Intel® oneAPI Data Analytics Library Developer Guide and Reference
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Z-score
Z-score normalization is an algorithm that produces data with each feature (column) having zero mean and unit variance.
Details
Given a set X of n feature vectors 
 of dimension p, the problem is to compute the matrix 
 of dimension 
 as following:
 
   where:
 is the mean of j-th component of set 
, where 
value of
 depends omn a computation mode
oneDAL provides two modes for computing the result matrix. You can enable the mode by setting the flag doScale to a certain position (for details, see Algorithm Parameters). The mode may include:
Centering only. In this case,
 and no scaling is performed. After normalization, the mean of j-th component of result set 
 will be zero.Centering and scaling. In this case,
, where 
 is the standard deviation of j-th component of set 
. After normalization, the mean of j-th component of result set 
 will be zero and its variance will get a value of one.
Batch Processing
Algorithm Input
Z-score normalization algorithm accepts an input as described below. Pass the Input ID as a parameter to the methods that provide input for your algorithm. For more details, see Algorithms.
Input ID  |  
        Input  |  
       
|---|---|
data  |  
        Pointer to the numeric table of size  
            NOTE: 
            This table can be an object of any class derived from NumericTable. 
          |  
       
Algorithm Parameters
Z-score normalization algorithm has the following parameters. Some of them are required only for specific values of the computation method parameter method:
Parameter  |  
        method  |  
        Default Value  |  
        Description  |  
       
|---|---|---|---|
algorithmFPType  |  
        defaultDense or sumDense  |  
        float  |  
        The floating-point type that the algorithm uses for intermediate computations. Can be float or double.  |  
       
method  |  
        Not applicable  |  
        defaultDense  |  
        Available computation methods: 
  |  
       
moments  |  
        defaultDense  |  
        SharedPtr<low_order_moments::Batch<algorithmFPType, low_order_moments::defaultDense> >  |  
        Pointer to the low order moments algorithm that computes means and standard deviations to be used for Z-score normalization with the defaultDense method.  |  
       
doScale  |  
        defaultDense or sumDense  |  
        true  |  
        If true, the algorithm applies both centering and scaling. Otherwise, the algorithm provides only centering.  |  
       
resultsToCompute  |  
        defaultDense or sumDense  |  
        Not applicable  |  
        Optional. Pointer to the data collection containing the following key-value pairs for Z-score: 
 Provide one of these values to request a single characteristic or use bitwise OR to request a combination of them.  |  
       
Algorithm Output
Z-score normalization algorithm calculates the result as described below. Pass the Result ID as a parameter to the methods that access the results of your algorithm. For more details, see Algorithms.
Result ID  |  
        Result  |  
       
|---|---|
normalizedData  |  
        Pointer to the  
            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. 
          |  
       
means  |  
        Optional. Pointer to the  If the function result is not requested through the resultsToCompute parameter, the numeric table contains a NULL pointer.  |  
       
variances  |  
        Optional. Pointer to the  If the function result is not requested through the resultsToCompute parameter, the numeric table contains a NULL pointer. -  |  
       
Examples
C++ (CPU)
Batch Processing:
Python*
Batch Processing:
 numeric table that contains mean values for each feature.