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Scalers & Encoders

Summary

The pipes API provides a good foundation to construct data processing pipelines, in this section we show how it is extended for application to a specific application i.e. attribute scaling & transformation.

Transforming data attributes is an often repeated task, some examples include re-scaling values in a finite domain $[min, max]$, gaussian centering, principal component analysis (PCA), discreet Haar wavelet (DWT) transform etc.

The pipes API contains traits for these tasks, they are abstract skeletons which can be extended by the user to create arbitrary feature re-scaling transformations.

Encoders

Encoder[I, J] are an extension of DataPipe[I, J] class which has an extra value member i: DataPipe[J, I] which represents the inverse transformation.

Note

Encoder[I, J] implies a reversible, one to one transformation of the input. Mathematically this can be expressed as

$$\begin{align} g: \mathcal{X} &\rightarrow \mathcal{Y} \\ h: \mathcal{Y} &\rightarrow \mathcal{X} \\ h(g(x)) &= x \ \ \ \forall x \in \mathcal{X} \\ h &\equiv g^{-1} \end{align}$$

An encoder can be created by calling the apply method of the Encoder object.

//Converts a point expressed in cartesian coordinates
//into a point expressed in polar coordinates and vice versa.
val cartesianToPolar = Encoder(
  (pointCart: (Double, Double)) => {
    val (x,y) = pointCart
    val r = math.sqrt(x*x + y*y)
    if(r != 0.0) (r, math.arcsin(y/r)) else (0.0, 0.0)
  }),
  (pointPolar: (Double, Double)) => {
    val (r, theta) = pointPolar
    (r*math.cos(theta), r*math.sin(theta))
  }
)

Note

In the above example, we created a cartesian to polar coordinate converter by specifying the forward and reverse transformations as anonymous scala functions. But we could as well have passed the forward and reverse transforms as DataPipe instances.

val forwardTransform: DataPipe[I, J] = _
val reverseTransform: DataPipe[J, I] = _
//Still works.
val enc = Encoder(forwardTransform, reverseTransform)

Scalers

Scaler[I] is an extension of the DataPipe[I, I] trait. Represents transformations of inputs which don't change their type.

val linTr = Scaler((x: Double) => x*5.0 + -1.5)

Reversible Scalers

ReversibleScaler[I] extends Scaler[I] along with Encoder[I, J], a reversible re-scaling of inputs.

The > and * for scalers and encoders

Since Encoder[S, D], Scaler[S] and ReversibleScaler[S, D] are inherit the DataPipe trait, they can be composed with any data pipeline as usual, but there are special cases.

If an Encoder[I, J] instance is composed with Encoder[J, K], the result is of type Encoder[I, K] and accordingly for Scaler[I] and ReversibleScaler[I].

The * can be used to create cartesian products of encoders and scalers.

val enc1: Encoder[I, J] = _
val enc2: Encoder[K, L] = _
val enc3: Encoder[(I, K), (J, L)] = enc1*enc2

Tip

Common attribute transformations like gaussian centering, min-max scaling, etc are included in the dynaml.utils package, click here to see their syntax.

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