Here is one way to subsample the data to produce almost identical plots:
X = 10.^randn(2e4,1);
Y = 10.^randn(2e4,1);
figure()
scatter(X,Y,'filled')
set(gca,'xscale','log','yscale','log','title','AllData')
Xb = log10(X);
Yb = log10(Y);
Xf = 0.05;
Yf = 0.05;
Xb = Xf*round(Xb/Xf);
Yb = Yf*round(Yb/Yf);
[~,idx] = unique([Xb,Yb],'rows');
figure()
scatter(X(idx),Y(idx),'filled')
set(gca,'xscale','log','yscale','log','title','SubData')
The number of points plotted:
>> numel(X)
ans = 20000
>> nnz(idx)
ans = 6653
You can also see that all extrema are still clearly visible.
PS: you might be able to save some memory by putting the merging onto one line:
[~,idx] = unique([Xf*round(log10(X)/Xf),Yf*round(log10(Y)/Yf)],'rows');
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