| DecisionTree (version 1.6.1, 2012-June-22) |
DecisionTree.py
Version: 1.6.1
Author: Avinash Kak (kak@purdue.edu)
Date: 2012-June-22
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CHANGES:
Version 1.6.1:
Fixed a bug in the method that generates synthetic test data.
Version 1.6:
This version includes several upgrades: The module now includes code
for generating synthetic training and test data for experimenting with
the DecisionTree classifier. Another upgrade in the new version is
that, after training, a decision tree can now be used in an interactive
mode in which the user is asked to supply answers for the feature tests
at the nodes as the classification process descends down the tree.
Version 1.5:
This is a Python 3.x compliant version of the DecisionTree module.
This version should work with both Python 2.x and Python 3.x.
Version 1.0:
This is a Python implementation of the author's Perl module
Algorithm::DecisionTree, Version 1.41. The Python version should work
faster for large decision trees since it uses probability and entropy
caching much more extensively than Version 1.41 of the Perl module.
(Note: I expect my next release of the Perl module to catch up with
this Python version in terms of performance.)
USAGE:
The DecisionTree module is a pure-Python implementation for
constructing a decision tree from multidimensional training data and
for using the decision tree thus constructed for classifying unlabeled
data.
For constructing a decision tree and for classifying a sample:
dt = DecisionTree( training_datafile = "training.dat", debug1 = 1 )
dt.get_training_data()
dt.show_training_data()
root_node = dt.construct_decision_tree_classifier()
root_node.display_decision_tree(" ")
test_sample = ['exercising=>never', 'smoking=>heavy',
'fatIntake=>heavy', 'videoAddiction=>heavy']
classification = dt.classify(root_node, test_sample)
print "Classification: ", classification
print "Number of nodes created: ", root_node.how_many_nodes()
For the above calls to work, the format in which the training data is
made available to the decision-tree constructor must meet certain
assumptions. (See the 'training.dat' file in the Examples directory
for how to format the training data in a file.) 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.
If your training file specifies a large number of features or a large
number of values for the features, the above constructor call could
result in a decision tree that is simply much too large (and much too
slow to construct). For such cases, consider using following
additional options in the constructor call shown above:
dt = DecisionTree( training_datafile = "training.dat",
max_depth_desired = some_number,
entropy_threshold = some_value,
debug1 = 1,
)
where for max_depth_desired you should choose a number that is less
than the number of features in your training file. This will set the
depth of your decision tree to max_depth_desired. The algorithm will
automatically use the BEST max_depth_desired features --- best in the
sense of being the most discriminative --- for constructing the
decision tree. The parameter entropy_threshold sets the granularity
with which the entropies will be sampled. Its default value is 0.001.
The larger the value you choose for entropy_threshold, the smaller the
tree.
INTRODUCTION:
DecisionTree is a pure Python module for constructing a decision tree
from a training datafile containing multidimensional data in the form
of a table. In one form or another, decision trees have been around for
the last fifty years. However, 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.
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/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 five criteria:
price_to_earnings_ratio (P_to_E)
price_to_sales_ratio (P_to_S)
return_on_equity (R_on_E)
market_share (M_S)
sentiment (S)
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 M_S S
====================================================================
example_1 buy high low medium low high
example_2 buy medium medium low low medium
example_3 sell low medium low high low
....
....
This data would constitute your training file. You could feed this file
into the module by calling:
dt = DecisionTree( training_datafile = "training.dat" )
dt.get_training_data()
and then construct a decision tree by calling:
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
sentiment => low
All that your computer would need to do would be to construct a data
vector like
test_case = [ 'P_to_E=>low',
'P_to_S=>very_low',
'R_on_E=>none',
'M_S=>medium',
'S=>low' ]
and call the decision tree classifier you just constructed by
classification = dt.classify(root_node, test_case)
print "Classification: ", classification
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
convey the sense in which the current module can be used.
WHAT HAPPENS IF THE NUMBER OF FEATURES AND/OR VALUES IS LARGE?
If n is the number of features and m the largest number for the
possible values for any of the features, then, in only the worst case,
the algorithm would want to construct m**n nodes. In other words, in
the worst case, 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 have two constructor parameters at your disposal for controlling
the size of the decision tree: The parameter max_depth_desired controls
the depth of the constructed tree from its root node, and the parameter
entropy_threshold controls the granularity with which the entropy space
will be sampled. The smaller the max_depth_desired and the larger the
entropy_threshold, the smaller the size of the decision tree. The
default value for max_depth_desired is the number of features specified
in the training datafile, and the the default value for
entropy_threshold is 0.001.
The users of this module with a need to create very large decision
trees should also consider storing the tree once constructed in a
diskfile and then using the stored tree for classification work. The
scripts store_dt_on_disk.py and classify_from_diskstored_dt.py in the
Examples directory show you how you can do that with the help of
Python's pickle module. (NOTE: At this time, this feature works only
with Python 2.x.)
Also note that it is always a good idea to keep the debug1 option set
anytime you are experimenting with a new datafile --- especially if
your training datafile is likely 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
numeric in nature are constructed differently, as explained in the
tutorial at
https://engineering.purdue.edu/kak/DecisionTreeClassifiers.pdf
METHODS:
The module provides the following methods for decision-tree induction
from training data in a diskfile, and for data classification with the
decision tree.
Constructing a decision tree:
dt = DecisionTree( training_datafile = "training.dat", debug1 = 1 )
This yields a new instance of the 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.)
If your training file specifies a large number of features or a large
number of values for the features, the above constructor call could
result in a decision tree that is simply much too large (and much too
slow to construct). For such cases, consider using following
additional options in the constructor call shown above:
dt = DecisionTree( training_datafile = "training.dat",
max_depth_desired = some_number,
entropy_threshold = some_value,
debug1 = 1,
)
where for max_depth_desired you should choose a number that is less
than the number of features in your training file. This will set the
depth of your decision tree to max_depth_desired. The algorithm will
automatically use the BEST max_depth_desired features --- best in the
sense of being the most discriminative --- for constructing the
decision tree. The parameter entropy_threshold sets the granularity
with which the entropies will be sampled. Its default value is 0.001.
The larger the value you choose for entropy_threshold, the smaller the
tree.
Reading in the training data:
After you have constructed a new instance of the 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 be 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.
Displaying the training data:
If you wish to see the training data that was just digested by the
module, call
dt.show_training_data()
Constructing a decision-tree classifier:
After the training data is ingested, it is time to construct a decision
tree classifier. This you do by
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.
Displaying the decision tree:
You display a decision tree by calling
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().
Classifying new data:
You classify new data by first constructing a new data vector:
test_sample = ['exercising=>never', 'smoking=>heavy',
'fatIntake=>heavy', 'videoAddiction=>heavy']
and calling the classify() method as follows:
classification = dt.classify(root_node, test_sample)
where, again, root_node is an instance of type Node that was returned
by calling construct_decision_tree_classifier(). The variable
classification is a dictionary whose keys are the class labels and
whose values the associated probabilities. You can print it out by
print "Classification: ", classification
Displaying the number of nodes created:
You can print out the number of nodes in a decision tree by calling
root_node.how_many_nodes()
Determining the condition of the training data:
The following 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()
Using the decision tree interactively:
Starting with Version 1.6 of the module, you can use the DecisionTree
classifier in an interactive mode. In this mode, after you have
constructed the decision tree, the user is prompted for answers to the
questions regarding the feature tests at the nodes of the tree.
Depending on the answer supplied by the user at a node, the classifier
takes a path corresponding to the answer to descend down the tree to
the next node, and so on. The following method makes this mode
possible. Obviously, you can call this method only after you have
constructed the decision tree.
dt.classify_by_asking_questions(root_node)
Generating synthetic training data:
To generate synthetic training data, you first construct an instance of
the class TrainingDataGenerator that is incorporated in the
DecisionTree module. A call to the constructor of this class will look
like:
training_data_gen = TrainingDataGenerator(
output_datafile = an_output_data_file,
parameter_file = a_parameter_file,
write_to_file = 1,
number_of_training_samples = some_number,
)
The training data that is generated is according to the specifications
described in the parameter file. The structure of this file must be as
shown in the file 'param.txt' in the 'Examples' directory. The
parameter file names the classes, the features for the classes, the
possible values for the features, and these values are biased for the
different classes.
Generating synthetic test data:
To generate synthetic test data, you first construct an instance of the
class TestDataGenerator that is incorporated in the DecisionTree
module. A call to the constructor of this class will look like:
test_data_gen = TrainingDataGenerator(
output_test_datafile = an_output_data_file,
output_class_labels_file = a_file_for_class_labels,
parameter_file = a_parameter_file,
write_to_file = 1,
number_of_test_samples = some_number,
)
The main difference between the training data and the test data is that
the class labels are NOT mentioned in the latter. Instead, the class
labels are placed in a separate file whose name is supplied through the
constructor option 'output_class_labels_file' shown above. The test
data that is generated is according to the specifications described in
the parameter file. In general, this parameter file would be the same
that you used for generating the training data.
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 vector at a time into
the classifier.
In general, the classifier returns soft classification for a 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. For the
sort of data that is in the 'training.dat' file in the Examples
directory, the result of classification for a single data vector
would look like:
malignant with probability 0.744186046511628
benign with probability 0.255813953488372
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.py
in the 'Examples' directory. 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. The test datafile must mention the order in which
the features values are presented. For an example, see the file
'testdata.dat' in the 'Examples' directory.
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.
THE EXAMPLES DIRECTORY:
See the 'Examples' directory in the distribution for 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
construct_dt_and_classify_one_sample.py
to classify the data record that is in the script. Next run the script
as it is
classify_test_data_in_a_file.py training.dat testdata.dat out.txt
This call will first construct a decision tree using the training data
in the file 'training.dat'. It will then calculate the class label for
each data record in the file 'testdata.dat'. The estimated class
labels will be written out to the file 'out.txt'.
The 'Examples' directory also contains the script 'store_dt_on_disk.py'
that shows how you can use Python's pickle module to store a decision
tree in a disk file. The file 'classify_from_diskstored_dt.py' in the
same directory shows how you can classify new data vectors with the
stored decision tree. This is expected to be extremely useful for
situations that involve tens of thousands or millions of decision
nodes. (NOTE: At this time, this feature only works with Python 2.x)
The following script in the 'Examples' directory
classify_by_asking_questions.py*
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.
The 'Examples' directory also contains the following scripts:
generate_training_data.py
generate_test_data.py
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 the parameter file. See the file
'param.txt' in the 'Examples' directory for an example.
INSTALLATION:
The DecisionTree class was packaged using Distutils. For installation,
execute the following command-line in the source directory (this is the
directory that contains the setup.py file after you have downloaded and
uncompressed the package):
python setup.py install
You have to have root privileges for this to work. On Linux
distributions, this will install the module file at a location that
looks like
/usr/lib/python2.6/site-packages/
If you do not have root access, you have the option of working directly
off the directory in which you downloaded the software by simply
placing the following statements at the top of your scripts that use
the DecisionTree class:
import sys
sys.path.append( "pathname_to_DecisionTree_directory" )
To uninstall the module, simply delete the source directory, locate
where the DecisionTree module was installed with "locate DecisionTree"
and delete those files. As mentioned above, the full pathname to the
installed version is likely to look like
/usr/lib/python2.6/site-packages/DecisionTree*
If you want to carry out a non-standard install of the DecisionTree
module, look up the on-line information on Disutils by pointing your
browser to
http://docs.python.org/dist/dist.html
BUGS:
Please notify the author if you encounter any bugs. When sending
email, please place the string 'DecisionTree' in the subject line.
ACKNOWLEDGMENTS:
The importance of the 'sentiment' feature in the "What Practical Problem
is Solved by this Module" section was mentioned to the author by John
Gorup. Thanks John.
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:
Python Software Foundation License
Copyright 2012 Avinash Kak
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| __author__ = 'Avinash Kak (kak@purdue.edu)' __copyright__ = '(C) 2012 Avinash Kak. Python Software Foundation.' __date__ = '2012-June-22' __url__ = 'https://engineering.purdue.edu/kak/distDT/DecisionTree-1.6.1.html' __version__ = '1.6.1' | ||
| Author | ||
| Avinash Kak (kak@purdue.edu) | ||