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:

minmax_dense_batch.cpp

oneDAL documentation