how to plot 4 dimensional data?

Hi

I want to plot my data in 4D map. data matrix is of 5000 by 4. each coloumn represent 1 quantity or variable. sample of data is given below.

z=
[1.000000000000000   1.100000000000000   2.300000000000000  16.000000000000000
   1.000000000000000   1.100000000000000   2.400000000000000  16.000000000000000
   1.000000000000000   1.100000000000000   2.500000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   2.600000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   2.700000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   3.800000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   3.900000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   4.000000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   4.100000000000000  15.000000000000000
   1.000000000000000   1.100000000000000   4.200000000000000  15.000000000000000]

how to effeciently plot the given data in more easy visualiztion way. Please help me i will be highly thankful to you

with best regards
Mudasir.

[Walter Roberson]

can that be reshaped into a cuboid of data with regular 3d coordinates and one resulting value ?

[Mudasir Ahmed]

Dear Sir Walter Roberson

first three columns are independent values (patterns) and final column is the result of that pattern (dependent value). so i need to represent that data in a easiest visualization way so can reader can easily understand. I have to put that graph in my research paper.

[Walter Roberson]

Attach your data .

[Mudasir Ahmed]

Dear Sir Walter Roberson

I am attaching the data file which is comprisedof a matrix 2000 by 4. it is incomplete data because my iterations are running for continuously last three days and may still run further three days more. So I just copy data to where I get the results till now. The total matrix will be 5000 by 4. Also sir, this is only the one case in which first colunm is constant and remain 1. however, in other cases it also varies as others are varying.

Answer 1

[Walter Roberson]

Provided that you have complete data, then your data forms are regular cuboid

x = unique(data(:,1));
y = unique(data(:,2));
z = unique(data(:,3));
w = permute(reshape(data(:,4), length(z), length(y), []), [3 2 1]);

The data sample you provided is 2000 samples long; 2002 samples would have been required to complete a single cycle, so the sample data as is will not work with the above and would need to be padded first, such as with

data(2001:2002,:) = [1 3.1 9.9 1;1 3.1 10 1];

The marginal coordinates are stored in x, y, z .

The resulting w would be (for the sample data) 1 x 22 x 91.

After that you have the question of how best to plot data that has 3 input dimensions and 1 output dimension.

Typical ways to plot multidimensional data include:

• isosurface
• slice
• volumeViewer
• vol3d v2 (from File Exchange)
• projections along different views
• pointsize = 20; scatter3(data(:,1), data(:,2), data(:,3), pointsize, data(:,4)) -- that is, encoding the resultant dimension as color

In the case of your sample data (as padded) some of these will not work because your x data is singleton. However you can use

surf( y, z, squeeze(w).', 'edgecolor', 'none')

[Mudasir Ahmed]

Thank you so much sir

Answer 2

[madhan ravi]

Read about isosurface.

Answer 3

[Bartlomiej Mroczek]

Hello,

Anyone have any idea or experience?

I would like to get a spatial plot for the function f, but it is 4 dimensional.

How can this be done?

Script:

V2 = zeros(21,21); % zero value irrelevant

V4 = zeros(21,21); % zero value irrelevant

V6 = zeros(21,21); % zero value irrelevant

f = @(V1, V2, V3, V4, V5, V6) V1.*(10*V1-10*V2+20*V3-21*V4+30*V5-31*V6) - V2.*(10*V1-11*V2+22*V3-21*V4+30*V5-31*V6);

[V1, V3, V5] = meshgrid(0.9:0.01:1.1, 0.9:0.01:1.1, 0.9:0.01:1.1);

Z = f(V1, V3, V5, V2, V4, V6);

[Walter Roberson]

Typical ways to plot multidimensional data include:

    isosurface
    slice
    volumeViewer
    vol3d v2 (from File Exchange)
    projections along different views
    pointsize = 20; scatter3(data(:,1), data(:,2), data(:,3), pointsize, data(:,4)) -- that is, encoding the resultant dimension as color

If you had another dimension then you could encode it as point size.

[Bartlomiej Mroczek]

Thanx.

1. isosurface - it works
2. slice - i have a prob with error:

h = slice(V_n1, V_n3, V_n5, v, xs, ys, zs); xs = 1; 
%Attempt to execute SCRIPT grid as a function:
%/Users/bartlomiejmroczek/Documents/MATLAB/grid.m
%Error in slice (line 141)
   %     grid(cax,'on');
ys = 1; 
zs = 1; 
colormap hsv

why's that ?

[Walter Roberson]

What shows up for

which -all grid

You have some third-party file that is interfering.

[Bartlomiej Mroczek]

actually the file connected, weird thanx

[Walter Roberson]

You need to delete or rename /Users/bartlomiejmroczek/Documents/MATLAB/grid.m as it is interfering with using MATLAB's grid() function .