variance explained & pca

Hi! I want to report in a graph the variances explained as a function of PCs as shown in the graph. I have used the function "pareto(ExplVar)" but only the first 10 are represented and not all (there are 20 PCs in total). How can I represent them all?

[Anmol Dhiman]

Hi Alberto ,

Could you share your code for better resolution of the issue

[Alberto Acri]

The code is long. I have considered

p = pareto(ExplVar)

where ExplVar is an array 10000x1.

Answer 1

[Ive J]

pareto only shows the first 10 bars at maximum. You can do it easily with help of cumsum:

[~, ~, ~, ~, explained] = pca(rand(100,20));
hold on
bar(explained)
plot(1:numel(explained), cumsum(explained), 'o-', 'MarkerFaceColor', 'r')
yyaxis right
h = gca;
h.YAxis(2).Limits = [0 100];
h.YAxis(2).Color = h.YAxis(1).Color;
h.YAxis(2).TickLabel = strcat(h.YAxis(2).TickLabel, '%');

[Alberto Acri]

thanks, but I obtained the PCs through the pareto function and I can't apply what you told me to my case.

[Ive J]

What do you mean you obtained PCs through the pareto function?! Pareto charts display the values in the vector Y as bars drawn in descending order. Values in Y must be nonnegative and not include NaNs. Only the first 95% of the cumulative distribution is displayed. So how did you obtain your PCs through pareto?!

As you mentioned above you use it as

pareto(ExplVar)

Whatever ExplVar is (either PC scores themselves or explained variances) this example does similar to what pareto does.

[Alberto Acri]

In this

[~, ~, ~, ~, explained] = pca(rand(100,20))

Should I introduce the PCs I found?

[Ive J]

If you are calculating PCs with MATLAB pca built-in function, it can also return explained variances of PCs (explained in above example). If you want to show these explained variances (cumulatively), use explained; otherwise use PC scores if you prefer. It depends on your purposes of course (even you can use anything else to plot), but regardless, you can use my above example to reproduce similar graphs as pareto does, but without it's limitations (i.e. max 10 bars).