Standardize
Standardize[list]
shifts and rescales the elements of list to have zero mean and unit sample variance.
Standardize[list,f1]
shifts the elements in list by f1[list] and rescales them to have unit sample variance.
Standardize[list,f1,f2]
shifts by f1[list] and scales by f2[list].
Details
- Standardize shifts by a location and rescales by a scale estimated from the elements of list.
- Standardize[list] is effectively (list-Mean[list])/StandardDeviation[list] for nonzero StandardDeviation[list].
- Standardize[list,f1] is effectively (list-f1[list])/StandardDeviation[list].
- Standardize[list,f1,f2] is effectively (list-f1[list])/f2[list].
- Common choices for f1 and f2 include:
-
Mean StandardDeviation zero mean and unit variance Mean 1& shift to mean 0 Median 1& shift by the median 0& StandardDeviation scale to have unit variance - Standardize handles both numerical and symbolic data.
- Standardize[{{x1,y1,…},{x2,y2,…},…}] effectively gives Transpose[{Standardize[{x1,x2,…}],Standardize[{y1,y2,…}],…}]. »
- Standardize works with SparseArray objects. »
Examples
open allclose allBasic Examples (3)
Compute standard scores for data:
Shift to have mean zero without scaling:
Shift by the Median and scale by the InterquartileRange:
Scope (5)
Standardize exact numeric data:
Standardize arbitrary‐precision data:
Standardize matrix data by column:
Standardize a TimeSeries:
Generalizations & Extensions (1)
Standardize a SparseArray:
Applications (3)
Shift normally distributed values to a standard normal:
Center a data matrix by subtracting column means:
The mean of the centered data is 0:
The covariance structure is unchanged:
Use Standardize to centralize a TimeSeries:
Properties & Relations (1)
Compute MeanDeviation using Standardize: