Scipy linkage() function returning inconsistent results - scipy

I have a C# program that does some analysis, prints out a full 2D matrix of distance values, and then launches a scipy python process (anaconda, fwiw) to do hierarchical clustering. Here's the problem: I need to impose some kind of ordering on them so that they have an ordering along each axis. My code looks more or less like this:
var set = set.OrderBy(x => x.GetHashCode());
foreach(Point p1 in set)
{
foreach(Point p2 in set)
{
double distance = Distance(p1,p2);
//save out the distance so that it can be written to a 2d matrix
}
}
//write out the 2d matrix...
//call python...
Here's the trick: when I change the ordering scheme - maybe sort by size, or even a random number generator - python calculates different numbers of clusters for the same cutoff. I know the distance values are the same - I print them all ordered by size to a single string and calculate an md5 hash on that string, and the hash is always the same. I know that the linkage() function in scipy doesn't like 2d matrices (some bug I read about), but once the 2d matrix is read in, I convert it to a compressed matrix with squareform(distMatrix) as shown here: Use Distance Matrix in scipy.cluster.hierarchy.linkage()?.
Anyway, any ideas? I really have a hard time believing that scipy has the bug, but I'm running out of options...
thanks!
-denny-

Related

Spreading one matrix elements to another with weighted random numbers MATLAB

So I was trying to spread one matrix elements, which were generated with poissrnd, to another with using some bigger (wider?) probability function (for example 100 different possibilities with different weights) to plot both of them and see if the fluctuations after spread went down. After seeing it doesn't work right (fluctuations got bigger) I tried to identify what I did wrong on a really simple example. After testing it for a really long time I still can't understand what's wrong. The example goes like this:
I generate vector with poissrnd and vector for spreading (filled with zeros at the start)
Each element from the poiss vector tells me how many numbers (0.1 of the element value) to generate from the possible options which are: [1,2,3] with corresponding weights [0.2,0.5,0.2]
I spread what I got to my another vector on 3 elements: the corresponding (k-th one), one bofore the corresponding one and one after the corresponding one (so for example if k=3, the elements should be spread like this: most should go into 3rd element of another vector, and rest should go to 2nd and 1st element)
Plot both 0.1*poiss vector and vector after spreading to compare if fluctuations went down
The way I generate weighted numbers is from this thread: Weighted random numbers in MATLAB
and this is the code I'm using:
clear all
clc
eta=0.1;
N=200;
fot=10000000;
ix=linspace(-100,100,N);
mn =poissrnd(fot/N, 1, N);
dataw=zeros(1,N);
a=1:3;
w=[.25,.5,.25];
for k=1:N
[~,R] = histc(rand(1,eta*mn(1,k)),cumsum([0;w(:)./sum(w)]));
R = a(R);
przydz=histc(R,a);
if (k>1) && (k<N)
dataw(1,k)=dataw(1,k)+przydz(1,2);
dataw(1,k-1)=dataw(1,k-1)+przydz(1,1);
dataw(1,k+1)=dataw(1,k+1)+przydz(1,3);
elseif k==1
dataw(1,k)=dataw(1,k)+przydz(1,2);
dataw(1,N)=dataw(1,N)+przydz(1,1);
dataw(1,k+1)=dataw(1,k+1)+przydz(1,3);
else
dataw(1,k)=dataw(1,k)+przydz(1,2);
dataw(1,k-1)=dataw(1,k-1)+przydz(1,1);
dataw(1,1)=dataw(1,1)+przydz(1,3);
end
end
plot(ix,eta*mn,'g',ix,dataw,'r')
The fluctuations are still bigger, and I can't identify what's wrong... Is the method for generating weighted numbers wrong in this situation? Cause it doesn't seem so. The way I'm accumulating data from the first vector seems fine too. Is there another way I could do it (so I could then optimize it for using 'bigger' probability functions)?
Sorry for my terrible English.
[EDIT]:
Here is simple pic to show what I meant (I hope it's understandable)
How about trying negative binomial distribution? It is often used as a hyper-dispersed analogue of Poisson distribution. Additional links can be found in this paper, as well as some apparatus in supplement.

Interpolation of scattered scalar values in 3D volume

I have an unknown scalar fonction defined into a partial space (a pyramid portion), for this function, I have several measurements points into the coordonates mesurePoints, where the mesure mesure is known :
size(mesurePoints) = [n 3]
size(mesure) = n
I also have my space discretized into a clood of equidistant points wich I'll call interpolPoints,
I would like to obtain interpolated values interp_mesure on the points interpolPoints based on my measurements mesure on the points mesurePoints.
I tried to use interp3,
interp_mesure = interp3(...
mesurePoints(:,1),mesurePoints(:,2),mesurePoints(:,2),...
mesure,...
interpolPoints(:,1),interpolPoints(:,2),interpolPoints(:,3));
but I get the error that V (mesure) should be a 3D array, but I am confuse, my data isn't 3D, it is 3D dependant, but it's a scalar data, how can I proceed? Is interpol3 not adapted to my problem?
Edit 1 : Here is a similar problem to illustrate mine : how do you interpolate temperature in a volume if you have some temperature measurements in this volume?
Edit 2 : as no matlab solution have come to mind yet, I use a hand-made interpolation weighted by inverse distance with a power factor, the result is good close to points but as my points are quite scattered, the result is not good in empty areas.
I'm having trouble understanding exactly what is your data, but I get the impression that maybe interp1 or interp2 would be better suited to your needs, as your data isn't organized as a 3-D array

computing PCA matrix for set of sift descriptors

I want to compute a general PCA matrix for a dataset, and I will use it to reduce dimensions of sift descriptors. I have already found some algorithms to compute it, but I couldn't find a way to compute it by using MATLAB.
Can someone help me?
[coeff, score] = princomp(X)
is the right thing to do, but knowing how to use it is a little tricky.
My understanding is that you did something like:
sift_image = sift_fun(img)
which gives you a binary image: sift_feature?
(Even if not binary, this still works.)
Inputs, formulating X:
To use princomp/pca formulate X so that each column is a numel(sift_image) x 1 vector (i.e. sift_image(:))
Do this for all your images and line them up as columns in X. So X will be numel(sift_image) x num_images.
If your images aren't the same size (e.g. pixel dimensions different, more or less of a scene in the images), then you'll need to bring them into some common space, which is a whole different problem.
Unless your stuff is binary, you'll probably want to de-mean/normalize X, both in the column direction (i.e. normalizing each individual image) and row direction (de-meaning the whole dataset).
Outputs
score is the set of eigen vectors: it will be num_pixels * num_images.
To get, say the first eigen vector back into an image shape, do:
first_component = reshape(score(:,1),size(im));
And so on for the rest of the components. There are as many components as input images.
Each row of coeff is the num_images (equal to num_components) set of weights that can be applied to generate each input image. i.e.
input_image_1 = reshape(score * coeff(:,1) , size(original_im));
where input_image_1 is the correct, original shape
coeff(1,:) is a vector (num_images x 1)
score is pixels x num_images
(Disclaimer: I may have the columns/rows mixed up, but the descriptions are correct.)
Does that help?
If you have access to Statistics Toolbox, you can use the command princomp, or in recent versions the command pca.

Controlled random number/dataset generation in MATLAB

Say, I have a cube of dimensions 1x1x1 spanning between coordinates (0,0,0) and (1,1,1). I want to generate a random set of points (assume 10 points) within this cube which are somewhat uniformly distributed (i.e. within certain minimum and maximum distance from each other and also not too close to the boundaries). How do I go about this without using loops? If this is not possible using vector/matrix operations then the solution with loops will also do.
Let me provide some more background details about my problem (This will help in terms of what I exactly need and why). I want to integrate a function, F(x,y,z), inside a polyhedron. I want to do it numerically as follows:
$F(x,y,z) = \sum_{i} F(x_i,y_i,z_i) \times V_i(x_i,y_i,z_i)$
Here, $F(x_i,y_i,z_i)$ is the value of function at point $(x_i,y_i,z_i)$ and $V_i$ is the weight. So to calculate the integral accurately, I need to identify set of random points which are not too close to each other or not too far from each other (Sorry but I myself don't know what this range is. I will be able to figure this out using parametric study only after I have a working code). Also, I need to do this for a 3D mesh which has multiple polyhedrons, hence I want to avoid loops to speed things out.
Check out this nice random vectors generator with fixed sum FEX file.
The code "generates m random n-element column vectors of values, [x1;x2;...;xn], each with a fixed sum, s, and subject to a restriction a<=xi<=b. The vectors are randomly and uniformly distributed in the n-1 dimensional space of solutions. This is accomplished by decomposing that space into a number of different types of simplexes (the many-dimensional generalizations of line segments, triangles, and tetrahedra.) The 'rand' function is used to distribute vectors within each simplex uniformly, and further calls on 'rand' serve to select different types of simplexes with probabilities proportional to their respective n-1 dimensional volumes. This algorithm does not perform any rejection of solutions - all are generated so as to already fit within the prescribed hypercube."
Use i=rand(3,10) where each column corresponds to one point, and each row corresponds to the coordinate in one axis (x,y,z)

Using triplequad to calculate density (in Matlab)

As i've explained in a previous question: I have a dataset consisting of a large semi-random collection of points in three dimensional euclidian space. In this collection of points, i am trying to find the point that is closest to the area with the highest density of points.
As high performance mark answered;
the most straightforward thing to do would be to divide your subset of
Euclidean space into lots of little unit volumes (voxels) and count
how many points there are in each one. The voxel with the most points
is where the density of points is at its highest. Perhaps initially
dividing your space into 2 x 2 x 2 voxels, then choosing the voxel
with most points and sub-dividing that in turn until your criteria are
satisfied.
Mark suggested i use triplequad for this, but this is not a function i am familiar with, or understand very well. Does anyone have any pointers on how i could go about using this function in Matlab for what i am trying to do?
For example, say i have a random normally distributed matrix A = randn([300,300,300]), how could i use triplequad to find the point i am looking for? Because as i understand currently, i also have to provide triplequad with a function fun when using it. Which function should that be for this problem?
Here's an answer which doesn't use triplequad.
For the purposes of exposition I define an array of data like this:
A = rand([30,3])*10;
which gives me 30 points uniformly distributed in the box (0:10,0:10,0:10). Note that in this explanation a point in 3D space is represented by each row in A. Now define a 3D array for the counts of points in each voxel:
counts = zeros(10,10,10)
Here I've chosen to have a 10x10x10 array of voxels, but this is just for convenience, it would be only a little more difficult to have chosen some other number of voxels in each dimension, and there don't have to be the same number of voxels along each axis. Then the code
for ix = 1:size(A,1)
counts(ceil(A(ix,1)),ceil(A(ix,2)),ceil(A(ix,3))) = counts(ceil(A(ix,1)),ceil(A(ix,2)),ceil(A(ix,3)))+1
end
will count up the number of points in each of the voxels in counts.
EDIT
Unfortunately I have to do some work this afternoon and won't be able to get back to wrestling with the triplequad solution until later. Hope this is OK in the meantime.