Introduction to FunctionXform in PmmlTransformations

Introduction

This vignette provides examples of how to use the FunctionXform transformation to create new data features for PMML models.

Given a WrapData object and a transformation expression, FunctionXform calculates data for a new feature and creates a new WrapData object. When PMML is produced with pmml::pmml(), the transformation is inserted into the LocalTransformations node as a DerivedField.

FunctionXform makes it possible to use multiple data fields and functions to produce a new feature.

While FunctionXform is part of the pmmlTransformations package, the code to produce pmml from R is in the pmml package. The following examples assume that both these packages are installed and loaded. The kable function is part of knitr, and is used to make tables more readable.

Single numeric field

Using the iris dataset as an example, let’s construct a new feature by transforming one variable. Load the dataset and show the first few lines:

data(iris)
kable(head(iris,3))

Create the irisBox object with WrapData:

irisBox <- WrapData(iris)

irisBox contains the data and transform information that will be used to produce PMML later. The original data is in irisBox$data. Any new features created with a transformation are added as columns to this data frame.

kable(head(irisBox$data,3))

Transform and field information is in irisBox$fieldData. The fieldData data frame contains information on every field in the dataset, as well as every transform used. The functionXform column contains expressions used in the FunctionXform transform.

kable(irisBox$fieldData)

Now add a new feature, Sepal.Length.Sqrt, using FunctionXform:

irisBox <- FunctionXform(irisBox,origFieldName="Sepal.Length",
                         newFieldName="Sepal.Length.Sqrt",
                         formulaText="sqrt(Sepal.Length)")

The new feature is calculated and added as a column to the irisBox$data data frame:

kable(head(irisBox$data,3))

irisBox$fieldData now contains a new row with the transformation expression:

kable(irisBox$fieldData[6,c(1:3,14)])

Construct a linear model for Petal.Width using this new feature:

fit <- lm(Petal.Width ~ Sepal.Length.Sqrt, data=irisBox$data)

# Convert to PMML:
# fit_pmml <- pmml(fit, transform=irisBox)

Since the model predicts Petal.Width using a variable based on Sepal.Length, the PMML will contain these two fields in the DataDictionary and MiningSchema:

# fit_pmml[[2]] #Data Dictionary node
# fit_pmml[[3]][[1]] #Mining Schema node

The LocalTransformations node contains Sepal.Length.Sqrt as a derived field:

# fit_pmml[[3]][[3]]

Single categorical field

FunctionXform can also operate on categorical data. In this example, let’s create a boolean feature that equals 1 only when Species is setosa:

irisBox <- WrapData(iris)
irisBox <- FunctionXform(irisBox,origFieldName="Species",
                         newFieldName="Species.Setosa",
                         formulaText="if (Species == 'setosa') {1} else {0}")
kable(head(irisBox$data,3))

Create a linear model and check the LocalTransformations node:

fit <- lm(Petal.Width ~ Species.Setosa, data=irisBox$data)
# fit_pmml <- pmml(fit, transform=irisBox)
# fit_pmml[[3]][[3]]

Multiple input fields

It is possible to create new features by combining several fields. Let’s create a new field from the ratio of sepal and petal lengths:

irisBox <- WrapData(iris)
irisBox <- FunctionXform(irisBox,origFieldName="Sepal.Length,Petal.Length",
                         newFieldName="Length.Ratio",
                         formulaText="Sepal.Length / Petal.Length")

As before, the new field is added as a column to the irisBox$data data frame:

kable(head(irisBox$data,3))

Fit a linear model using this new feature:

fit <- lm(Petal.Width ~ Length.Ratio, data=irisBox$data)

# Convert to pmml:
# fit_pmml <- pmml(fit, transform=irisBox)

The pmml will contain Sepal.Length and Petal.Length in the DataDictionary and MiningSchema, since these were used in FormulaXform:

# fit_pmml[[2]] #Data Dictionary node
# fit_pmml[[3]][[1]] #Mining Schema node

The Local.Transformations node contains Length.Ratio as a derived field:

# fit_pmml[[3]][[3]]

Using a previously derived feature

It is possible to pass a feature derived with FunctionXform to another FunctionXform call. To do this, the second call to FunctionXform must use the original data field names (instead of the derived field) in the origFieldName argument.

irisBox <- WrapData(iris)
irisBox <- FunctionXform(irisBox,origFieldName="Sepal.Length,Petal.Length",
                         newFieldName="Length.Ratio",
                         formulaText="Sepal.Length / Petal.Length")

irisBox <- FunctionXform(irisBox,origFieldName="Sepal.Length,Petal.Length,Sepal.Width",
                         newFieldName="Length.R.Times.S.Width",
                         formulaText="Length.Ratio * Sepal.Width")
kable(irisBox$fieldData[6:7,c(1:3,14)])

fit <- lm(Petal.Width ~ Length.R.Times.S.Width, data=irisBox$data)
# Convert to pmml:
# fit_pmml <- pmml(fit, transform=irisBox)

The pmml will contain Sepal.Length, Petal.Length, and Sepal.Width in the DataDictionary and MiningSchema, since these were used in FormulaXform:

# fit_pmml[[2]] #Data Dictionary node
# fit_pmml[[3]][[1]] #Mining Schema node

The Local.Transformations node contains Length.Ratio and Length.R.Times.S.Width as derived fields:

# fit_pmml[[3]][[3]]

PMML functions supported by FunctionXform

The following R functions and operators are directly supported by FunctionXform. Their PMML equivalents are listed on the second line:

• • / * ^ < <= > >= && & | || == != ! ceiling prod log — — — — —- ——— ———— ———— ————— —- —- — — —— ——— —- ——– ——– —-
• • / * ^ < <= > >= && & | || == != ! ceiling prod log
• • / * pow lessThan lessOrEqual greaterThan greaterOrEqual and and or or equal notEqual not ceil product ln

For these functions, no extra code is required for translation.

The R function prod can be used as long as only numeric arguments are specified. That is, prod can take an na.rm argument, but specifying this in FunctionXform directly will not produce PMML equivalent to the R expression.

Similarly, the R function log can be used directly as long as the second argument (the base) is not specified.

PMML functions not supported by FunctionXform

There are built-in functions defined in PMML that cannot be directly translated to PMML using FunctionXform as described above.

In this case, an error will be thrown when R tries to calculate a new feature using the function passed to FunctionXform, but does not see that function in the environment.

It is still possible to make FunctionXform work, but the PMML function must be defined in the R environment first.

Let’s use isIn, a PMML function, as an example. The function returns a boolean indicating whether the first argument is contained in a list of values. Detailed specification for this function is available on this DMG page.

One way to implement this in R is by using %in%, with the list of values being represented by ...:

isIn <- function(x, ...) {
  dots <- c(...)
  if (x %in% dots) {
    return(TRUE)
  } else {
    return(FALSE)
  }
}

isIn(1,2,1,4)
#> [1] TRUE

This function can now be passed to FunctionXform. The following code creates a feature that indicates whether Species is either setosa or versicolor:

irisBox <- WrapData(iris)
irisBox <- FunctionXform(irisBox,origFieldName="Species",
                         newFieldName="Species.Setosa.or.Versicolor",
                         formulaText="isIn(Species,'setosa','versicolor')")

The data data frame now contains the new feature:

kable(head(irisBox$data,3))

Create a linear model and view the corresponding PMML for the function:

fit <- lm(Petal.Width ~ Species.Setosa.or.Versicolor, data=irisBox$data)
# fit_pmml <- pmml(fit, transform=irisBox)
# fit_pmml[[3]][[3]]

PMML Function not supported by FunctionXform - another example

As another example, let’s use R’s mean function to create a new feature. PMML has a built-in avg, so we will define an R function with this name.

avg <- function(...) {
  dots <- c(...)
  return(mean(dots))
}

Now use this function to take an average of several other features and combine with another field:

irisBox <- WrapData(iris)
irisBox <- FunctionXform(irisBox,origFieldName="Sepal.Length,Petal.Length,Sepal.Width",
                         newFieldName="Length.Average.Ratio",
                         formulaText="avg(Sepal.Length,Petal.Length)/Sepal.Width")

The data data frame now contains the new feature:

kable(head(irisBox$data,3))

Create a simple linear model and view the corresponding PMML for the function:

fit <- lm(Petal.Width ~ Length.Average.Ratio, data=irisBox$data)
# fit_pmml <- pmml(fit, transform=irisBox)
# fit_pmml[[3]][[3]]

In the PMML, avg will be recognized as a valid function.

PMML for arbitrary functions

The function functionToPMML (part of the pmml package) makes it possible to convert an R expression into PMML directly, without creating a model or calculating values.

As long as the expression passed to the function is a valid R expression (e.g., no unbalanced parentheses), it can contain arbitrary function names not defined in R. Variables in the expression passed to FunctionXform are always assumed to be field names, and not substituted. That is, even if x has a value in the R environment, the resulting expression will still use x.

# functionToPMML("1 + 2")

# x <- 3
# functionToPMML("foo(bar(x * y))")

More notes on functions

There are several limitations to parsing expressions in FunctionXform.

Each transformation operates on one data row at a time. For example, it is not possible to compute the mean of an entire feature column in FunctionXform.

An expression such as foo(x) is treated as a function foo with argument x. Consequently, passing in an R vector c(1,2,3) will produce PMML where c is a function and 1,2,3 are the arguments:

# functionToPMML("c(1,2,3)")

We can also see what happens when passing an na.rm argument to prod, as mentioned in an above example:

# functionToPMML("prod(1,2,na.rm=FALSE)") #produces incorrect PMML
# functionToPMML("prod(1,2)") #produces correct PMML

Additionally, passing in a vector to prod produces incorrect PMML:

# prod(c(1,2,3))
# functionToPMML("prod(c(1,2,3))")

More examples of functions

The following are additional examples of pmml produced from R expressions.

Extra parentheses:

# functionToPMML("pmmlT(((1+2))*(x))")

If-else expressions:

# functionToPMML("if(a<2) {x+3} else if (a>4) {4} else {5}")

References

• PMML 4.3 official specification