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Min-max

Min-max normalization is an algorithm to linearly scale the observations by each feature (column) into the range \([a, b]\).

Problem Statement

Given a set \(X\) of \(n\) feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\) of dimension \(p\), the problem is to compute the matrix \(Y = (y_{ij})_{n \times p}\) where the \(j\)-th column \((Y)_j = (y_{ij})_{i = 1, \ldots, n}\) is obtained as a result of normalizing the column \((X)_j = (x_{ij})_{i = 1, \ldots, n}\) of the original matrix as:

\[y_{ij} = a + \frac {x_{ij} - \min(j)}{\max(j) - \min(j)} (b-a),\]

where:

\[\min(j) = \min _{i = 1, \ldots, n} x_{ij},\]
\[\max(j) = \max _{i = 1, \ldots, n} x_{ij},\]

\(a\) and \(b\) are the parameters of the algorithm.

Batch Processing

Algorithm Input

The min-max normalization algorithm accepts the input described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.

Algorithm Input for Min-max (Batch Processing)

Input ID

Input

data

Pointer to the numeric table of size \(n \times p\).

Note

This table can be an object of any class derived from NumericTable.

Algorithm Parameters

The min-max normalization algorithm has the following parameters:

Algorithm Parameters for Min-max (Batch Processing)

Parameter

Default Value

Description

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

Performance-oriented computation method, the only method supported by the algorithm.

lowerBound

\(0.0\)

The lower bound of the range to which the normalization scales values of the features.

upperBound

\(1.0\)

The upper bound of the range to which the normalization scales values of the features.

moments

SharedPtr<low_order_moments::Batch<algorithmFPType, low_order_moments::defaultDense> >

Pointer to the low order moments algorithm that computes minimums and maximums to be used for min-max normalization with the defaultDense method. For more details, see Batch Processing for Moments of Low Order.

Algorithm Output

The min-max normalization algorithm calculates the result described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.

Algorithm Output for Min-max (Batch Processing)

Result ID

Result

normalizedData

Pointer to the \(n \times p\) numeric table that stores the result of normalization.

Note

By default, the result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedTriangularMatrix, PackedSymmetricMatrix, and CSRNumericTable.

Examples

Batch Processing:

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