Visualization of Tall Arrays
Visualizing large data sets requires that the data is summarized, binned, or sampled in
some way to reduce the number of points that are plotted on the screen. In some cases,
functions such as histogram
and pie
bin the data to
reduce the size, while other functions such as plot
and
scatter
use a more complex approach that avoids plotting duplicate
pixels on the screen. For problems where the pixel overlap is relevant to the analysis, the
binscatter
function also offers an efficient way to visualize density
patterns.
Visualizing tall arrays does not require the use of gather
. MATLAB^{®} immediately evaluates and displays visualizations of tall arrays. Currently, you
can visualize tall arrays using the functions and methods in this table.
Function  Required Toolboxes  Notes 

plot  — 
These functions plot in iterations, progressively adding to the plot as more data is read. During the updates, a progress indicator shows the proportion of data that has been plotted. Zooming and panning is supported during the updating process, before the plot is complete. To stop the update process, press the pause button in the progress indicator. 
scatter  —  
binscatter  —  
histogram  —  
histogram2  —  
pie  — 
For visualizing categorical data only. 
binScatterPlot (Statistics and Machine Learning Toolbox)  Statistics and Machine Learning Toolbox™ 
Figure contains a slider to control the brightness and color detail in the
image. The slider adjusts the value of the 
ksdensity (Statistics and Machine Learning Toolbox)  Statistics and Machine Learning Toolbox 
Produces a probability density estimate for the data, evaluated at 100 points for univariate data, or 900 points for bivariate data. 
datasample (Statistics and Machine Learning Toolbox)  Statistics and Machine Learning Toolbox 

Tall Array Plotting Examples
This example shows several different ways you can visualize tall arrays.
Create a datastore for the airlinesmall.csv
data set, which contains rows of airline flight data. Select a subset of the table variables to work with and remove rows that contain missing values.
ds = tabularTextDatastore('airlinesmall.csv','TreatAsMissing','NA'); ds.SelectedVariableNames = {'Year','Month','ArrDelay','DepDelay','Origin','Dest'}; T = tall(ds); T = rmmissing(T)
T = Mx6 tall table Year Month ArrDelay DepDelay Origin Dest ____ _____ ________ ________ _______ _______ 1987 10 8 12 {'LAX'} {'SJC'} 1987 10 8 1 {'SJC'} {'BUR'} 1987 10 21 20 {'SAN'} {'SMF'} 1987 10 13 12 {'BUR'} {'SJC'} 1987 10 4 1 {'SMF'} {'LAX'} 1987 10 59 63 {'LAX'} {'SJC'} 1987 10 3 2 {'SAN'} {'SFO'} 1987 10 11 1 {'SEA'} {'LAX'} : : : : : : : : : : : :
Pie Chart of Flights by Month
Convert the numeric Month
variable into a categorical variable that reflects the name of the month. Then plot a pie chart showing how many flights are in the data for each month of the year.
T.Month = categorical(T.Month,1:12,{'Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec'})
T = Mx6 tall table Year Month ArrDelay DepDelay Origin Dest ____ _____ ________ ________ _______ _______ 1987 Oct 8 12 {'LAX'} {'SJC'} 1987 Oct 8 1 {'SJC'} {'BUR'} 1987 Oct 21 20 {'SAN'} {'SMF'} 1987 Oct 13 12 {'BUR'} {'SJC'} 1987 Oct 4 1 {'SMF'} {'LAX'} 1987 Oct 59 63 {'LAX'} {'SJC'} 1987 Oct 3 2 {'SAN'} {'SFO'} 1987 Oct 11 1 {'SEA'} {'LAX'} : : : : : : : : : : : :
pie(T.Month)
Evaluating tall expression using the Local MATLAB Session:  Pass 1 of 2: Completed in 1.1 sec  Pass 2 of 2: Completed in 0.81 sec Evaluation completed in 2.5 sec
Histogram of Delays
Plot a histogram of the arrival delays for each flight in the data. Since the data has a long tail, limit the plotting area using the BinLimits
namevalue pair.
histogram(T.ArrDelay,'BinLimits',[50 150])
Evaluating tall expression using the Local MATLAB Session:  Pass 1 of 2: Completed in 2.1 sec  Pass 2 of 2: Completed in 0.96 sec Evaluation completed in 3.5 sec
Scatter Plot of Delays
Plot a scatter plot of arrival and departure delays. You can expect a strong correlation between these variables since flights that leave late are also likely to arrive late.
When operating on tall arrays, the plot
, scatter
, and binscatter
functions plot the data in iterations, progressively adding to the plot as more data is read. During the updates the top of the plot has a progress indicator showing how much data has been plotted. Zooming and panning is supported during the updates before the plot is complete.
scatter(T.ArrDelay,T.DepDelay) xlabel('Arrival Delay') ylabel('Departure Delay') xlim([140 1000]) ylim([140 1000])
The progress bar also includes a Pause/Resume button. Use the button to stop the plot updates early once enough data is displayed.
Fit Trend Line
Use the polyfit
and polyval
functions to overlay a linear trend line on the plot of arrival and departure delays.
hold on p = polyfit(T.ArrDelay,T.DepDelay,1); x = sort(T.ArrDelay,1); yp = polyval(p,x); plot(x,yp,'r') hold off
Visualize Density
The scatter plot of points is helpful up to a certain point, but it can be hard to decipher information from the plot if the points overlap extensively. In that case, it helps to visualize the density of points in the plot to spot trends.
Use the binscatter
function to visualize the density of points in the plot of arrival and departure delays.
binscatter(T.ArrDelay,T.DepDelay,'XLimits',[100 1000],'YLimits',[100 1000]) xlim([100 1000]) ylim([100 1000]) xlabel('Arrival Delay') ylabel('Departure Delay')
Adjust the CLim
property of the axes so that all bin values greater than 150 are colored the same. This prevents a few bins with very large values from dominating the plot.
ax = gca; ax.CLim = [0 150];