training data is digested, 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 Node. The Node class is defined within the main package file, at its end. So, don't forget, that $root_node in the above example call will be instantiated to an instance of type Node.

$root_node`->`display_decision_tree(" "):

          $root_node->display_decision_tree("   ");

  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 Node instance returned by the call to `construct_decision_tree_classifier()`.

classify($root_node, @test_sample):

          my @test_sample = qw /exercising=>never
                                smoking=>heavy
                                fatIntake=>heavy
                                videoAddiction=>heavy /;

          my $classification = $dt->classify($root_node, @test_sample);

  where, again, $root_node is an instance of type Node returned by the call to `construct_decision_tree_classifier()`. The variable $classification holds a reference to a hash whose keys are the class labels and whose values the associated probabilities.

determine_data_condition():

  This method, automatically invoked when debug1 option is set in the call to the decision-tree constructor, displays useful information regarding your training data file. This method also warns you if you are trying to construct a decision tree that may simply be much too large.

          $dt->determine_data_condition();

training_data_generator():

  The training data generator is created by using its own constructor:

          my $parameter_file = "param2.txt";
          my $output_data_file = "training.dat";
          my $training_data_gen = Algorithm::DecisionTree->training_data_generator(
                                    output_datafile => $output_data_file,
                                    parameter_file    => $parameter_file,
                                    number_of_training_samples => 35,
          );

$training_data_gen`->`read_parameter_file():

  After you have constructed an instance of the training data generator, you need to ask it to read the parameter file:

          $training_data_gen->read_parameter_file();

  The parameter file is expected to be in the following format:

          # comment lines begin with the hash mark

          class names:  malignant benign
          class priors: 0.4 0.6

          feature: smoking
          values: heavy medium light never

          feature: exercising
          values: never occasionally regularly

          feature: fatIntake
          values: low medium heavy

          feature: videoAddiction
          values:  none low medium heavy

          bias:  class: malignant

                smoking:    heavy=0.7
                exercising: never=0.7
                fatIntake:  heavy=0.5
                videoAddiction:

          bias:  class: benign

                smoking:     heavy=0.1
                exercising:  regularly=0.7
                fatIntake:   low=0.6
                videoAddiction:

  See the parameter file param.txt in the example directory. Initially, it might be best to modify that file to suit your needs.

  IMPORTANT: You can use any names for the classes, can have any number of classes, can use any names for the features and their values.

  Also note the the important role played by the biasing information. Without the biasing, your training data will be uniformly distributed with respect to all of the feature values and you will only get ambiguous classifications from the resulting decision tree classifier. The biasing allows you to express a higher or lower probability that a particular feature value should have for a given class. The probability weight that is unused for each feature is distributed uniformly amongst the remaining feature values. I did experiment with the idea of assigning probability weights to multiple (or even all) of the values for a given feature --- it does not add to the educational value you derive from the resulting training data.

  NOTE: if you do NOT express a bias for a feature (as is the case with the feature 'videoAddiction' above), equal weight is given to all its values.

$training_data_gen`->`gen_training_data():

  This call generators the training data from your parameter file:

          $training_data_gen->gen_training_data();

$training_data_gen`->`write_training_data_to_file():

  To write out the training data to a disk file:

          $training_data_gen->write_training_data_to_file();

  This call will also display the training data in your terminal window if the $debug1 is on.

test_data_generator():

  The test data is generated by using its own constructor:

          my $parameter_file = "param.txt";
          my $output_test_datafile = "testdata1.dat";
          my $output_class_label_file = "test_data_class_labels.dat";

          my $test_data_gen = Algorithm::DecisionTree->test_data_generator(
                             output_test_datafile    => $output_test_datafile,
                             output_class_label_file => $output_class_label_file,
                             parameter_file          => $parameter_file,
                             write_to_file           => 1,
                             number_of_test_samples  => 10,
          );

$test_data_gen`->`read_parameter_file():

  After you have constructed an instance of the test data generator, you need to ask it to read the parameter file.

          $test_data_gen->read_parameter_file();

  This parameter file named in the call to the test-data generator constructor must possess the same structure as for generating the training data. In most cases, you would want to use the same paramter file both for generating the training data and the test data.

$test_data_gen`->`gen_test_data():

  This call generates the test data from your parameter file:

          $training_data_gen->gen_training_data();

$test_data_gen`->`write_test_data_to_file():

  To write out the test data to a disk file:

          $test_data_gen->write_test_data_to_file();

  This call will also display the test data in your terminal window if the $debug1 is on.

# HOW THE CLASSIFICATION RESULTS ARE DISPLAYED

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.

For large test datasets, you would obviously want to process an entire file of test data at a time. The best way to do this is to follow my script

        classify_test_data_in_a_file.pl

in the examples directly. This 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.

You can also invoke the classifier on one data sample at a time. A call such as

        my @test_sample = qw /exercising=>never
                              smoking=>heavy
                              fatIntake=>heavy
                              videoAddiction=>heavy /;

        my $classification = $dt->classify($root_node, @test_sample);
        print "The classification:\n";
        foreach my $class ($dt->get_class_names()) {
            print "    $class with probability $classification->{$class}\n";
        }

will print out the classification results in the following form:

        The classification:
            malignant with probability 0.744186046511628
            benign with probability 0.255813953488372

Note again the soft classification returned. That is, if the probability distributions for the different classes overlap in the underlying feature space, the classifier will 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 corresponding to a 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

See the examples directory in the distribution for how to generate the training data, how to induce a decision tree, and how to then classify new data using the decision tree.

To become more familiar with the module, run the script

        training_data_generator.pl

to generate a training datafile according to the information placed in the file param.txt and then run the script

        construct_dt_and_classify_one_sample.pl

to classify a new data sample that is in the script. Next generate a test dataset by calling

        generate_test_data.pl*

This will deposit the test data in a file. You can invoke the classifier on this file by an invocation like

        classify_test_data_in_a_file.pl   training.dat   testdata2.dat   out.txt

# EXPORT

None by design.

# BUGS

Please notify the author if you encounter any bugs. When sending email, please place the string 'DecisionTree' in the subject line.

# INSTALLATION

The usual

        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

# AUTHOR

Avinash Kak, kak@purdue.edu

If you send email, please place the string "DecisionTree" in your subject line to get past my spam filter.

# COPYRIGHT

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

     Copyright 2011 Avinash Kak