Plotting distance of each point in a grid from a mean

I'm trying to shade in a grid using p-color to represent the mahalanobis distance from a certain 2d mean point. However I can't seem to get it right. I think my problem is in iterating over every point in the 179 by 179 grid, I'm not constructing the loop right to get the iteration right. I am new to matlab and really struggling with the syntax and "matrix algebra" approach to data analysis.

here is my code:

M = 179
N=179
x = linspace(-0.5, 1.0, M);
y = linspace(-0.5, 1..0, N);
D = zeros(M,N);
for i = 1:M;
  j = 1:N
    D(i, j) = sqrt(([x(i),y(j)] -mean(Xtr(I, :)))'.*cov(Xtr).*([x(i),y(j)] -mean(Xtr(I,:))));
  end
end
h = pcolor(x, y, D)
set(h, 'EdgeColor', 'none')
axis equal
axis tight
colorbar
scatter(Xtr)
hold on
I = find(ttr == 0)
scatter(Xtr(I, 1), Xtr(I,2), 10, 'bx')
hold on
II = find(ttr == 1)
scatter(Xtr(II,1), Xtr(II,2), 10, 'ro')
hold on

[dpb]

One problem is in

for i = 1:M;
  j = 1:N
    D(i,j)=sqrt(([x(i),y(j)]-mean(Xtr(I,:)))'.*cov(Xtr).*([x(i),y(j)]-mean(Xtr(I,:))));

in that Matlab is case-sensitive so that I isn't the same variable as i and I is undefined prior to its use in the above loop.

What is I intended to be here; and probably can eliminate the loops once we know what it is that is actually intended to be calculated.

If you have the Statistics TB, look at

doc mahal
which -all mahal  % there are overloaded specialty versions besides base

One of them may do what you're wanting more directly.

[Philip Gigliotti]

Sorry for the confusion. I is actually defined the same as in the lower code block. It identifies all the rows of Xtr such that ttr ==0.

I want to create the p plot that is shaded to represent distance from the mean point in the loop.

I don't know how to do that, but I think what I need to do is iterate over every i by j block of the grid x, y I've defined and calculate the distance of that grid from the point.

[dpb]

Well, in that case, that leads to the Q? of what is ttr?

What are dimensions for Xtr and ttr?

[Philip Gigliotti]

Xtr are features which are being used to predict ttr. Xtr is 179x2, ttr is 179x1.

Answer 1

[Image Analyst]

Definitions I see have the inverse of the covariance matrix in there, not the covariance matrix itself.

Answer 2

[dpb]

M=size(Xtr,1);
N=size(ttr,1);
mnXtr=mean(Xtr(Xtr~=0),:);
[X Y]=meshgrid(linspace(-0.5, 1.0, M),linspace(-0.5, 1..0, N));
D=sqrt(mahal([X Y],Xtr));

[Philip Gigliotti]

Hmm. I need the distance of the grid points from what you've designated as mnXtr. but that is 2 columns since Xtr is 179x2.

when I run this line of code:

Dp1 = mahal([X Y], mean(Xtr(I, :)))

I get the following error:

Error using mahal (line 34) Requires the inputs to have the same number of columns.

[dpb]

I also overlooked writing the trailing ":" for the second dimension in computing the mean vector...fixed that in the Answer.

And, yeah, meshgrid builds a 2D array for each...to use w/ mahal, have to build the combination vector to make the list of points pairwise...

D=sqrt(mahal([X(:) Y(:)],Xtr));

but then it says

"The number of rows of X must exceed number of columns."

I'll admit I don't understand the function at all; don't see why that has any bearing on anything.

Seems as though it should just compute the distance to the given feature vector it's given and be satisfied with that.

I surrender... :)

As IA suggests, perhaps pdist2?

Answer 3

[Image Analyst]

Why not use pdist2() if you have the Statistics and Machine Learning Toolbox?