C5.0: An Informal Tutorial

Welcome to C5.0, a system that extracts informative patterns from data. The following sections show how to prepare data files for C5.0 and illustrate the options for using the system.

In this tutorial, file names and C5.0 input appear in blue fixed-width font while file extensions and other general forms are shown highlighted in green.


Preparing Data for C5.0

We will illustrate C5.0 using a medical application -- mining a database of thyroid assays from the Garvan Institute of Medical Research, Sydney, to construct diagnostic rules for hypothyroidism. Each case concerns a single referral and contains information on the source of the referral, assays requested, patient data, and referring physician's comments. Here are three examples:

        Attribute                 Case 1    Case 2    Case 3    .....

	age                       41        23        46
	sex                       F         F         M
	on thyroxine              f         f         f
	query on thyroxine        f         f         f
	on antithyroid medication f         f         f
	sick                      f         f         f
	pregnant                  f         f         not applicable
	thyroid surgery           f         f         f
	I131 treatment            f         f         f
	query hypothyroid         f         f         f
	query hyperthyroid        f         f         f
	lithium                   f         f         f
	tumor                     f         f         f
	goitre                    f         f         f
	hypopituitary             f         f         f
	psych                     f         f         f
	TSH                       1.3       4.1       0.98
	T3                        2.5       2         unknown
	TT4                       125       102       109
	T4U                       1.14      unknown   0.91
	FTI                       109       unknown   unknown
	referral source           SVHC      other     other
	diagnosis                 negative  negative  negative
	ID                        3733      1442      2965

This is exactly the sort of task for which C5.0 was designed. Each case belongs to one of a small number of mutually exclusive classes (negative, primary, secondary, compensated). Properties of every case that may be relevant to its class are provided, although some cases may have unknown or non-applicable values for some attributes. There are 24 attributes in this example, but C5.0 can deal with any number of attributes.

C5.0's job is to find how to predict a case's class from the values of the other attributes. C5.0 does this by constructing a classifier that makes this prediction. As we will see, C5.0 can construct classifiers expressed as decision trees or as sets of rules.

Application files

Every C5.0 application has a short name called a filestem; we will use the filestem hypothyroid for this illustration. All files read or written by C5.0 for an application have names of the form filestem.extension, where filestem identifies the application and extension describes the contents of the file.

Here is a summary table of the extensions used by C5.0 (to be described in later sections):

Names file

Two files are essential for all C5.0 applications and there are three further optional files, each identified by its extension. The first essential file is the names file (e.g. hypothyroid.names) that describes the attributes and classes. There are two important subgroups of attributes:

The file hypothyroid.names looks like this:

diagnosis.                     | the target attribute

age:                           continuous.
sex:                           M, F.
on thyroxine:                  f, t.
query on thyroxine:            f, t.
on antithyroid medication:     f, t.
sick:                          f, t.
pregnant:                      f, t.
thyroid surgery:               f, t.
I131 treatment:                f, t.
query hypothyroid:             f, t.
query hyperthyroid:            f, t.
lithium:                       f, t.
tumor:                         f, t.
goitre:                        f, t.
hypopituitary:                 f, t.
psych:                         f, t.
TSH:                           continuous.
T3:                            continuous.
TT4:                           continuous.
T4U:                           continuous.
FTI:=                          TT4 / T4U.
referral source:               WEST, STMW, SVHC, SVI, SVHD, other.

diagnosis:                     primary, compensated, secondary, negative.

ID:                            label.

What's in a name?

Names, labels, classes, and discrete values are represented by arbitrary strings of characters, with some fine print: Whitespace (blank lines, spaces, and tab characters) is ignored except inside a name or value and can be used to improve legibility. Unless it is escaped as above, the vertical bar `|' causes the remainder of the line to be ignored and is handy for including comments. This use of `|' should not occur inside a value.

Specifying the classes

The first entry in the names file specifies the classes in one of three formats:

This first entry defining the classes is followed by definitions of the attributes in the order that they will be given for each case.

Explicitly-defined attributes

The name of each explicitly-defined attribute is followed by a colon `:' and a description of the values taken by the attribute. The attribute name is arbitrary, except that each attribute must have a distinct name, and case weight is reserved for setting weights for individual cases. There are eight possibilities for the description of attribute values:
continuous
The attribute takes numeric values.
date
The attribute's values are dates in the form YYYY/MM/DD or YYYY-MM-DD, e.g. 2005/09/30 or 2005-09-30.
time
The attribute's values are times in the form HH:MM:SS with values between 00:00:00 and 23:59:59.
timestamp
The attribute's values are times in the form YYYY/MM/DD HH:MM:SS or YYYY-MM-DD HH:MM:SS, e.g. 2005-09-30 15:04:00. (Note that there is a space separating the date and time.)
a comma-separated list of names
The attribute takes discrete values, and these are the allowable values. The values may be prefaced by [ordered] to indicate that they are given in a meaningful ordering, otherwise they will be taken as unordered. For instance, the values low, medium, high are ordered, while meat, poultry, fish, vegetables are not. The former might be declared as
grade: [ordered] low, medium, high.
If the attribute values have a natural order, it is better to declare them as such so that C5.0 can exploit the ordering. (NB: The target attribute should not be declared as ordered.)
discrete N for some integer N
The attribute has discrete, unordered values, but the values are assembled from the data itself; N is the maximum number of such values. This form can be handy for unordered discrete attributes with many values, but its use means that the data values cannot be checked. (NB: This form cannot be used for the target attribute.)
ignore
The values of the attribute should be ignored.
label
This attribute contains an identifying label for each case, such as an account number or an order code. The value of the attribute is ignored when classifiers are constructed, but is used when referring to individual cases. A label attribute can make it easier to locate errors in the data and to cross-reference results to individual cases. If there are two or more label attributes, only the last is used.

Attributes defined by formulas

The name of each implicitly-defined attribute is followed by `:=' and then a formula defining the attribute value. The formula is written in the usual way, using parentheses where needed, and may refer to any attribute defined up to this point. Constants in the formula can be numbers written in decimal notation, dates, times, and discrete attribute values enclosed in string quotes `"'. The operators and functions that can be used in the formula are The value of such an attribute is either continuous or true/false depending on the formula. For example, the attribute
	FTI:=  TT4 / T4U.
is continuous since its value is obtained by dividing one number by another. The value of a hypothetical attribute such as
	strange := referral source = "WEST" or age > 40.
would be either t or f since the value given by the formula is either true or false.

If the value of the formula cannot be determined for a particular case because one or more of the attributes appearing in the formula have unknown or non-applicable values, the value of the implicitly-defined attribute is unknown.

Dates, times, and timestamps

Dates are stored by C5.0 as the number of days since a particular starting point so some operations on dates make sense. Thus, if we have attributes
	d1: date.
	d2: date.
we could define
	interval := d2 - d1.
	gap := d1 <= d2 - 7.
	d1-day-of-week := (d1 + 1) % 7 + 1.
interval then represents the number of days from d1 to d2 (non-inclusive) and gap would have a true/false value signaling whether d1 is at least a week before d2. The last definition is a slightly non-obvious way of determining the day of the week on which d1 falls, with values ranging from 1 (Monday) to 7 (Sunday).

Similarly, times are stored as the number of seconds since midnight. If the names file includes

	start: time.
	finish: time.
	elapsed := finish - start.
the value of elapsed is the number of seconds from start to finish.

Timestamps are a little more complex. A timestamp is rounded to the nearest minute, but limitations on the precision of floating-point numbers mean that the values stored for timestamps from more than thirty years ago are approximate. If the names file includes

	departure: timestamp.
	arrival: timestamp.
	flight time := arrival - departure.
the value of flight time is the number of minutes from departure to arrival.

Selecting the attributes that can appear in classifiers

An optional final entry in the names file affects the way that C5.0 constructs classifiers. This entry takes one of the forms
	attributes included:
	attributes excluded:
followed by a comma-separated list of attribute names. The first form restricts the attributes used in classifiers to those specifically named; the second form specifies that classifiers must not use any of the named attributes.

Excluding an attribute from classifiers is not the same as ignoring the attribute (see `ignore' above). As an example, suppose that numeric attributes A and B are defined in the data, but background knowledge suggests that only their difference is important. The names file might then contain the following entries:

	. . .
	A: continuous.
	B: continuous.
	Diff := A - B.
	   . . .
	attributes excluded: A, B.
In this example the attributes A and B could not be defined as ignore because the definition of Diff would then be invalid.

Data file

The second essential file, the application's data file (e.g. hypothyroid.data) provides information on the training cases from which C5.0 will extract patterns. The entry for each case consists of one or more lines that give the values for all explicitly-defined attributes. If the classes are listed in the first line of the names file, the attribute values are followed by the case's class value. Values are separated by commas and the entry is optionally terminated by a period. Once again, anything on a line after a vertical bar `|' is ignored. (If the information for a case occupies more than one line, make sure that the line breaks occur after commas.)

For example, the first three cases from file hypothyroid.data are:

	41,F,f,f,f,f,f,f,f,f,f,f,f,f,f,f,1.3,2.5,125,1.14,SVHC,negative,3733
	23,F,f,f,f,f,f,f,f,f,f,f,f,f,f,f,4.1,2,102,?,other,negative,1442
	46,M,f,f,f,f,N/A,f,f,f,f,f,f,f,f,f,0.98,?,109,0.91,other,negative,2965
Don't forget the commas between values! If you leave them out, C5.0 will not be able to process your data.

Notice that `?' is used to denote a value that is missing or unknown. Similarly, `N/A' denotes a value that is not applicable for a particular case. Also note that the cases do not contain values for the attribute FTI since its values are computed from other attribute values.

Test and cases files (optional)

Of course, the value of predictive patterns lies in their ability to make accurate predictions! It is difficult to judge the accuracy of a classifier by measuring how well it does on the cases used in its construction; the performance of the classifier on new cases is much more informative. (For instance, any number of gurus tell us about patterns that `explain' the rise/fall behavior of the stock market in the past. Even though these patterns may appear plausible, they are only valuable to the extent that they make useful predictions about future rises and falls.)

The third kind of file used by C5.0 consists of new test cases (e.g. hypothyroid.test) on which the classifier can be evaluated. This file is optional and, if used, has exactly the same format as the data file.

Another optional file, the cases file (e.g. hypothyroid.cases), differs from a test file only in allowing the cases' classes to be unknown (`?'). The cases file is used primarily with the public source code described later on under linking to other programs.

Costs file (optional)

The last kind of file, the costs file (e.g. hypothyroid.costs), is also optional and sets out differential misclassification costs. In some applications there is a much higher penalty for certain types of mistakes. In this application, a prediction that hypothyroidism is not present could be very costly if in fact it is. On the other hand, predicting incorrectly that a patient is hypothyroid may be a less serious error. C5.0 allows different misclassification costs to be associated with each combination of real class and predicted class. We will return to this topic near the end of the tutorial.

Constructing Classifiers

Once the names, data, and optional files have been set up, everything is ready to use C5.0.

The general form of the Unix command is

        c5.0 -f filestem [options]
This invokes C5.0 with the -f option that identifies the application name (here hypothyroid). If no filestem is specified using this option, C5.0 uses a default filestem that is probably incorrect. (Moral: always use the -f option!) There are several options that affect the type of classifier that C5.0 produces and the way that it is constructed. Many of the options have default values that should be satisfactory for most applications.

Decision trees

When C5.0 is invoked with no options, as
	c5.0 -f hypothyroid
it constructs a decision tree and generates output like this:
C5.0 [Release 2.10]     Tue Mar 19 09:32:54 2013
-------------------

    Options:
        Application `hypothyroid'

Class specified by attribute `diagnosis'

Read 2772 cases (24 attributes) from hypothyroid.data

Decision tree:

TSH <= 6: negative (2472/2)
TSH > 6:
:...FTI <= 65:
    :...thyroid surgery = t:
    :   :...FTI <= 36.1: negative (2.1)
    :   :   FTI > 36.1: primary (2.1/0.1)
    :   thyroid surgery = f:
    :   :...TT4 <= 61: primary (51/3.7)
    :       TT4 > 61:
    :       :...referral source in {WEST,SVHD}: primary (0)
    :           referral source in {STMW,SVHC,SVI}: primary (4.9/0.8)
    :           referral source = other:
    :           :...TSH <= 22: negative (6.4/2.7)
    :               TSH > 22: primary (5.8/0.8)
    FTI > 65:
    :...on thyroxine = t: negative (37.7)
        on thyroxine = f:
        :...thyroid surgery = t: negative (6.8)
            thyroid surgery = f:
            :...TT4 > 153: negative (6/0.1)
                TT4 <= 153:
                :...TT4 <= 37: primary (2.5/0.2)
                    TT4 > 37: compensated (174.6/24.8)


Evaluation on training data (2772 cases):

            Decision Tree   
          ----------------  
          Size      Errors  

            12    7( 0.3%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            60     3                (a): class primary
                 153           1    (b): class compensated
                               2    (c): class secondary
                   1        2552    (d): class negative


        Attribute usage:

             90%  TSH
             18%  thyroid surgery
             17%  on thyroxine
             14%  TT4
             13%  T4U
             13%  FTI
              7%  referral source


Evaluation on test data (1000 cases):

            Decision Tree   
          ----------------  
          Size      Errors  

            12    4( 0.4%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            31                 1    (a): class primary
             1    39                (b): class compensated
                                    (c): class secondary
                   2         926    (d): class negative


Time: 0.0 secs

The first part identifies the version of C5.0, the run date, and the options with which the system was invoked. C5.0 constructs a decision tree from the 2772 training cases in the file hypothyroid.data, and this appears next. Although it may not look much like a tree, this output can be paraphrased as:

	if TSH is less than or equal to 6 then negative
	else
	if TSH is greater than 6 then
	    if FTI is less than or equal to 65 then
		if thyroid surgery equals t then
		    if FTI is less than or equal to 36.1 then negative
		    else
		    if FTI is greater than 36.1 then primary
		else
		if thyroid surgery equals f then
		    if TT4 is less than or equal to 61 then primary
		    else
		    if TT4 is greater than 61 then
		    . . . .
and so on.

The tree employs a case's attribute values to map it to a leaf designating one of the classes. Every leaf of the tree is followed by a cryptic (n) or (n/m). For instance, the last leaf of the decision tree is compensated (174.6/24.8), for which n is 174.6 and m is 24.8. The value of n is the number of cases in the file hypothyroid.data that are mapped to this leaf, and m (if it appears) is the number of them that are classified incorrectly by the leaf. (A non-integral number of cases can arise because, when the value of an attribute in the tree is not known, C5.0 splits the case and sends a fraction down each branch.)

The next section covers the evaluation of this decision tree shown in the second part of the output. Before we leave this output, though, its final line states the elapsed time for the run. (This differs from early releases of C5.0 which gave the CPU time.) The construction of a decision tree is usually completed quickly, even when there are many thousands of cases. Some of the options described later, such as ruleset generation and boosting, can slow things down considerably.

The progress of C5.0 on long runs can be monitored by examining the last few lines of the temporary file filestem.tmp (e.g. hypothyroid.tmp). This file displays the stage that C5.0 has reached and, for most stages, gives an indication of progress within that stage.

Evaluation

Classifiers constructed by C5.0 are evaluated on the training data from which they were generated, and also on a separate file of unseen test cases if available; evaluation by cross-validation is discussed elsewhere.

Results of the decision tree on the cases in hypothyroid.data are:

            Decision Tree   
          ----------------  
          Size      Errors  

            12    7( 0.3%)   <<
Size is the number of non-empty leaves on the tree and Errors shows the number and percentage of cases misclassified. The tree, with 12 leaves, misclassifies 7 of the 2772 given cases, an error rate of 0.3%. This might seem inconsistent with the errors recorded at the leaves -- the leaf mentioned above shows 24.8 errors! The discrepancy arises because parts of a case split as a result of unknown attribute values can be misclassified and yet, when the votes from all the parts are aggregated, the correct class can still be chosen.

When there are no more than twenty classes, performance on the training cases is further analyzed in a confusion matrix that pinpoints the kinds of errors made.

           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            60     3                (a): class primary
                 153           1    (b): class compensated
                               2    (c): class secondary
                   1        2552    (d): class negative
In this example, the decision tree misclassifies

When the number of classes is larger than twenty, a summary of performance broken down by class is shown instead. The entry for each class shows the number of cases for that class and the numbers of false positives and false negatives. A false positive for class C is a case of another class that is classified as C, while a false negative for C is a case of class C that is classified as some other class. Of course, the total number of errors must come to half the sum of the numbers of false positives and false negatives, since each error is counted twice--as a false negative for its true class, and as a false positive for the predicted class.

For some applications, especially those with many attributes, it may be useful to know how the individual attributes contribute to the classifier. This is shown in the next section:

        Attribute usage:

             90%  TSH
             18%  thyroid surgery
             17%  on thyroxine
             14%  TT4
             13%  T4U
             13%  FTI
              7%  referral source
The figure before each attribute is the percentage of training cases in hypothyroid.data for which the value of that attribute is known and is used in predicting a class. The second entry, for instance, shows that the decision tree uses a known value of thyroid surgery when classifying 18% of the training cases. Attributes for which this value is less than 1% are not shown. Two points are worth noting here:

If there are optional unseen test cases, the classifier's performance on these cases is summarized in a format similar to that for the training cases.

            Decision Tree   
          ----------------  
          Size      Errors  

            12    4( 0.4%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            31                 1    (a): class primary
             1    39                (b): class compensated
                                    (c): class secondary
                   2         926    (d): class negative
A very simple majority classifier predicts that every new case belongs to the most common class in the training data. In this example, 2553 of the 2772 training cases belong to class negative so that a majority classifier would always opt for negative. The 1000 test cases from file hypothyroid.test include 928 belonging to class negative, so a simple majority classifier would have an error rate of 7.2%. The decision tree has a lower error rate of 0.4% on the new cases, but notice that this is higher than its error rate on the training cases. The confusion matrix (or false positive/false negative summary if there are more than twenty classes) for the test cases again provides more details on correct and incorrect classifications.

Discrete value subsets

By default, a test on a discrete attributes has a separate branch for each of its values that is present in the data. Tests with a high fan-out can have the undesirable side-effect of fragmenting the data during construction of the decision tree. C5.0 has an option -s that can mitigate this fragmentation to some extent: attribute values are grouped into subsets and each subtree is associated with a subset rather than with a single value.

In the hypothyroid example, invoking this option by the command

	c5.0 -f hypothyroid -s
merely simplifies part of the tree as
	referral source in {WEST,STMW,SVHC,SVI,SVHD}: primary (4.9/0.8)
without affecting classification performance on either the training or test data.

Although it does not help much for this application, the -s option is recommended when there are important discrete attributes that have more than four or five values.

Rulesets

Decision trees can sometimes be quite difficult to understand. An important feature of C5.0 is its ability to generate classifiers called rulesets that consist of unordered collections of (relatively) simple if-then rules.

The option -r causes classifiers to be expressed as rulesets rather than decision trees. The command

	c5.0 -f hypothyroid -r

gives the following:

C5.0 [Release 2.10]     Tue Mar 19 09:34:55 2013
-------------------

    Options:
        Application `../hypothyroid'
        Rule-based classifiers

Class specified by attribute `diagnosis'

Read 2772 cases (24 attributes) from ../hypothyroid.data

Rules:

Rule 1: (31, lift 42.7)
        thyroid surgery = f
        TSH > 6
        TT4 <= 37
        ->  class primary  [0.970]

Rule 2: (63/6, lift 39.3)
        TSH > 6
        FTI <= 65
        ->  class primary  [0.892]

Rule 3: (270/116, lift 10.3)
        TSH > 6
        ->  class compensated  [0.570]

Rule 4: (2225/2, lift 1.1)
        TSH <= 6
        ->  class negative  [0.999]

Rule 5: (296, lift 1.1)
        on thyroxine = t
        FTI > 65
        ->  class negative  [0.997]

Rule 6: (240, lift 1.1)
        TT4 > 153
        ->  class negative  [0.996]

Rule 7: (29, lift 1.1)
        thyroid surgery = t
        FTI > 65
        ->  class negative  [0.968]

Default class: negative


Evaluation on training data (2772 cases):

                Rules     
          ----------------
            No      Errors

             7   14( 0.5%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            60     3                (a): class primary
             1   153                (b): class compensated
                               2    (c): class secondary
             5     3        2545    (d): class negative


        Attribute usage:

             90%  TSH
             20%  TT4
             14%  T4U
             14%  FTI
             11%  on thyroxine
              2%  thyroid surgery


Evaluation on test data (1000 cases):

                Rules     
          ----------------
            No      Errors

             7    5( 0.5%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            32                      (a): class primary
             1    39                (b): class compensated
                                    (c): class secondary
             1     3         924    (d): class negative


Time: 0.0 secs

Each rule consists of:

When a ruleset like this is used to classify a case, it may happen that several of the rules are applicable (that is, all their conditions are satisfied). If the applicable rules predict different classes, there is an implicit conflict that could be resolved in several ways: for instance, we could believe the rule with the highest confidence, or we could attempt to aggregate the rules' predictions to reach a verdict. C5.0 adopts the latter strategy -- each applicable rule votes for its predicted class with a voting weight equal to its confidence value, the votes are totted up, and the class with the highest total vote is chosen as the final prediction. There is also a default class, here negative, that is used when none of the rules apply.

Rulesets are generally easier to understand than trees since each rule describes a specific context associated with a class. Furthermore, a ruleset generated from a tree usually has fewer rules than than the tree has leaves, another plus for comprehensibility. (In this example, the first decision tree with 12 leaves is reduced to seven rules.)

Another advantage of ruleset classifiers is that they are often more accurate predictors than decision trees -- a point not illustrated here, since the ruleset has an error rate of 0.5% on the test cases. For very large datasets, however, generating rules with the -r option can require considerably more computer time.

For a given application, the attribute usage shown for a decision tree and for a ruleset can be a bit different. In the case of the tree, the attribute at the root is always used (provided its value is known) while an attribute further down the tree is used less frequently. For a ruleset, an attribute is used to classify a case if it is referenced by a condition of at least one rule that applies to that case; the order in which attributes appear in a ruleset is not relevant.

Rule utility ordering

In the example above, rules are ordered by class and sub-ordered by confidence. An alternative ordering by estimated contribution to predictive accuracy can be selected using the -u option. Under this option, the rule that most reduces the error rate appears first and the rule that contributes least appears last. Furthermore, results are reported in a selected number of bands so that the predictive accuracies of the more important subsets of rules are also estimated. For example, if the option -u 4 is selected, the hypothyroid rules are reordered as
Rule 1: (2225/2, lift 1.1)
        TSH <= 6
        ->  class negative  [0.999]

Rule 2: (270/116, lift 10.3)
        TSH > 6
        ->  class compensated  [0.570]

Rule 3: (63/6, lift 39.3)
        TSH > 6
        FTI <= 65
        ->  class primary  [0.892]

Rule 4: (296, lift 1.1)
        on thyroxine = t
        FTI > 65
        ->  class negative  [0.997]

Rule 5: (240, lift 1.1)
        TT4 > 153
        ->  class negative  [0.996]

Rule 6: (29, lift 1.1)
        thyroid surgery = t
        FTI > 65
        ->  class negative  [0.968]

Rule 7: (31, lift 42.7)
        thyroid surgery = f
        TSH > 6
        TT4 <= 37
        ->  class primary  [0.970]
The rules are divided into four bands of roughly equal sizes and a further summary is generated for both training and test cases. Here is the output for test cases:
Evaluation on test data (1000 cases):

                Rules     
          ----------------
            No      Errors

             7    5( 0.5%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            32                      (a): class primary
             1    39                (b): class compensated
                                    (c): class secondary
             1     3         924    (d): class negative

Rule utility summary:

        Rules         Errors
        -----         ------
        1-2        56( 5.6%)
        1-4        10( 1.0%)
        1-5         6( 0.6%)
This shows that, when only the first two rules are used, the error rate on the test cases is 5.6%, dropping to 1.0% when the first four rules are used, and so on. The performance of the entire ruleset is not repeated since it is shown above the utility summary.

Rule utility orderings are not given for cross-validations (see below).

Boosting

Another innovation incorporated in C5.0 is adaptive boosting, based on the work of Rob Schapire and Yoav Freund. The idea is to generate several classifiers (either decision trees or rulesets) rather than just one. When a new case is to be classified, each classifier votes for its predicted class and the votes are counted to determine the final class.

But how can we generate several classifiers from a single dataset? As the first step, a single decision tree or ruleset is constructed as before from the training data (e.g. hypothyroid.data). This classifier will usually make mistakes on some cases in the data; the first decision tree, for instance, gives the wrong class for 7 cases in hypothyroid.data. When the second classifier is constructed, more attention is paid to these cases in an attempt to get them right. As a consequence, the second classifier will generally be different from the first. It also will make errors on some cases, and these become the the focus of attention during construction of the third classifier. This process continues for a pre-determined number of iterations or trials, but stops if the most recent classifiers is either extremely accurate or inaccurate.

The option -t x instructs C5.0 to construct up to x classifiers in this manner; an alternative option -b is equivalent to -t 10. Naturally, constructing multiple classifiers requires more computation that building a single classifier -- but the effort can pay dividends! Trials over numerous datasets, large and small, show that on average 10-classifier boosting reduces the error rate for test cases by about 25%.

In this example, the command

	c5.0 -f hypothyroid -b

causes ten decision trees to be generated. The summary of the trees' individual and aggregated performance on the 1000 test cases is:

Trial       Decision Tree   
-----     ----------------  
          Size      Errors  

   0        12    4( 0.4%)
   1         7   52( 5.2%)
   2        11    9( 0.9%)
   3        16   28( 2.8%)
   4        11   40( 4.0%)
   5        22   38( 3.8%)
   6        21   16( 1.6%)
   7        21   18( 1.8%)
   8        23   76( 7.6%)
   9        25   15( 1.5%)
boost             2( 0.2%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            32                      (a): class primary
                  40                (b): class compensated
                                    (c): class secondary
                   2         926    (d): class negative

The performance of the classifier constructed at each trial is summarized on a separate line, while the line labeled boost shows the result of voting all the classifiers.

The decision tree constructed on Trial 0 is identical to that produced without the -b option. Some of the subsequent trees produced by paying more attention to certain cases have relatively high overall error rates. Nevertheless, when the trees are combined by voting, the final predictions have a lower error rate of 0.2% on the test cases.

Winnowing attributes

The decision trees and rulesets constructed by C5.0 do not generally use all of the attributes. The hypothyroid application has 22 predictive attributes (plus a class and a label attribute) but only six of them appear in the tree and the ruleset. This ability to pick and choose among the predictors is an important advantage of tree-based modeling techniques.

Some applications, however, have an abundance of attributes! For instance, one approach to text classification describes each passage by the words that appear in it, so there is a separate attribute for each different word in a restricted dictionary.

When there are numerous alternatives for each test in the tree or ruleset, it is likely that at least one of them will appear to provide valuable predictive information. In applications like these it can be useful to pre-select a subset of the attributes that will be used to construct the decision tree or ruleset. The C5.0 mechanism to do this is called "winnowing" by analogy with the process for separating wheat from chaff (or, here, useful attributes from unhelpful ones).

Winnowing is not obviously relevant for the hypothyroid application since there are relatively few attributes. To illustrate the idea, however, here are the results when the -w option is invoked:

C5.0 [Release 2.10]  	Tue Mar 19 09:38:19 2013
-------------------

    Options:
        Application `hypothyroid'
        Winnow attributes

Class specified by attribute `diagnosis'

Read 2772 cases (24 attributes) from hypothyroid.data

14 attributes winnowed
Estimated importance of remaining attributes:

    990%  TSH
    270%  FTI
    200%  on thyroxine
     30%  thyroid surgery
     <1%  age
     <1%  T3
     <1%  TT4
     <1%  referral source

Decision tree:

TSH <= 6: negative (2472/2)
TSH > 6:
:...FTI <= 65:
    :...thyroid surgery = t:
    :   :...FTI <= 36.1: negative (2.1)
    :   :   FTI > 36.1: primary (2.1/0.1)
    :   thyroid surgery = f:
    :   :...TT4 <= 61: primary (51/3.7)
    :       TT4 > 61:
    :       :...referral source in {WEST,SVHD}: primary (0)
    :           referral source in {STMW,SVHC,SVI}: primary (4.9/0.8)
    :           referral source = other:
    :           :...TSH <= 22: negative (6.4/2.7)
    :               TSH > 22: primary (5.8/0.8)
    FTI > 65:
    :...on thyroxine = t: negative (37.7)
        on thyroxine = f:
        :...thyroid surgery = t: negative (6.8)
            thyroid surgery = f:
            :...TT4 > 153: negative (6/0.1)
                TT4 <= 153:
                :...TT4 <= 37: primary (2.5/0.2)
                    TT4 > 37: compensated (174.6/24.8)


Evaluation on training data (2772 cases):

            Decision Tree   
          ----------------  
          Size      Errors  

            12    7( 0.3%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            60     3                (a): class primary
                 153           1    (b): class compensated
                               2    (c): class secondary
                   1        2552    (d): class negative


        Attribute usage:

             90%  TSH
             18%  thyroid surgery
             17%  on thyroxine
             14%  TT4
             13%  T4U
             13%  FTI
              7%  referral source


Evaluation on test data (1000 cases):

            Decision Tree   
          ----------------  
          Size      Errors  

            12    4( 0.4%)   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            31                 1    (a): class primary
             1    39                (b): class compensated
                                    (c): class secondary
                   2         926    (d): class negative


Time: 0.0 secs
After analyzing the training cases and before the decision tree is built, C5.0 winnows 14 of the 22 predictive attributes. This has the same effect as marking the attributes as excluded by an entry in the names file; winnowed attributes can still be used in the definition of other attributes. In this example, T4U is winnowed but is still available for use in the definition of FTI.

The remaining attributes are then listed in order of importance, C5.0's estimate of the factor by which the true error rate or misclassification cost would increase if that attribute were excluded. If TSH were excluded, for example, C5.0 expects the error rate on unseen test cases to increase to 4% (990% of the current rate of 0.4%). This estimate is intended only as a rough guide and should not be taken too literally!

We then see the decision tree that is constructed from the reduced set of attributes. In this case it is identical to the original tree, but winnowing will usually lead to a different classifier.

Since winnowing the attributes can be a time-consuming process, it is recommended primarily for large applications (10,000 cases or more) where there is reason to suspect that many of the attributes have at best marginal relevance to the classification task.

Softening thresholds

The top of our initial decision tree tests whether the value of the attribute TSH is less than or equal to, or greater than, 6. If the former holds, we go no further and predict that the case's class is negative, while if it does not we look at other information before making a decision. Thresholds like this are sharp by default, so that a case with a hypothetical value of 5.99 for TSH is treated quite differently from one with a value of 6.01.

For some domains, this sudden change is quite appropriate -- for instance, there are hard-and-fast cutoffs for bands of the income tax table. For other applications, though, it is more reasonable to expect classification decisions to change more slowly with changes in attribute values.

C5.0 contains an option -p to `soften' thresholds such as 6 above. When this is invoked, each threshold is broken into three ranges -- let us denote them by a lower bound lb, an upper bound ub, and a central value t. If the attribute value in question is below lb or above ub, classification is carried out using the single branch corresponding to the `<=' or '>' result respectively. If the value lies between lb and ub, both branches of the tree are investigated and the results combined probabilistically. The values of lb and ub are determined by C5.0 based on an analysis of the apparent sensitivity of classification to small changes in the threshold. They need not be symmetric -- a fuzzy threshold can be sharper on one side than on the other.

The command

	c5.0 -f hypothyroid -p
gives the following decision tree:
TSH <= 6 (6.05): negative (2472/2)
TSH >= 6.1 (6.05):
:...FTI <= 61 (65.35):
    :...thyroid surgery = t:
    :   :...FTI <= 24 (38.25): negative (2.1)
    :   :   FTI >= 52.5 (38.25): primary (2.1/0.1)
    :   thyroid surgery = f:
    :   :...TT4 <= 44 (61.5): primary (51/3.7)
    :       TT4 >= 63 (61.5):
    :       :...referral source in {WEST,SVHD}: primary (0)
    :           referral source in {STMW,SVHC,SVI}: primary (4.9/0.8)
    :           referral source = other:
    :           :...TSH <= 14 (22.5): negative (6.4/2.7)
    :               TSH >= 44 (22.5): primary (5.8/0.8)
    FTI >= 66 (65.35):
    :...on thyroxine = t: negative (37.7)
        on thyroxine = f:
        :...thyroid surgery = t: negative (6.8)
            thyroid surgery = f:
            :...TT4 >= 159 (153): negative (6/0.1)
                TT4 <= 146 (153):
                :...TT4 <= 14 (37.5): primary (2.5/0.2)
                    TT4 >= 61 (37.5): compensated (174.6/24.8)
Each threshold is now of the form <= lb (t) or >= ub (t). In this example, most of the thresholds are still relatively tight, but notice the asymmetric threshold values for the test FTI <= 61. For this application, soft thresholds slightly improve the classifier's accuracy on both training and test data.

A final point: soft thresholds affect only decision tree classifiers -- they do not change the interpretation of rulesets.

Advanced pruning options

Three further options enable aspects of the classifier-generation process to be tweaked. These are best regarded as advanced options that should be used sparingly (if at all), so that this section can be skipped without much loss.

C5.0 constructs decision trees in two phases. A large tree is first grown to fit the data closely and is then `pruned' by removing parts that are predicted to have a relatively high error rate. This pruning process is first applied to every subtree to decide whether it should be replaced by a leaf or sub-branch, and then a global stage looks at the performance of the tree as a whole.

The option -g disables this second pruning component and generally results in larger decision tees and rulesets. For the hypothyroid application, the tree increases in size from 12 to 13 leaves.

Turning off global pruning can be beneficial for some applications, particularly when rulesets are generated.

The option -c CF affects the way that error rates are estimated and hence the severity of pruning; values smaller than the default (25%) cause more of the initial tree to be pruned, while larger values result in less pruning.

The option -m cases constrains the degree to which the initial tree can fit the data. At each branch point in the decision tree, the stated minimum number of training cases must follow at least two of the branches. Values higher than the default (2 cases) can lead to an initial tree that fits the training data only approximately -- a form of pre-pruning. (This option is complicated by the presence of missing attribute values, and by the use of differential misclassification costs or weighting of individual cases as discussed elsewhere. All cause adjustments to the apparent number of cases following a branch.)

Sampling from large datasets

Even though C5.0 is relatively fast, building classifiers from large numbers of cases can take an inconveniently long time, especially when options such as boosting are employed. C5.0 incorporates a facility to extract a random sample from a dataset, construct a classifier from the sample, and then test the classifier on a disjoint collection of cases. By using a smaller set of training cases in this way, the process of generating a classifier is expedited, but at the cost of a possible reduction in the classifier's predictive performance.

The option -S x has two consequences. Firstly, a random sample containing x% of the cases in the application's data file is used to construct the classifier. Secondly, the classifier is evaluated on a non-overlapping set of test cases consisting of another (disjoint) sample of the same size as the training set (if x is less than 50%), or all cases that were not used in the training set (if x is greater than or equal to 50%).

In the hypothyroid example, using a sample of 60% would cause a classifier to be constructed from a randomly-selected 1663 of the 2772 cases in hypothyroid.data, then tested on the remaining 1109 cases.

By default, the random sample changes every time that a classifier is constructed, so that successive runs of C5.0 with sampling will usually produce different results. This re-sampling can be avoided by the option -I seed that uses the integer seed to initialize the sampling. Runs with the same value of the seed and the same sampling percentage will always use the same training cases.

Cross-validation trials

As we saw earlier, the performance of a classifier on the training cases from which it was constructed gives a poor estimate of its accuracy on new cases. The true predictive accuracy of the classifier can be estimated by sampling, as above, or by using a separate test file; either way, the classifier is evaluated on cases that were not used to build it. However, this estimate can be unreliable unless the numbers of cases used to build and evaluate the classifier are both large. If the cases in hypothyroid.data and hypothyroid.test were to be shuffled and divided into a new 2772-case training set and a 1000-case test set, C5.0 might construct a different classifier with a lower or higher error rate on the test cases.

One way to get a more reliable estimate of predictive accuracy is by f-fold cross-validation. The cases (including those in the test file, if it exists) are divided into f blocks of roughly the same size and class distribution. For each block in turn, a classifier is constructed from the cases in the remaining blocks and tested on the cases in the hold-out block. In this way, each case is used just once as a test case. The error rate of a classifier produced from all the cases is estimated as the ratio of the total number of errors on the hold-out cases to the total number of cases.

The option -X f runs such a f-fold cross-validation. For example, the command

	c5.0 -f hypothyroid -X 10 -r
selects 10-fold cross-validation using rulesets. After giving details of the individual rulesets, the output shows a summary like this:
Fold            Rules     
----      ----------------
            No      Errors

   0         7        0.5%
   1         8        0.5%
   2         8        0.8%
   3         7        0.3%
   4         7        0.8%
   5         7        0.0%
   6         7        0.8%
   7         7        0.0%
   8         7        1.3%
   9         7        0.8%

  Mean     7.2        0.6%
  SE       0.1        0.1%

This estimates the error rate of the rulesets produced from the 3772 cases in hypothyroid.data and hypothyroid.test at 0.6%. The SE figures (the standard errors of the means) provide an estimate of the variability of these results.

As with sampling above, each cross-validation run will normally use a different random division of the data into blocks, unless this is prevented by using the -I option.

The cross-validation procedure can be repeated for different random partitions of the cases into blocks. The average error rate from these distinct cross-validations is then an even more reliable estimate of the error rate of the single classifier produced from all the cases.

A shell script and associated programs for carrying out multiple cross-validations is included with C5.0. The shell script xval is invoked with any combination of C5.0 options and some further options that describe the cross-validations themselves:

If detailed results are retained via the +d option, they appear in files named filestem.ox[+suffix] where x is the cross-validation number (0 to repeats-1). A summary of the cross-validations is written to file filestem.res[+suffix].

As an example, the command

	xval -f hypothyroid -r R=10 +run1

has the effect of running ten 10-fold cross-validations using ruleset classifiers (i.e., 100 classifiers in all). File hypothyroid.res+run1 contains the following summary:

XVal          Rules     
----    ----------------
            No    Errors

  1        7.2      0.5%  
  2        7.2      0.6%  
  3        7.2      0.5%  
  4        7.2      0.6%  
  5        6.8      0.7%  
  6        7.0      0.5%  
  7        7.1      0.6%  
  8        7.3      0.6%  
  9        7.2      0.6%  
 10        7.2      0.6%  

Mean       7.1      0.6%  
SE         0.0      0.0%  

Since every cross-validation fold produces a different classifier using only part of the application's data, running a cross-validation does not cause a classifier to be saved. To save a classifier for later use, simply run C5.0 without employing cross-validation.

Differential misclassification costs

Up to this point, all errors have been treated as equal -- we have simply counted the number of errors made by a classifier to summarize its performance. Let us now turn to the situation in which the `cost' associated with a classification error depends on the predicted and true class of the misclassified case.

C5.0 allows costs to be assigned to any combination of predicted and true class via entries in the optional file filestem.costs. Each entry has the form

	predicted class, true class: cost

where cost is any non-negative value. The file may contain any number of entries; if a particular combination is not specified explicitly, its cost is taken to be 0 if the predicted class is correct and 1 otherwise.

To illustrate the idea, suppose that it was a much more serious error to classify a hypothyroid patient as negative than the converse. A hypothetical costs file hypothyroid.costs might look like this:

negative, primary: 5
negative, secondary: 5
negative, compensated: 5

This specifies that the cost of misclassifying any primary, secondary, or compensated patient as negative is 5 units. Since they are not given explicitly, all other errors have cost 1 unit. In other words, the first kind of error is five times more costly.

A costs file is automatically read by C5.0 unless the system is told to ignore it. (The option -e causes any costs file to be ignored and instructs C5.0 to focus only on errors.) The command

	c5.0 -f hypothyroid
now gives the following output:
C5.0 [Release 2.10]     Tue Mar 19 09:43:46 2013
-------------------

    Options:
        Application `../hypothyroid'

Class specified by attribute `diagnosis'

Read 2772 cases (24 attributes) from hypothyroid.data
Read misclassification costs from hypothyroid.costs

Decision tree:

TSH <= 6:
:...TT4 > 54: negative (2444.3)
:   TT4 <= 54:
:   :...query hypothyroid = f: negative (25.7/1)
:       query hypothyroid = t: secondary (2.1/1.1)
TSH > 6:
:...FTI <= 65:
    :...thyroid surgery = f: primary (68.1/11.7)
    :   thyroid surgery = t:
    :   :...FTI <= 36.1: negative (2.1)
    :       FTI > 36.1: primary (2.1/0.1)
    FTI > 65:
    :...on thyroxine = t: negative (37.7)
        on thyroxine = f:
        :...thyroid surgery = t: negative (6.8)
            thyroid surgery = f:
            :...TT4 > 153: negative (6/0.1)
                TT4 <= 153:
                :...TT4 <= 37: primary (2.5/0.2)
                    TT4 > 37: compensated (174.6/24.8)


Evaluation on training data (2772 cases):

               Decision Tree       
          -----------------------  
          Size      Errors   Cost  

            11   11( 0.4%)   0.01   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            60     3                (a): class primary
             1   153                (b): class compensated
                         1     1    (c): class secondary
             4     1     1  2547    (d): class negative


        Attribute usage:

             94%  TT4
             90%  TSH
             18%  thyroid surgery
             17%  on thyroxine
             13%  T4U
             13%  FTI
              7%  query hypothyroid


Evaluation on test data (1000 cases):

               Decision Tree       
          -----------------------  
          Size      Errors   Cost  

            11    4( 0.4%)   0.00   <<


           (a)   (b)   (c)   (d)    <-classified as
          ----  ----  ----  ----
            32                      (a): class primary
             1    39                (b): class compensated
                                    (c): class secondary
             1     2         925    (d): class negative


Time: 0.0 secs
The difference between this tree and the original becomes apparent when we compare the total cost of misclassified test cases for the two trees. The misclassification cost is 8 (3x1 + 1x5) for the original tree and 4 (4x1) for the new tree.

The new "Cost" column in the output shows the average misclassification cost, i.e. the total cost divided by the number of cases. For the new tree, the average cost is 19/2772 for the training cases and 4/1000 for the test cases.

Weighting individual cases

It is sometimes useful to attach different weights to cases depending on some measure of their importance. An application predicting whether a customer is likely to "churn," for example, might weight training cases by the size of the account.

C5.0 accommodates this by allowing a special attribute that contains the weight of each case. The attribute name must be case weight and it must be of type continuous. The relative weight assigned to each case is its value of this attribute divided by the average value; if the value is undefined ("?"), not applicable ("N/A"), or is less than or equal to zero, the case's relative weight is set to 1.

The case weight attribute itself is not used in the classifier!

Our sample hypothyroid application does not have any natural case-by-case weighting, since all patients are equal. For the purpose of illustration, though, we will add an implicitly-defined attribute to hypothyroid.names as follows:

With all default options, C5.0 now generates a different decision tree:

TSH <= 6: negative (2462.5/2.3)
TSH > 6:
:...FTI <= 64.5: primary (69.6/12.8)
    FTI > 64.5:
    :...on thyroxine = t: negative (39.6)
        on thyroxine = f:
        :...thyroid surgery = t: negative (9.2)
            thyroid surgery = f:
            :...TT4 > 153: negative (6.2/0.2)
                TT4 <= 153:
                :...TT4 > 61: compensated (179/29.3)
                    TT4 <= 61:
                    :...TSH <= 35: compensated (2.8/0.3)
                        TSH > 35: primary (3.2/0.3)
The case counts at the leaves now reflect the relative weights of the cases. (The counts associated with rules are affected similarly.) However, the error counts, rates, and costs shown in the evaluations use uniform case weighting.

A cautionary note: The use of case weighting does not guarantee that the classifier will be more accurate for unseen cases with higher weights. Predictive accuracy on more important cases is likely to be improved only when cases with similar values of the predictor attributes also have similar values of the case weight attribute, i.e. when relatively important cases "clump together." Without this property, case weighting can introduce an unhelpful element of randomness into the classifier generation process.

Using Classifiers

Once a classifier has been constructed, an interactive interpreter can be used to predict the classes to which new cases belong. The command to do this is

	predict
whose options are:

This is illustrated in the following dialog that uses the first decision tree to predict the class of a case. Input from the user is shown in bold face and the enter key as ¤.

TSH: 12¤
TT4: 110¤
T4U: 1.14¤
on thyroxine: f¤
thyroid surgery: f¤

    ->	compensated  [0.85]
	negative  [0.13]
	primary  [0.01]

Retry, new case or quit [r,n,q]: r¤

TSH [12]: ¤
TT4 [110]: ?¤
T4U [1.14]: ?¤
thyroid surgery [f]: ¤
referral source: WEST¤
on thyroxine [f]: ¤

    ->	compensated  [0.63]
	primary  [0.22]
	negative  [0.15]

Retry, new case or quit [r,n,q]: q¤
The values of some attributes might not affect the classification, so predict prompts for the values of those attributes that are required. The reply `?' indicates that a requested attribute value is unknown. (Similarly, use `N/A' for non-applicable values.) When all the relevant information has been entered, the most likely class (or classes) are printed, each with a confidence value.

Next, predict asks whether the same case is to be tried again with changed attribute values (a kind of `what if' scenario), a new case is to be classified, or all cases are complete. If a case is retried, each prompt for an attribute value shows the previous value in square brackets. A new value can be entered, followed by the enter key, or the enter key alone can be used to indicate that the value is unchanged.

Classifiers can also be used in batch mode. The sample application provided in the public source code reads cases from a cases file and shows the predicted class and the confidence for each.

Segmentation fault errors

For applications with very many cases or attributes, C5.0 may crash with a message like Segmentation fault (core dumped). This usually occurs because a C5.0 thread has exhausted its allocated stack space.

Different releases of Linux have varying default stack sizes; for example, Fedora Core uses a default 10MB while Ubuntu uses 8MB. If you experience a segmentation fault error, you must override the default stack size setting by typing the following before running C5.0:

where new limit is the new stack size limit in kilobytes. For example, a csh user might type limit stacksize 20000 to increase the default stack size limit to 20MB.

Please note! You should not set the stack size limit to unlimited -- this will not change the default stack size limit for subsidiary threads. You must use a specific value in KB. A little experimentation may be necessary to find a value that works with your application.

Linux GUI

Linux users who have installed a recent version of Wine can invoke a slightly simplified version of the See5 user interface. The executable program gui starts the graphical user interface whose main window is similar to See5's, with five buttons:

Locate Data
invokes a browser to find the files for your application, or to change the current application;
Construct Classifier
selects the type of classifier to be constructed and sets other options;
Stop
interrupts the classifier-generating process;
Review Output
re-displays the output from the last classifier construction (if any), saved automatically in a file filestem.out; and
Cross-Reference
shows how cases in training or test data relate to (parts of) a classifier and vice versa.
For more details on these, please see the See5 tutorial.

The graphical interface calls C5.0 directly, so use of the GUI has minimal impact on performance when generating a classifier.

Please note: C5.0 should be run for the first time from the command-line interface, not the GUI. The first run installs the licence in C5.0 -- after that, C5.0 can be used from either interface.

Linking to Other Programs

The classifiers generated by C5.0 are retained in files filestem.tree (for decision trees) and filestem.rules (for rulesets). Free C source code is available to read these classifier files and to make predictions with them, enabling you to use C5.0 classifiers in other programs.

As an example, the source includes a program to input new cases and to show how each is classified by boosted or single trees or rulesets. The program reads the application's names file, the tree or rules file generated by C5.0, and an optional costs file. It then reads cases from a cases file in a format similar to a data file, except that a case's class can be given as `?' meaning "unknown". For each case, the program outputs the given class, the class predicted by the classifier, and the confidence with which this prediction is made.

Please see the file sample.c for compilation instructions and program options.

Click here to download a gzipped tar file containing the public source code.

Appendix: Summary of Options

© RULEQUEST RESEARCH 2013 Last updated March 2013


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