Normalize Data - Center and scale data in the Live Editor - MATLAB (original) (raw)

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.

More

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

Examples

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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

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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 typesingle or double, select All supported variables. To choose which single ordouble 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.

More About

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_Z_-Score

For a random variable X with mean μ and standard deviation σ, the _z_-score of a value x is z=(x−μ)σ. For sample data with mean X¯ and standard deviation S, the_z_-score of a data point x is z=(x−X¯)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 X˜ of the data: MAD=median(|x−X˜|). 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

where p is any positive real value orInf. 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 ‖v‖∞=maxi(|v(i)|).

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

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 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

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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 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 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.