I have written a simple SOM algorithm in MATLAB. My big challenge is that, how can I visualize/plot data in the format of U-Matrix, Sample Hits and Component/Input Planes? These three plots exists in the SOM toolbox in MATLAB. But the problem is that I cannot call them to visualize my data over my written code. Because they need a 'net' as input in which my code does not make any 'net'.
Is there any guidance?
You can create your own functions as they are not too complicated. I will assume a SOM of 20x20x10 (400 nodes, 4 features) for explanation.
The Hit-Map is no more than giving each sample to the already learned SOM and incrementing +1 to the node that was chosen as the Best Matching Unit (BMU). Then you plot this map. So if node(1,1) fires 10 times, and node(1,2) fires 100 times, then you will have an image where node(1,2) has a higher intensity than node(1,1).
The U-Matrix is a map representing the average distance between the node's weight vector and its closest neighbours. So here you can calculate the Euclidean distance between the feature vector of node X to every neighbour. So if you had a feature vector for node(1,1,:)=[1,1,2,3], node(1,2,:)=[2,2,1,1], and node(2,1,:)=[1,1,1,1], then the value of the U-matrix for node(1,1) could be U(1,1)=norm(squeeze(node(1,1,:)-node(1,2,:)))+norm(squeeze(node(1,1,:)-node(2,1,:)))=4.8818
The Component/Input Planes is the simplest one and does not require any processing. You just basically pick each feature of the SOM map and plot. So in our example of a 20x20x4 SOM, you would have 4 features and therefore 4 components, which you can plot through imagesc(node(:,:,1)) for feature 1
Related
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.
A proof of concept prototype I have to do for my final year project is to implement K-Means Clustering on a big data set and display the results on a graph. I only know object-oriented languages like Java and C# and decided to give MATLAB a try. I notice that with a functional language the approach to solving problems is very different, so I would like some insight on a few things if possible.
Suppose I have the following data set:
raw_data
400.39 513.29 499.99 466.62 396.67
234.78 231.92 215.82 203.93 290.43
15.07 14.08 12.27 13.21 13.15
334.02 328.79 272.2 306.99 347.79
49.88 52.2 66.35 47.69 47.86
732.88 744.62 687.53 699.63 694.98
And I picked row 2 and 4 to be the 2 centroids:
centroids
234.78 231.92 215.82 203.93 290.43 % Centroid 1
334.02 328.79 272.2 306.99 347.79 % Centroid 2
I want to now compute the euclidean distances of each point to each centroid, then assign each point to it's closest centroid and display this on a graph. Let's say I want I want to classify the centroids as blue and green. How can I do this in MATLAB? If this was Java I would initialise each row as an object and add to separate ArrayLists (representing the clusters).
If rows 1, 2 and 3 all belong to the first centroid / cluster, and rows 4, 5 and 6 belong to the second centroid / cluster - how can I classify these to display them as blue or green points on a graph? I am new to MATLAB and really curious about this. Thanks for any help.
(To begin with, Matlab has a flexible distance measuring function, pdist2 and also kmeans implementation, but I'm assuming that you want to build your code from scratch).
In Matlab, you try to implement everything as matrix algebra, without loops over elements.
In your case, if R is the raw_data matrix and C is the centroids matrix,
you can shift the dimension that represents centroid number to the 3rd place by
permC=permute(C,[3 2 1]); Then the bsxfun function allows you to subtract C from R while expanding R's third dimension as necessary: D=bsxfun(#minus,R,permC). Element-wise square followed by summation across columns SqD=sum(D.^2,2) will give you the squared distances of each observation from each centroid. Performing all these operations within a single statement and shifting the third (centroid) dimension back to the 2nd place will look like this:
SqD=permute(sum(bsxfun(#minus,R,permute(C,[3 2 1])).^2,2),[1 3 2])
Picking the centroid of minimal distance is now straightforward: [minDist,minCentroid]=min(SqD,[],2)
If this looks complex, I recommend inspecting the product of each sub-step and reading the help of each command.
I am trying to implement a classification NN in Matlab.
My inputs are clusters of coordinates from an image. (Corresponding to delaunay triangulation vertexes)
There are 3 clusters (results of the optics algorithm) in this format:
( Not all clusters are of the same size.). Elements represent coordinates in euclidean 2d space . So (110,12) is a point in my image and the matrix depicted represents one cluster of points.
Clustering was done on image edges. So coordinates refer to logical values (always 1s in this case) on the image matrix.(After edge detection there are 3 "dense" areas in an image, and these collections of pixels are used for classification). There are 6 target classes.
So, my question is how can I format them into single column vector inputs to use in a neural network?
(There is a relevant answer here but I would like some elaboration if possible. ( I am probably too tired right now from 12 hours of trying stuff and dont get it 100% :D :( )
Remember, there are 3 different coordinate matrices for each picture, so my initial thought was, create an nn with 3 inputs (of different length). But how to serialize this?
Here's a cluster with its tags on in case it helps:
For you to train the classifier, you need a matrix X where each row will correspond to an image. If you want to use a coordinate representation, this means all images will have to be of the same size, say, M by N. So, the row of an image will have M times N elements (features) and the corresponding feature values will be the cluster assignments. Class vector y will be whatever labels you have, that is one of the six different classes you mentioned through the comments above. You should keep in mind that if you use a coordinate representation, X can get very high-dimensional, and unless you have a large number of images, chances are your classifier will perform very poorly. If you have few images, consider using fractions of pixels belonging to clusters that I suggested in one of the comments: this can give you a shorter feature description that is invariant to rotation and translation, and may yield better classification.
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)
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.