# Data Transformations

In general, data transformations change raw feature vectors into a representation that is more suitable for various estimators.

## Standardization a.k.a Z-score Normalization

**Standardization**, also known as Z-score normalization, is a common requirement for many machine learning techniques. These techniques might perform poorly if the individual features do not more or less look like standard normally distributed data.

Standardization transforms data points into corresponding standard scores by subtracting mean and scaling to unit variance.

The **standard score**, also known as Z-score, is the signed number of standard deviations by which the value of an observation or data point is above the mean value of what is being observed or measured.

Standardization can be performed using `t = fit(ZScoreTransform, ...)`

followed by `StatsBase.transform(t, ...)`

or `StatsBase.transform!(t, ...)`

. `standardize(ZScoreTransform, ...)`

is a shorthand to perform both operations in a single call.

`StatsAPI.fit`

— Method`fit(ZScoreTransform, X; dims=nothing, center=true, scale=true)`

Fit standardization parameters to vector or matrix `X`

and return a `ZScoreTransform`

transformation object.

**Keyword arguments**

`dims`

: if`1`

fit standardization parameters in column-wise fashion; if`2`

fit in row-wise fashion. The default is`nothing`

, which is equivalent to`dims=2`

with a deprecation warning.`center`

: if`true`

(the default) center data so that its mean is zero.`scale`

: if`true`

(the default) scale the data so that its variance is equal to one.

**Examples**

```
julia> using StatsBase
julia> X = [0.0 -0.5 0.5; 0.0 1.0 2.0]
2×3 Matrix{Float64}:
0.0 -0.5 0.5
0.0 1.0 2.0
julia> dt = fit(ZScoreTransform, X, dims=2)
ZScoreTransform{Float64, Vector{Float64}}(2, 2, [0.0, 1.0], [0.5, 1.0])
julia> StatsBase.transform(dt, X)
2×3 Matrix{Float64}:
0.0 -1.0 1.0
-1.0 0.0 1.0
```

## Unit Range Normalization

**Unit range normalization**, also known as min-max scaling, is an alternative data transformation which scales features to lie in the interval `[0; 1]`

.

Unit range normalization can be performed using `t = fit(UnitRangeTransform, ...)`

followed by `StatsBase.transform(t, ...)`

or `StatsBase.transform!(t, ...)`

. `standardize(UnitRangeTransform, ...)`

is a shorthand to perform both operations in a single call.

`StatsAPI.fit`

— Method`fit(UnitRangeTransform, X; dims=nothing, unit=true)`

Fit a scaling parameters to vector or matrix `X`

and return a `UnitRangeTransform`

transformation object.

**Keyword arguments**

`dims`

: if`1`

fit standardization parameters in column-wise fashion;

if `2`

fit in row-wise fashion. The default is `nothing`

.

`unit`

: if`true`

(the default) shift the minimum data to zero.

**Examples**

```
julia> using StatsBase
julia> X = [0.0 -0.5 0.5; 0.0 1.0 2.0]
2×3 Matrix{Float64}:
0.0 -0.5 0.5
0.0 1.0 2.0
julia> dt = fit(UnitRangeTransform, X, dims=2)
UnitRangeTransform{Float64, Vector{Float64}}(2, 2, true, [-0.5, 0.0], [1.0, 0.5])
julia> StatsBase.transform(dt, X)
2×3 Matrix{Float64}:
0.5 0.0 1.0
0.0 0.5 1.0
```

## Methods

`StatsBase.transform`

— Function`transform(t::AbstractDataTransform, x)`

Return a standardized copy of vector or matrix `x`

using transformation `t`

.

`StatsBase.transform!`

— Function`transform!(t::AbstractDataTransform, x)`

Apply transformation `t`

to vector or matrix `x`

in place.

`StatsBase.reconstruct`

— Function`reconstruct(t::AbstractDataTransform, y)`

Return a reconstruction of an originally scaled data from a transformed vector or matrix `y`

using transformation `t`

.

`StatsBase.reconstruct!`

— Function`reconstruct!(t::AbstractDataTransform, y)`

Perform an in-place reconstruction into an original data scale from a transformed vector or matrix `y`

using transformation `t`

.

`StatsBase.standardize`

— Function`standardize(DT, X; dims=nothing, kwargs...)`

Return a standardized copy of vector or matrix `X`

along dimensions `dims`

using transformation `DT`

which is a subtype of `AbstractDataTransform`

:

`ZScoreTransform`

`UnitRangeTransform`

**Example**

```
julia> using StatsBase
julia> standardize(ZScoreTransform, [0.0 -0.5 0.5; 0.0 1.0 2.0], dims=2)
2×3 Matrix{Float64}:
0.0 -1.0 1.0
-1.0 0.0 1.0
julia> standardize(UnitRangeTransform, [0.0 -0.5 0.5; 0.0 1.0 2.0], dims=2)
2×3 Matrix{Float64}:
0.5 0.0 1.0
0.0 0.5 1.0
```

## Types

`StatsBase.UnitRangeTransform`

— TypeUnit range normalization

`StatsBase.ZScoreTransform`

— TypeStandardization (Z-score transformation)