2D heatmap based on weight (not density)

I have an X, Y and X matrix, each N x M of size, where X indicates a location on the x axis, Y indicates the y data point and Z is the weight. Currently, I use scatter in order to plot X and Y with a weight of Z to indicate the "importance" of each X/Y data point.

I'd like to create something like a heatmap instead, where the x/y coordinates are colored, instead of changed in size, based on the Z weight. For example, large Z values could be red, small Z values could be green and the color vector linearly interpolates between red and green as Z changes.

The code below will create an example setup similar to what I am working with.

X = randi(100, [100 1]); X = sort(X);
Y = randi(50, [100 1]);
Z = linspace(100, 1, 100);
figure;
scatter(X, Y, Z, 'k', 'o', 'filled');

I could see one of 3 options:

1. something like either "hotspots" where large circles are and decreasing intensity of hotspots as the circles get smaller
2. "color spots" for which large circles might start out red and change in color from red to yellow to green as they get smaller
3. something like a "segmentation" of the entire background of the plot into "red, yellow, green" zones (e.g. as Z decreases, certain thresholds indicate a change from red to yellow to green, so "patches" could indicate such changes). However, I have no idea how to draw the lines of the patch (e.g. where data points with Z = 90 and above lay could be red, 89 and below could be orange, ..), and maybe smooth them a bit.

Any help will be greatly appreciated.

Answer 1

[Shivam]

Hi @Michaela Warnecke,

You can achieve the above 3 implementations using the scatter, imagesc and contourf functions respectively. You can have a look at each of the implementation below:

• Colour spots using scatter

% Example data
X = randi(100, [100, 1]);
Y = randi(50, [100, 1]);
Z = linspace(100, 1, 100);

% Create the scatter plot
figure;
scatter(X, Y, 100, Z, 'filled'); % Use Z for color

% Set colormap from red to green
colormap(jet); % Or use other colormaps like 'hot', 'cool', etc.
colorbar; % Show color scale

• Using imagesc for heatmap: This approach bins your data into a grid.

% Define grid size
x_edges = linspace(min(X), max(X), 50);
y_edges = linspace(min(Y), max(Y), 25);

% Create a 2D histogram
heatmap_data = zeros(length(y_edges)-1, length(x_edges)-1);

for i = 1:length(X)
    x_idx = find(X(i) >= x_edges, 1, 'last');
    y_idx = find(Y(i) >= y_edges, 1, 'last');
    
    if x_idx < length(x_edges) && y_idx < length(y_edges)
        heatmap_data(y_idx, x_idx) = heatmap_data(y_idx, x_idx) + Z(i);
    end
end

% Plot the heatmap
figure;
imagesc(x_edges, y_edges, heatmap_data);
set(gca, 'YDir', 'normal'); % Correct the y-axis direction
colormap(jet); % Or any other colormap
colorbar;

• Segmentation for contourf

% Create a grid for contour
[X_grid, Y_grid] = meshgrid(linspace(min(X), max(X), 100), linspace(min(Y), max(Y), 100));

% Interpolate Z values on the grid
Z_grid = griddata(X, Y, Z, X_grid, Y_grid, 'cubic');

Warning: Duplicate x-y data points detected: using average values for duplicate points.

% Plot the contour map
figure;
contourf(X_grid, Y_grid, Z_grid, 10, 'LineColor', 'none'); % 10 levels
colormap(jet);
colorbar;

You can adjust the number of levels in contourf to change how many segments are displayed.

I hope it helps.

Thanks

[Michaela Warnecke]

Thanks so much, this is exactly what I was looking for! It works splendidly.