Normalize Data

Center and scale data in the Live Editor

Since R2021b

Description

The Normalize Data task lets you interactively normalize data by choosing centering and scaling methods, such as z-score. The task automatically generates MATLAB^® code for your live script.

Using this task, you can:

• Customize how to center and scale data in a workspace variable such as a table or timetable.

• Visualize the input data compared to the normalized data.

• Return the centering and scaling values used to compute the normalization.

For more information on Live Editor tasks, see Add Interactive Tasks to a Live Script.

Related Functions

Normalize Data generates code that uses the normalize function.

Open the Task

To add the Normalize Data task to a live script in the MATLAB Editor:

• On the Live Editor tab, select Task > Normalize Data.

• In a code block in the script, type a relevant keyword, such as normalize, range, or scale. Select Normalize Data from the suggested command completions. For some keywords, the task automatically updates one or more corresponding parameters.

Examples

Normalize Multiple Data Sets with Same Parameters

Interactively normalize a data set and return the computed parameter values using the Normalize Data task in the Live Editor. Then, reuse the parameters to apply the same normalization to another data set.

Create a timetable with two variables: Temperature and WindSpeed. Then create a second timetable with the same variables, but with the samples taken a year later.

Time1 = (datetime(2019,1,1):days(1):datetime(2019,1,10))';
Temperature = randi([10 40],10,1);
WindSpeed = randi([0 20],10,1);
T1 = timetable(Temperature,WindSpeed,RowTimes=Time1)

T1=10×2 timetable
       Time        Temperature    WindSpeed
    ___________    ___________    _________

    01-Jan-2019        35             3    
    02-Jan-2019        38            20    
    03-Jan-2019        13            20    
    04-Jan-2019        38            10    
    05-Jan-2019        29            16    
    06-Jan-2019        13             2    
    07-Jan-2019        18             8    
    08-Jan-2019        26            19    
    09-Jan-2019        39            16    
    10-Jan-2019        39            20    

Time2 = (datetime(2020,1,1):days(1):datetime(2020,1,10))';
Temperature = randi([10 40],10,1);
WindSpeed = randi([0 20],10,1);
T2 = timetable(Temperature,WindSpeed,RowTimes=Time2)

T2=10×2 timetable
       Time        Temperature    WindSpeed
    ___________    ___________    _________

    01-Jan-2020        30            14    
    02-Jan-2020        11             0    
    03-Jan-2020        36             5    
    04-Jan-2020        38             0    
    05-Jan-2020        31             2    
    06-Jan-2020        33            17    
    07-Jan-2020        33            14    
    08-Jan-2020        22             6    
    09-Jan-2020        30            19    
    10-Jan-2020        15             0    

Open the Normalize Data task in the Live Editor. To normalize the first timetable, select T1 as the input data and normalize all supported variables.

By default, the Normalize Data task returns the normalized data. In addition to the normalized data, return the centering and scaling parameter values that the task uses to perform the normalization by selecting Return center and scale values in the Specify method and parameters section of the task.

The output arguments newTable, centerValue, and scaleValue represent the normalized values, the centering values, and the scaling values, respectively.

% Normalize Data
[newTable,centerValue,scaleValue] = normalize(T1);

% Display results
figure
tiledlayout(2,1);
nexttile
plot(T1.Time,T1.Temperature,"SeriesIndex",6,"DisplayName","Input data")
legend
ylabel("Temperature")
xlabel("Time")

nexttile
plot(T1.Time,newTable.Temperature,"SeriesIndex",1,"LineWidth",1.5, ...
    "DisplayName","Normalized data")
legend
ylabel("Temperature")
xlabel("Time")

set(gcf,"NextPlot","New")

You can use the output arguments of a Live Editor task in subsequent code. Use the normalize function to normalize the second timetable T2 using the parameter values from the first normalization. This technique ensures that the data in T2 is centered and scaled in the same way as T1.

T2_norm = normalize(T2,"center",centerValue,"scale",scaleValue)

T2_norm=10×2 timetable
       Time        Temperature    WindSpeed
    ___________    ___________    _________

    01-Jan-2020      0.11165      0.084441 
    02-Jan-2020      -1.6562       -1.8858 
    03-Jan-2020      0.66992       -1.1822 
    04-Jan-2020        0.856       -1.8858 
    05-Jan-2020       0.2047       -1.6044 
    06-Jan-2020      0.39078       0.50665 
    07-Jan-2020      0.39078      0.084441 
    08-Jan-2020      -0.6327       -1.0414 
    09-Jan-2020      0.11165       0.78812 
    10-Jan-2020       -1.284       -1.8858 

Related Examples

• Add Interactive Tasks to a Live Script
• Clean Messy Data and Locate Extrema Using Live Editor Tasks

Parameters

Input data — Valid input data from workspace

vector | table | timetable

This task operates on input data contained in a vector, table, or timetable. The data can be of type single or double.

For table or timetable input data, to clean all variables with type single or double, select All supported variables. To choose which single or double variables to clean, select Specified variables.

Normalization method — Method and parameters for normalizing data

Z-score | Norm | Range | ...

Specify the method and related parameters for normalizing data as one of these options.

Method	Method Parameters	Description
Z-score	Standard deviation	Center and scale to have mean 0 and standard deviation 1.
	Median absolute deviation	Center and scale to have median 0 and median absolute deviation 1.
Norm	Positive numeric scalar (default is 2) or Inf for infinity norm	Scale data by p-norm.
Range	Upper and lower range limits (default is 0 for lower limit and 1 for upper limit)	Rescale range of data to an interval of the form [a, b], where a < b.
Median IQR	Not applicable	Center and scale data to have median 0 and interquartile range 1.
Center	Mean (default)	Center to have mean 0.
	Median	Center to have median 0.
	Numeric scalar	Shift center by a specified numeric value.
	From workspace	Shift center using values in a numeric array or in a table whose variable names match the specified table variables from the input data.
Scale	Standard deviation (default)	Scale data by standard deviation.
	Median absolute deviation	Scale data by median absolute deviation.
	First element	Scale data by first element of data.
	Interquartile range	Scale data by interquartile range.
	Numeric scalar (default is 1)	Scale data by dividing by a specified numeric value.
	From workspace	Scale data using values in a numeric array or in a table whose variable names match the specified table variables from the input data.
Center and scale	See the Center and Scale method parameters	Both center and scale data using the specified parameters.

More About

Z-Score

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 $$z=\frac{\left(x-\overline{X}\right)}{S}.$$

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 it retains the shape properties of the original data set (same skewness and kurtosis).

Median Absolute Deviation

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. 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 MAD.

P-Norm

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

$${\Vert v\Vert }_p={\left[{\displaystyle \sum _{k=1}^N{\left|v_k\right|}^p}\right]}^{1/p},$$

where p is any positive real value or Inf. For common values of p:

• If p is 1, then the resulting 1-norm is the sum of the absolute values of the vector elements.

• If p is 2, then the resulting 2-norm is the vector magnitude or Euclidean length of the vector.

• If p is Inf, then $${\Vert v\Vert }_{\infty }={\max }_i\left(\left|v\left(i\right)\right|\right)$$.

Rescaling

Rescaling changes the distance between the minimum and maximum 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

$$X_{rescaled}=a+\left[\frac{X-{\min }_X}{{\max }_X-{\min }_X}\right]\left(b-a\right).$$

Interquartile Range

The interquartile range (IQR) of a data set describes the range of the middle 50% of values when the values are sorted. If the median of the data is Q2, the median of the lower half of the data is Q1, and the median of the upper half of the data is Q3, then $$\text{IQR = Q3 - Q1}$$.

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

Version History

Introduced in R2021b

R2022b: Plot multiple table variables

Simultaneously plot multiple table variables in the display of this Live Editor task. For table or timetable data, to visualize all selected table variables at once in a tiled chart layout, set the Variable to display field.

R2022b: Append normalized variables

Append input table variables with table variables containing normalized data. For table or timetable input data, to append the normalized data, set the Output format field.

R2022a: Live Editor task does not run automatically if inputs have more than 1 million elements

This Live Editor task does not run automatically if the inputs have more than 1 million elements. In previous releases, the task always ran automatically for inputs of any size. If the inputs have a large number of elements, then the code generated by this task can take a noticeable amount of time to run (more than a few seconds).

When a task does not run automatically, the Autorun indicator is disabled. You can either run the task manually when needed or choose to enable the task to run automatically.