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PMML 3.1 - General Structure of a PMML Document

PMML uses XML to represent mining models. The structure of the models is described by an XML Schema. One or more mining models can be contained in a PMML document. A PMML document is an XML document with a root element of type PMML. The general structure of a PMML document is:


  <?xml version="1.0"?>
  <PMML version="3.1"
    xmlns="http://www.dmg.org/PMML-3_1" 
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >

    <Header copyright="Example.com"/>
    <DataDictionary> ... </DataDictionary>

    ... a model ...

  </PMML>

The namespaces in the PMML Schema itself are defined as:

 
  <xs:schema 
    xmlns:xs="http://www.w3.org/2001/XMLSchema"
    targetNamespace="http://www.dmg.org/PMML-3_1"
    xmlns="http://www.dmg.org/PMML-3_1"
    elementFormDefault="unqualified">

Note that because of the namespace declaration in its current form, PMML cannot be mixed with content of a different namespace.

Although a PMML document must be valid with respect to the PMML XSD, a document must not require a validating parser, which would load external entities. In addition to being a valid XML document, a valid PMML document must obey a number of further rules which are described at various places in the PMML specification. See also the conformance rules for valid PMML documents, producers, and consumers.

The root element of a PMML document must have type PMML.


  <xs:element name="PMML">
    <xs:complexType>
      <xs:sequence>
        <xs:element ref="Header"/>
        <xs:element ref="MiningBuildTask" minOccurs="0"/>
        <xs:element ref="DataDictionary"/>
        <xs:element ref="TransformationDictionary" minOccurs="0"/>
        <xs:sequence minOccurs="0" maxOccurs="unbounded">
         <xs:choice>
            <xs:element ref="AssociationModel"/>
            <xs:element ref="ClusteringModel"/>
            <xs:element ref="GeneralRegressionModel"/>
            <xs:element ref="MiningModel"/>
            <xs:element ref="NaiveBayesModel"/>
            <xs:element ref="NeuralNetwork"/>
            <xs:element ref="RegressionModel"/>
            <xs:element ref="RuleSetModel"/>
            <xs:element ref="SequenceModel"/>
            <xs:element ref="SupportVectorMachineModel"/>
            <xs:element ref="TextModel"/>
            <xs:element ref="TreeModel"/>
          </xs:choice>
        </xs:sequence>
        <xs:element ref="Extension" minOccurs="0" maxOccurs="unbounded"/>
      </xs:sequence>
      <xs:attribute name="version" type="xs:string" use="required"/>
    </xs:complexType>
  </xs:element>

A PMML document can contain more than one model. If the application system provides a means of selecting models by name and if the PMML consumer specifies a model name, then that model is used; otherwise the first model is used.

A PMML compliant system is not required to provide model selection by name.

The list of mining models in a PMML document may even be empty. The document can be used to carry the initial metadata before an actual model is computed. A PMML document containing no model is not meant to be useful for a PMML consumer.

For PMML 3.1 the attribute version must have the value 3.1

The element MiningBuildTask can contain any XML value describing the configuration of the training run that produced the model instance. This information is not directly needed by a PMML consumer, but in many cases it is helpful for maintenance and visualization of the model. The particular content structure of MiningBuildTask is not defined by PMML. Though, this element would be the natural container for task specifications as defined by other mining standards, e.g., in SQL or Java.


  <xs:element name="MiningBuildTask">
    <xs:complexType>
      <xs:sequence>
        <xs:element ref="Extension" minOccurs="0" maxOccurs="unbounded"/>
      </xs:sequence>
    </xs:complexType>
  </xs:element>

The fields in the DataDictionary and in the TransformationDictionary taken together are identified by unique names. Other elements in the models can refer to these fields by name. Multiple models on one PMML document can share the same fields in the TransformationDictionary. Nevertheless, a model can also define its 'own' derived fields in the element LocalTransformations. Furthermore, various models use DerivedField elements directly in the definition of the model. For example, DerivedFields appear inline in the input layer of neural networks.

Certain types of PMML models such as neural networks or logistic regression can be used for different purposes. That is, some instances implement prediction of numeric values, while others can be used for classification. Therefore, PMML defines five different mining functions. Each model has an attribute functionName which specifies the mining function.


  <xs:simpleType name="MINING-FUNCTION">
    <xs:restriction base="xs:string">
      <xs:enumeration value="associationRules"/>
      <xs:enumeration value="sequences"/>
      <xs:enumeration value="classification"/>
      <xs:enumeration value="regression"/>
      <xs:enumeration value="clustering"/>
    </xs:restriction>
  </xs:simpleType>

For all PMML models the structure of the top-level model element is similar to the template of ExampleModel as below


  <xs:element name="ExampleModel">
    <xs:complexType>
      <xs:sequence>
        <xs:element ref="Extension" minOccurs="0" maxOccurs="unbounded"/>
        <xs:element ref="MiningSchema"/>
        <xs:element ref="Output" minOccurs="0"/>
        <xs:element ref="ModelStats" minOccurs="0"/>
        <xs:element ref="Targets" minOccurs="0"/>
        <xs:element ref="LocalTransformations" minOccurs="0" />
        ...
        <xs:element ref="ModelVerification" minOccurs="0"/>
        <xs:element ref="Extension" minOccurs="0" maxOccurs="unbounded"/>
      </xs:sequence>
      <xs:attribute name="modelName" type="xs:string" use="optional"/>
      <xs:attribute name="functionName" type="MINING-FUNCTION" use="required"/>
      <xs:attribute name="algorithmName" type="xs:string" use="optional"/>
    </xs:complexType>
  </xs:element>

The non-empty list of mining fields define a mining schema. The output element gives a list of result values and internal results such as confidences or probabilities that can be computed by the model. The univariate statistics contain global statistics on (a subset of the) mining fields. The targets section holds more information on the target values and accompanying information like prior probabilities, optypes and the like. LocalTransformations holds derived fields that are local to the model. Other model specific elements follow after that, in the content of ExampleModel. Finally, the ModelVerification part gives sample data and results of the model so consumers can instantly validate.
For a list of models that have been defined in PMML 3.1 see the element PMML above.

modelName: the value in modelName identifies the model with a unique name in the context of the PMML file. This attribute is not required. Consumers of PMML models are free to manage the names of the models at their discretion.

functionName and algorithmName describe the kind of mining model, e.g., whether it is intended to be used for clustering or for classification. The algorithm name is free-type and can be any description for the specific algorithm that produced the model. This attribute is for information only.


Naming Conventions

The naming conventions for PMML are:

  • Element Names are in mixed case, first uppercase.
  • AttributeNames are in mixed case, first lowercase.
  • Constants in enumerations are in mixed case, first lowercase.
  • SimpleTypes are all uppercase.
Usage of the character '-' is discouraged in order to avoid confusion with mathematical notation.


Extension Mechanism

The PMML schema contains a mechanism for extending the content of a model. Extension elements should be present as the first child in all elements and groups defined in PMML. This way it is possible to place information in the Extension elements which affects how the remaining entries are treated. The main element in each model should have Extension elements as the first and the last child for maximum flexibility.


  <xs:element name="Extension">
    <xs:complexType>
      <xs:complexContent mixed="true">
        <xs:restriction base="xs:anyType">
          <xs:sequence>
            <xs:any processContents="skip" minOccurs="0" maxOccurs="unbounded"/>
          </xs:sequence> 
          <xs:attribute name="extender" type="xs:string" use="optional"/>
          <xs:attribute name="name" type="xs:string" use="optional"/>
          <xs:attribute name="value" type="xs:string" use="optional"/>
        </xs:restriction>
      </xs:complexContent>
    </xs:complexType>
  </xs:element>

These extension elements have a content model of ANY, where vendor specific extension elements can be included. However, element types must start with X-. This convention helps to avoid conflicts with possible future extensions to standard PMML.
Extension also features the attributes name and value to specify single extension attributes, where name will specify the name of the extension attribute and value the respective value.

If a document uses local namespaces, then the name of the namespace should not start with PMML or DMG or any variant of these names with lowercase characters. They are reserved for future use in PMML.

Up to PMML 2.1, extension attributes could be added to all elements in PMML if the prefix x- was used. This mechanism is deprecated, extension elements should be used instead. PMML documents with extension attributes using the old convention are still considered to be valid PMML. However, note that PMML documents containing old-style x- extension attributes will not validate in XML schema, but one can use XSL transformation to remove all x- extension attributes and receive an XML document that will validate.

Examples

An extension attribute format can be added to a DataField like this:


  <DataField name="foo" optype="continuous" >
    <Extension name="format" value="%9.2f"/>
  </DataField >

An extension element DataFieldSource can be added to a DataField in the PCDATA section like this:


  <DataField name="foo" optype="continuous">
    <Extension>
      <DataFieldSource sourceKnown="yes">
        <Source>derivedFromInput</Source>
      </DataFieldSource>
    </Extension>
  </DataField >


Basic data types and entities

The definition


  <xs:simpleType name="NUMBER">
    <xs:restriction base="xs:double">
    </xs:restriction>
  </xs:simpleType>

is commonly used for distinguishing numeric values from other data. Numbers may have a leading sign, fractions, and an exponent. The type float in XML Schema supports numbers represented as INF, -INF, and NaN. These tokens are not allowed for NUMBER. In addition to NUMBER there are a couple of more specific types, they are like subtypes of NUMBER:


  <xs:simpleType name="INT-NUMBER">
    <xs:restriction base="xs:integer">
    </xs:restriction>
  </xs:simpleType>

An INT-NUMBER must be an integer, no fractions or exponent.


  <xs:simpleType name="REAL-NUMBER">
    <xs:restriction base="xs:double">
    </xs:restriction>
  </xs:simpleType>

A REAL-NUMBER can be any number covered by the C/C++ types float, long or double. Scientific notation, eg., 1.23e4, is allowed. Literals INF, -INF, and NaN are not supported.

PMML uses the character '.' as decimal point in the representation of REAL-NUMBER values.


  <xs:simpleType name="PROB-NUMBER">
    <xs:restriction base="xs:decimal">
    </xs:restriction>
  </xs:simpleType>

A PROB-NUMBER is a REAL-NUMBER between 0.0 and 1.0, usually describing a probability.


  <xs:simpleType name="PERCENTAGE-NUMBER">
    <xs:restriction base="xs:decimal">
    </xs:restriction>
  </xs:simpleType>

A PERCENTAGE-NUMBER is a REAL-NUMBER between 0.0 and 100.0.

Note that these entities do not enforce the XML parser to check the data types. However they still define requirements for a valid PMML document.

Many elements contain references to input fields. PMML does not use IDREF to represent field names because field names are not necessarily valid XML identifiers. However, given the definition


  <xs:simpleType name="FIELD-NAME">
    <xs:restriction base="xs:string">
    </xs:restriction>
  </xs:simpleType>

then references to input fields will be obvious from the schema syntax. Note that a model can refer to two kinds of input fields. One is the set of MiningFields in the MiningSchema. The others are the DerivedFields as defined in TransformationDictionary or LocalTransformations. Further note that field names, like all other elements of PMML and in XML in general, are case sensitive.


Plain Arrays of Values

Instances of mining models often contain sets with a large number of values. The type Array is defined as a container structure which implements arrays of numbers and strings in a fairly compact way.


  <xs:complexType name="ArrayType" mixed="true">
    <xs:attribute name="n" type="INT-NUMBER" use="optional"/>
    <xs:attribute name="type" use="required">
      <xs:simpleType>
        <xs:restriction base="xs:string">
          <xs:enumeration value="int"/>
          <xs:enumeration value="real"/>
          <xs:enumeration value="string"/>
        </xs:restriction>
      </xs:simpleType>
    </xs:attribute>
  </xs:complexType>

 <xs:element name="Array" type="ArrayType"/>

The content of Array is a blank separated sequence of values, multiple blanks are as good as one blank. The attribute n determines the number of elements in the sequence. If n is given it must match the number of values in the content, otherwise the PMML document is invalid. The attribute type is required since parsing an array is simpler if the type of the values in the content is specified up-front. This is particularly true for SAX based parsing. In many cases the type of the values is known from the context where the Array appears. But there are also cases where Arrays can be mixed e.g., in the statistics elements. String values may be enclosed within double quotes ", which are not considered to be part of the value. If a string value contains the double quote character " , then it must be escaped by a backslash character \ (that is the same escaping mechanism as used in C/C++).

Example:


  <Array n="3" type="int">1 22 3</Array>
  <Array n="3" type="string">ab  "a b"   "with \"quotes\" "</Array>

The second array contains the three strings 'ab', 'a b', and 'with "quotes" '.

Similar to the entities for different types of numbers we define entities for arrays which should have a specific content type. Again, these entities just map to a single XML markup.


  <xs:group name="NUM-ARRAY">
    <xs:choice>
      <xs:element ref="Array"/>
    </xs:choice>
  </xs:group>

  <xs:group name="INT-ARRAY">
    <xs:choice>
      <xs:element ref="Array"/>
    </xs:choice>
  </xs:group>

  <xs:group name="REAL-ARRAY">
    <xs:choice>
      <xs:element ref="Array"/>
    </xs:choice>
  </xs:group>

  <xs:group name="STRING-ARRAY">
    <xs:choice>
      <xs:element ref="Array"/>
    </xs:choice>
  </xs:group>

A NUM-ARRAY is an array of numbers. The other entities define arrays which contain integers, reals or strings.


Sparse Arrays of Values

A special case of arrays are sparse arrays which only store elements with non-zero values.


  <xs:element name="INT-SparseArray">
    <xs:complexType>
      <xs:sequence>
        <xs:element ref="Indices" minOccurs="0"/>
        <xs:element ref="Entries" minOccurs="0"/>
      </xs:sequence>
      <xs:attribute name="n" type="INT-NUMBER" use="optional"/>
      <xs:attribute name="defaultValue" type="INT-NUMBER" use="optional" default="0"/>
    </xs:complexType>
  </xs:element>

  <xs:element name="REAL-SparseArray">
    <xs:complexType>
      <xs:sequence>
        <xs:element ref="Indices" minOccurs="0"/>
        <xs:element ref="Entries" minOccurs="0"/>
      </xs:sequence>
      <xs:attribute name="n" type="INT-NUMBER" use="optional"/>
      <xs:attribute name="defaultValue" type="REAL-NUMBER" use="optional" default="0"/>
    </xs:complexType>
  </xs:element>

  <xs:element name="Indices">
    <xs:simpleType>
      <xs:list itemType="xs:int"/>
    </xs:simpleType>
 </xs:element>

  <xs:element name="Entries">
    <xs:simpleType>
      <xs:union>
        <xs:simpleType>
          <xs:list itemType="xs:int"/>
        </xs:simpleType>
        <xs:simpleType>
          <xs:list itemType="xs:double"/>
        </xs:simpleType>
      </xs:union>
    </xs:simpleType>
  </xs:element>

The content of SparseArray is two arrays, Indices and Entries. In both cases, the length is implicitly implied, and the content is defined by the kind of the sparse array. Indices contains the indices of entries that do not have the defaultValue; the index starts with 1. Entries contains the respective values for the indices specified in Indices. Or, to put it another way: The identifiers of the first array correspond to the data values to the second array in the same order. Hence, both arrays, Indices and Entries, must have the same length. If both, Indices and Entries, are omitted, then the sparse array has the default value for all entries (see second example below). Either both arrays, Indices and Entries, or none must be present - otherwise the PMML is not valid.
The attribute n specifies the length of the sparse array, which is especially useful in case the last entries are not explicitly specified. defaultValue can be used to specify an arbitrary default value for all positions which are not specified by the two arrays.

Examples:

The array 0 3 0 0 42 0 0 can be written like this:


  <INT-SparseArray n="7">
    <Indices>2 5</Indices>
    <Entries>3 42</Entries>
  </INT-SparseArray>

The array 0 0 0 0 0 0 can be written like this:


  <INT-SparseArray n="7"/>


Matrix

In order to save space, a matrix can be stored as a diagonal or even sparse matrix.


  <xs:element name="Matrix">
    <xs:complexType>
      <xs:choice minOccurs="0">
        <xs:group ref="NUM-ARRAY" maxOccurs="unbounded" />
        <xs:element ref="MatCell" maxOccurs="unbounded" />
      </xs:choice>
      <xs:attribute name="kind" use="optional" default="any" >
        <xs:simpleType>
          <xs:restriction base="xs:string">
            <xs:enumeration value="diagonal"/>
            <xs:enumeration value="symmetric"/>
            <xs:enumeration value="any"/>
          </xs:restriction>
        </xs:simpleType>
      </xs:attribute>
      <xs:attribute name="nbRows" type="INT-NUMBER" use="optional"/>
      <xs:attribute name="nbCols" type="INT-NUMBER" use="optional"/>
      <xs:attribute name="diagDefault" type="REAL-NUMBER" use="optional"/>
      <xs:attribute name="offDiagDefault" type="REAL-NUMBER" use="optional"/>
    </xs:complexType>
  </xs:element>

  <xs:element name="MatCell">
    <xs:complexType >
      <xs:simpleContent>
        <xs:extension base="xs:string">
          <xs:attribute name="row" type="INT-NUMBER" use="required" />
          <xs:attribute name="col" type="INT-NUMBER" use="required" />
        </xs:extension>
      </xs:simpleContent>
    </xs:complexType>
  </xs:element>

The matrix is internally represented as a sequence of Arrays or MatCells. If arrays are used, then each array contains elements of one row in the matrix.
On the other hand MatCells contain the numeric value of the cell specified by row and col. Indices for rows and columns start with 1. If a sparse representation is used, diagDefault and/or offDiagDefault must be set to fill in if no value is given for a certain cell.
nbRows and nbCols give the dimensions of the Matrix. If one of them is not specified, the respective dimension is implicitly given by the representation. In case of sparse representation using MatCells, the respective dimension is given by the respective maximum filled entry.

The actual representation is triggered by the kind of the Matrix:

  • diagonal: The content is just one array of numbers representing the diagonal values.
  • symmetric: The content must be represented by Arrays. The first array contains the matrix element M(0,0), the second array contains M(1,0), M(1,1), and so on (that is the lower left triangle). Other elements are defined by symmetry.
  • any: Either specify all values via Arrays, or choose sparse structures using MatCells.

Evaluating a matrix element M(i,j) proceeds as follows:

  1. The element is explicitly given, either in a MatCell with row=i and col=j, or in the j-th element of the i-th array of Matrix.
  2. The attribute kind of the matrix is symmetric, and the element M(j,i) is explicitely given.
  3. A default value is given, either in the attribute diagDefault, or in the attribute offDiagDefault.
  4. No value can be calculated at this step. Calculation will be done only if a default behavior or additional information are given at a higher level.

Example:
The matrix
  0  0  0 42  0
  0  1  0  0  0
  5  0  0  0  0
  0  0  0  0  7
  0  0  9  0  0
can be written in the following ways (non-sparse and sparse representation):

  <Matrix nbRows="5" nbCols="5">
    <Array type="real">0 0 0 42 0</Array>
    <Array type="real">0 1 0 0 0</Array>
    <Array type="real">5 0 0 0 0</Array>
    <Array type="real">0 0 0 0 7</Array>
    <Array type="real">0 0 9 0 0</Array>
  </Matrix>

  <Matrix diagDefault="0" offDiagDefault="0">
    <MatCell row="1" col="4">42</MatCell>
    <MatCell row="2" col="2">1</MatCell>
    <MatCell row="3" col="1">5</MatCell>
    <MatCell row="4" col="5">7</MatCell>
    <MatCell row="5" col="3">9</MatCell>
  </Matrix>

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