I'm working on Magnetic Resonance Imaging data, on Matlab R2020a. In particular, i have to characterize the background noise of the image and i know it has a noncentral chi distribution. Now, i'm trying the mle method whitout results:
[phat,pci] = mle(data,'pdf',#(data,v,d)ncx2pdf(data,v,d),'start',[1 1]);
data is a row vector (1024,1), v are the dof of the distribution and d the noncentrality parameter (the two parameters that i have to find).
The problem lies in the fact that the distribution strongly depends on the value of the mean, and the order of magnitude of my data is 10^-6.
histogram of the data:
Does anyone know a method to fit the data to a noncentral chi distribution? I already tried the 0-1 and 0-255 normalization, but they produces unreliable mean values. Any suggestions are welcome.
data.mat
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I have run into a very peculiar problem. It might seem silly to a lot of you. But I am in dire need of a way out. I am analyzing sets of high-speed images with MATLAB. The image of interest (https://www.dropbox.com/s/h4h26y3mvpao8m6/sample.png?dl=0) is an average of 3000 images (background subtracted). As shown in the picture, I am reading the pixel intensities/values along columns. As this is a laser beam, the shape or beam profile away from the wall has the shape of a Gaussian distribution. As I approach to the wall (the brightest part at the right of the image) because of some effect the shape is turning into one like a log-normal distribution. In this spreadsheet (https://www.dropbox.com/s/yeim06a5cq3iqg8/sample.xlsx?dl=0) I have pasted the raw intensities as I read thru from point A to point B. The column D has the raw intensities and the column E has the values achieved with a 'sgolay' fit of the column D values. If I plot these it pretty much has the shape of a lognormal distribution. I can get the mu and sigma with the 'lognfit' or 'fitdist' functions. Now the question is what is the equation [expressed as a function of pixel location (x) or the pixel intensity (y)] of the fitted 'lognormal curve' that could be used to recreate the fitted curve? Your help is highly appreciated.
The lognfit extracts the mu and the sigma of the lognormal distribution. The mu is the mean of logarithmic values and sigma the standard deviation of logarithmic values. You can refer to https://en.wikipedia.org/wiki/Log-normal_distribution for the shape of the function given mu and sigma.
With logrnd(mu,sigma) you can generate samples from the same distribution:
https://it.mathworks.com/help/stats/lognrnd.html?searchHighlight=lognrnd&s_tid=srchtitle_lognrnd_1
I have a question about multivariate kernel density in matlab, which is my first time using it.
I have a 3-dimensional sample data (x, y, z in axes) and want to find a probability of being in a certain volume using kernel density estimation. So, I used the mvksdensity function in matlab and got the probability density (estimated function values) for the points I decided.
What I originally wanted to do was to (if I could fine the function) triple integral the multivariate function for a given volume. But the mvksdensity function only returns the density estimates and does not return the function. I thought there will be an easy way to compute the probability from the density, but I’m stuck. Does anyone have any useful information for this? Thanks in advance.
I thought about fitdist function to find the distribution, but it only works for univariate kernel distribution.
I also tried to use mvncdf, which is a function that returns the cdf of the multivariate normal distribution for the row of the sample data after setting the mean and the std. But then I have to calculate the probability for a given volume for every normal distribution in each data point and then add it, which will be inefficient for a large amount of data and I don't know if it's a correct way.
I can suggest the following Monte-Carlo approach. You find a master volume that contains the entire mass of the estimated probability density. This should be as small as possible for the sake of efficiency. Then you generate a large number of test points in the master volume, either on a grid or randomly according to a uniform distribution. The probability content of a specific volume V can be estimated by the sum of the density values of the test points in V over the sum of the density values of all test points. I am afraid, however, that in 3D you would need at least 1E6 test points, probably more. If you give me access to your sample, I would be pleased to try out my suggestion. It should also be fairly easy to work out an estimate of the standard error of the estimated probability content of V.
I want to evaluate the grid quality where all coordinates differ in the real case.
Signal is of a ECG signal where average life-time is 75 years.
My task is to evaluate its age at the moment of measurement, which is an inverse problem.
I think 2D approximation of the 3D case is hard (done here by Abo-Zahhad) with with 3-leads (2 on chest and one at left leg - MIT-BIT arrhythmia database):
where f is a piecewise continuous function in R^2, \epsilon is the error matrix and A is a 2D matrix.
Now, I evaluate the average grid distance in x-axis (time) and average grid distance in y-axis (energy).
I think this can be done by Matlab's Image Analysis toolbox.
However, I am not sure how complete the toolbox's approaches are.
I think a transform approach must be used in the setting of uneven and noncontinuous grids. One approach is exact linear time euclidean distance transforms of grid line sampled shapes by Joakim Lindblad et all.
The method presents a distance transform (DT) which assigns to each image point its smallest distance to a selected subset of image points.
This kind of approach is often a basis of algorithms for many methods in image analysis.
I tested unsuccessfully the case with bwdist (Distance transform of binary image) with chessboard (returns empty square matrix), cityblock, euclidean and quasi-euclidean where the last three options return full matrix.
Another pseudocode
% https://stackoverflow.com/a/29956008/54964
%// retrieve picture
imgRGB = imread('dummy.png');
%// detect lines
imgHSV = rgb2hsv(imgRGB);
BW = (imgHSV(:,:,3) < 1);
BW = imclose(imclose(BW, strel('line',40,0)), strel('line',10,90));
%// clear those masked pixels by setting them to background white color
imgRGB2 = imgRGB;
imgRGB2(repmat(BW,[1 1 3])) = 255;
%// show extracted signal
imshow(imgRGB2)
where I think the approach will not work here because the grids are not necessarily continuous and not necessary ideal.
pdist based on the Lumbreras' answer
In the real examples, all coordinates differ such that pdist hamming and jaccard are always 1 with real data.
The options euclidean, cytoblock, minkowski, chebychev, mahalanobis, cosine, correlation, and spearman offer some descriptions of the data.
However, these options make me now little sense in such full matrices.
I want to estimate how long the signal can live.
Sources
J. Müller, and S. Siltanen. Linear and nonlinear inverse problems with practical applications.
EIT with the D-bar method: discontinuous heart-and-lungs phantom. http://wiki.helsinki.fi/display/mathstatHenkilokunta/EIT+with+the+D-bar+method%3A+discontinuous+heart-and-lungs+phantom Visited 29-Feb 2016.
There is a function in Matlab defined as pdist which computes the pairwisedistance between all row elements in a matrix and enables you to choose the type of distance you want to use (Euclidean, cityblock, correlation). Are you after something like this? Not sure I understood your question!
cheers!
Simply, do not do it in the post-processing. Those artifacts of the body can be about about raster images, about the viewer and/or ... Do quality assurance in the signal generation/processing step.
It is much easier to evaluate the original signal than its views.
I'm trying to fit a multivariate normal distribution to data that I collected, in order to take samples from it.
I know how to fit a (univariate) normal distribution, using the fitdist function (with the 'Normal' option).
How can I do something similar for a multivariate normal distribution?
Doesn't using fitdist on every dimension separately assumes the variables are uncorrelated?
There isn't any need for a specialized fitting function; the maximum likelihood estimates for the mean and variance of the distribution are just the sample mean and sample variance. I.e., compute the sample mean and sample variance and you're done.
Estimate the mean with mean and the variance-covariance matrix with cov.
Then you can generate random numbers with mvnrnd.
It is also possible to use fitmgdist, but for just a multivariate normal distribution mean and cov are enough.
Yes, using fitdist on every dimension separately assumes the variables are uncorrelated and it's not what you want.
You can use [sigma,mu] = robustcov(X) function, where X is your multivariate data, i.e. X = [x1 x2 ... xn] and xi is a column vector data.
Then you can use Y = mvnpdf(X,mu,sigma) to get the values of the estimated normal probability density function.
https://www.mathworks.com/help/stats/normfit.html
https://www.mathworks.com/help/stats/mvnpdf.html
I have a data of dimension 50x100000. (100000 features, each has a dimension of 50).
I would like to fit a gaussian mixture model using this data. I used the following code.
obj = gmdistribution.fit(X',3);
What I need is when I give a new data Y I should be able to get the likelihood probabilities $p(Y|\theta)$, where $\theta$ are the gaussing mixture model parameters.
I used the following code to get the probability values.
P = pdf(obj,X');
But I am getting very low values all are about 0. Whay it is happning? How can i get the appropreate probability values?
In one dimension, the maximum value of the pdf of the Gaussian distribution is 1/sqrt(2*PI). So in 50 dimensions, the maximum value is going to be 1/(sqrt(2*PI)^50) which is around 1E-20. So the values of the pdf are all going to be of that order of magnitude, or smaller.