Normalize data - MATLAB normalize (2024)

N = normalize(A)

N = normalize(A,dim)

N = normalize(___,method)

N = normalize(___,method,methodtype)

N = normalize(___,"center",centertype,"scale",scaletype)

N = normalize(___,Name,Value)

[N,C,S] = normalize(___)

N = normalize(A) returns the vectorwise z-score of the data in A with center 0 and standard deviation 1.

N = normalize(___,"center",centertype,"scale",scaletype) uses the "center" and "scale" methods at the same time. These are the only methods you can use together. If you do not specify centertype or scaletype, then normalize uses the default method type for that method (centering to have a mean of 0 and scaling by the standard deviation).

Use this syntax with any center and scale type to perform both methods together. For instance, N = normalize(A,"center","median","scale","mad"). You can also use this syntax to specify centering and scaling values C and S from a previously computed normalization. For instance, normalize one data set and save the parameters with [N1,C,S] = normalize(A1). Then, reuse those parameters on a different data set with N2 = normalize(A2,"center",C,"scale",S).

[N,C,S] = normalize(___) additionally returns the centering and scaling values C and S used to perform the normalization. Then, you can normalize different input data using the values in C and S with N = normalize(A2,"center",C,"scale",S).

Alternative

You can use normalize functionality interactively by adding the Normalize Data task to a live script.

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: normalize(T,ReplaceValues=false)

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: normalize(T,"ReplaceValues",false)

z-scores measure the distance of a data point from the mean in terms of the standard deviation. The standardized data set has mean 0 and standard deviation 1, and retains the shape properties of the original data set (same skewness and kurtosis).

For a random variable X with mean μ and standard deviation σ, the z-score of a value x is $$z=\frac{\left(x-\mu \right)}{\sigma }.$$ For sample data with mean $$\overline{X}$$ and standard deviation S, the z-score of a data point x is $$z=\frac{\left(x-\overline{X}\right)}{S}.$$

The general definition for the p-norm of a vector v that has N elements is

where p is any positive real value, Inf, or -Inf. Some common values of p are 1, 2, and Inf.

Rescaling changes the distance between the min and max values in a data set by stretching or squeezing the points along the number line. The z-scores of the data are preserved, so the shape of the distribution remains the same.

The equation for rescaling data X to an arbitrary interval [a b] is

If A is constant, then normalize returns the lower bound of the interval (0 by default) or NaN (when the specified interval contains Inf).

While the normalize and rescale functions can both rescale data to any arbitrary interval, rescale also permits clipping the input data to specified minimum and maximum values.

The interquartile range (IQR) of a data set describes the range of the middle 50% of values when the values are sorted. If Q1 is the 25th percentile of the data and Q3 is the 75th percentile of the data, then $$\text{IQR=Q3-Q1}$$.

If A is constant, then the interquartile range of A is 0, but if the values are missing or infinite, then the interquartile range of A is NaN.

The IQR is generally preferred over looking at the full range of the data when the data contains outliers (very large or very small values) because the IQR excludes the largest 25% and smallest 25% of values in the data.

The median absolute deviation (MAD) of a data set is the median value of the absolute deviations from the median $$\tilde{X}$$ of the data: $$\text{MAD}=\text{median}\left(\left|x-\tilde{X}\right|\right)$$. Therefore, the MAD describes the variability of the data in relation to the median.

The MAD is generally preferred over using the standard deviation of the data when the data contains outliers (very large or very small values) because the standard deviation squares deviations from the mean, giving outliers an unduly large impact. Conversely, the deviations of a small number of outliers do not affect the value of the MAD.

• The outputs C and S are not supported.

• The "center" and "scale" methods cannot be specified at the same time.

• The supported method types for "center" are: "mean", "median", or a numeric scalar.

• The supported method types for "scale" are: "std", "mad", "first", or a numeric scalar.

• The DataVariables name-value argument cannot specify a function handle.

• Normalization methods that require calculation of the median or interquartile range along the first dimension only support tall column vector data. This includes the methods normalize(___,"zscore","robust"), normalize(___,"scale","mad"), normalize(___,"scale","iqr"), normalize(___,"center","median"), and normalize(___,"medianiqr").

• When the method types for "center" and "scale" are both tables and DataVariables is not provided, the method types must have table variable names in the same order.

• The syntax normalize(___,"medianiqr") is not supported.

• The syntax normalize(___,"scale","iqr") is not supported.

You can now append, instead of replace, input table variables with table variables containing normalized data by setting the ReplaceValues name-value argument to false.

The ReplaceValues name-value argument is supported only for table and timetable input data.

Return and reuse the centering and scaling normalization parameter values to normalize subsequent data sets. For example, normalize array A and then normalize array B with the same parameters.

[Anorm,C,S] = normalize(A);Bnorm = normalize(B,"center",C,"scale",S);

The new outputs, centering value C and scaling parameter S, allow for reuse in a later normalization step. Specify the "center" and "scale" normalization methods at the same time. These are the only two normalization methods that you can specify together.

When method is "center" or "scale", the possible values of methodtype include arrays and tables. While these methodtype values are intended to work with the new outputs C and S, you also can compute your own normalization parameters to specify.