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Notebook[{
Cell[CellGroupData[{
Cell[BoxData[
\(Supervised\ Analysis\)], "Title",
CellFrame->{{0, 0}, {2, 0}}],
Cell[TextData[{
StyleBox["machine learning framework",
FontWeight->"Bold",
FontSlant->"Italic"],
" for ",
StyleBox["Mathematica",
FontSlant->"Italic"]
}], "Subtitle"],
Cell[TextData[{
"The most common task in data analysis is to find any relationships of a \
set of ",
StyleBox["input parameters",
FontSlant->"Italic"],
" to one or more ",
StyleBox["output parameters",
FontSlant->"Italic"],
". This kind of analysis is called ",
StyleBox["supervised",
FontSlant->"Italic"],
", as the goal of the analysis is given by the user. In the case that no \
explicit goal parameter is available, the analysis is called ",
StyleBox[ButtonBox["unsupervised",
ButtonData:>{"unsupervised.nb", None},
ButtonStyle->"Hyperlink"],
FontSlant->"Italic"],
". We will describe unsupervised analysis in another example. "
}], "Text"],
Cell["Initialization of the system", "MathCaption"],
Cell[BoxData[{
\(Needs["\"]\), "\[IndentingNewLine]",
\(Needs["\"]\)}], "Input",
CellLabel->"In[1]:=",
InitializationCell->True],
Cell[CellGroupData[{
Cell[TextData[{
"Basics",
StyleBox["\[LongDash]",
FontSize->12,
FontVariations->{"CompatibilityType"->0},
CharacterEncoding->"WindowsANSI"],
"iris data set"
}], "Section"],
Cell["\<\
In this example we will analyze a simple data file that contains \
data from about 150 iris flowers of different types. Each flower is described \
by five attributes. The first four characterize the blossom of the flower: \
sepal length, sepal width, petal length, and petal width. The fifth attribute \
specifies the category of irises to which the flower belongs. The goal of our \
analysis is to find out how we can decide to which category a new, \
unclassified flower belongs.\
\>", "Text"],
Cell["\<\
For that purpose we will create a decision tree and a set of rules, \
which allow us to classify new flowers by simply asking a few questions about \
its blossom.\
\>", "Text"],
Cell["\<\
In our data set we have four numerical attributes and one textual \
attribute. So we have four attributes describing the blossom of each flower \
and three classes of flowers. The data is stored in a text file where the \
first row contains the column headers. The textual attribute is in the last \
column.\
\>", "Text"],
Cell[CellGroupData[{
Cell["Setup data", "Subsection"],
Cell[BoxData[{
\(\(dataRaw =
Import[$TopDirectory <> "\", \
"\"];\)\), "\[IndentingNewLine]",
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dataRaw[\([1 +
Range[Length@dataRaw - 1]]\)];\)\), "\[IndentingNewLine]",
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Def["\",
DataSet[data, headers]];\)\), "\[IndentingNewLine]",
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CellLabel->"In[3]:="],
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"Now we can compute appropriate predicates with the ",
StyleBox["CreatePredicates[]",
FontFamily->"Courier"],
" and ",
StyleBox["DefPredicateVars[]",
FontFamily->"Courier"],
" commands for all input attributes and define the predicates for the goal \
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Cell[BoxData[{
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5];\)\), "\[IndentingNewLine]",
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CellLabel->"In[8]:="],
Cell[BoxData[{
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}, Open ]],
Cell[CellGroupData[{
Cell["Decision tree", "Subsection"],
Cell[CellGroupData[{
Cell["Compute a decision tree", "Subsubsection"],
Cell[TextData[{
"The decision tree rule induction method ",
StyleBox["FS-ID3",
FontSlant->"Italic"],
" is a generalization of Quinlan's ID3 method. A decision tree can be \
thought of as a series of if-then-else statements and can be used to solve \
arbitrary classification problems."
}], "Text"],
Cell["\<\
To generate a decision tree, we have to specify a desired goal \
predicate. In this example we will use the class attribute, which is the \
fifth column in our input file. Then we can compute the desired decision tree \
and finally plot the resulting tree.\
\>", "Text"],
Cell[TextData[{
"Now we can generate the decision tree using the ",
StyleBox["CreateID3[]",
FontFamily->"Courier"],
" command. The algorithm uses the data stored previously and tries to find \
rules to separate the three classes."
}], "Text"],
Cell[BoxData[
\(\(id3tree = CreateID3[irisData, testVars, goalVars];\)\)], "Input",
CellLabel->"In[12]:="],
Cell[TextData[{
"With the command ",
StyleBox["PlotID3[]",
FontFamily->"Courier"],
" it is very easy to plot the decision tree obtained."
}], "Text"],
Cell[CellGroupData[{
Cell[BoxData[
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To check if the computed decision tree is able to describe the \
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\>", "Text"],
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We can see that 86.57 percent of the first class have been \
classified correctly. However, 13.43 percent have been predicted to be from \
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\>", "Text"],
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To generate a rule base we have to specify a desired goal \
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column in our input file.\
\>", "Text"],
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In the output each, line corresponds to a rule, and its elements \
are connected by means of conjunction. The rules belonging to the same goal \
predicate can be interpreted as being disjointed.\
\>", "Text"],
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To check if the computed rule base is able to describe the data, we \
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\>", "Text"],
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We can see that 86.41 percent of the first class have been \
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\>", "Text"],
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To generate a rule base we have to specify a desired goal \
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"wine data set"
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This data set is taken from the UCI machine learning repository and \
contains the results of an analysis of 178 wines grown in the same region in \
Italy, but the wines are from three different vineyards. The analysis \
determined the quantities of constituents found in each of the three types of \
wines and some optical properties. All together, there are 13 input \
attributes, all of which are numerical. The goal predicate is Boolean \
categorical with 3 different classes/labels corresponding to the three \
vineyards. Accordingly, we use fuzzy predicates induced by appropriate fuzzy \
sets on the domains of the numerical input attributes. Although the goal \
predicate is Boolean categorical, the use of fuzzy predicates for the input \
predicates is not meaningless. The reason is that using fuzzy sets allows us \
to more easily model regions of overlapping goal classes and in a more \
natural way than by splitting the numerical attributes into Boolean \
classes.\
\>", "Text"],
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\[IndentingNewLine]",
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dataRaw[\([1 +
Range[Length@dataRaw - 1]]\)];\)\), "\[IndentingNewLine]",
\(\({trainData, testData} =
SplitDataRandomly[data, 0.8];\)\), "\[IndentingNewLine]",
\(\(wineData =
Def["\",
DataSet[trainData, headers]];\)\), "\[IndentingNewLine]",
\(\(wineTestData =
Def["\",
DataSet[testData, headers]];\)\), "\[IndentingNewLine]",
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CellLabel->"In[42]:="],
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CellLabel->"In[49]:="],
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CellLabel->"Out[49]="]
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Cell["\<\
Now we can compute appropriate predicates for all data dimensions \
and define the classes of the goal dimension.\
\>", "Text"],
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CellLabel->"In[50]:="],
Cell["This lists contain pairs of predicate names and definitions.", "Text"],
Cell["\<\
To assign variables with the names given to the corresponding \
definitions, we use the following macro.\
\>", "Text"],
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We now have a list of variables referring to our (now internal) \
predicates.\
\>", "Text"],
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HistogramCategories \[Rule] 20,
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In this example we will analyze data on 404 customers of a bank to \
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\>", "Text"],
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