Logistic regression in matlab using mnrfit - matlab

I'm trying to use the mnrfit function but I get the error
If Y is a column vector, it must contain positive integer category numbers. .
My data is in a double and my Y values are floats, e.g. 0.6667. Is there a way that I can adjust my data to be able to use the mnrfit function?
Thanks in advance!
An unexperienced beginner

Y should be a "nominal outcome", i.e. non-continuous, to use mnrfit. We don't need to turn Y into integers, just categoricals. A categorical array is discrete as far as MATLAB is concerned, regardless whether the categories are represented by double values.
X = rand(5,3); % Predictors (should be double or single)
Y = rand(5,1); % Response (doubles, will cause error)
B = mnrfit( X, Y )
% ERROR: If Y is a column vector, it must contain positive integer category numbers.
B = mnrfit( X, categorical(Y) )
% No error, regression matrix B is output successfully.
Be careful, if you're expecting a continuous response variable (hence why Y is a vector of doubles) then mnrfit may not be suitable in the first place!
Note the valid data types are specified in the docs
Y can be one of the following:
An n-by-k matrix, where Y(i,j) is the number of outcomes of the multinomial category j for the predictor combinations given by X(i,:). In this case, the number of observations are made at each predictor combination.
An n-by-1 column vector of scalar integers from 1 to k indicating the value of the response for each observation. In this case, all sample sizes are 1.
An n-by-1 categorical array indicating the nominal or ordinal value of the response for each observation. In this case, all sample sizes are 1.

Related

How can I generalize this function to `n` terms?

I'd like to create a function that adds several gaussian terms of various width over some specified region:
G(a,b,x) = a_1 exp(- b_1 x^2) + a_2 exp(- b_2 x^2) + ... a_N exp(-b_N x^2)
I'd like this function to output an array of length x, summing over the terms of parameters a,b provided, something like:
x = linspace(-2,2,1000);
N_gauss = #(a,b) a(:).*exp(-b(:)*x.^2);
This example actually works if a,b have only a single value, but when they become vectors it no longer works (I suppose Matlab doesn't know what should be added, multiplied or remain a vector). Is this even possible?
You can do this purely by matrix multiplication. Let's tackle the problem slowly and work our way up. You first need to form products of the elements of the vector b and scalar values stored in x. First create a 2D matrix of values where each row corresponds to the product-wise values between an element in b and an element in x. The element (i,j) in this matrix corresponds to the product of the ith element in x with the jth element in b.
You can achieve this by using the outer product. Make x a column vector and b a row vector, then perform the multiplication. Also, make sure you square each of the x terms as seen in your equation.
term1 = (x(:).^2)*b(:).';
Now you can apply the exponential operator and ensure you place a negative in the exponent so you can build the right side of each term (i.e. exp(- b_i x^2)):
term2 = exp(-term1);
The last thing you need to do is multiply each of the values in the 2D matrix with the right coefficient from the a vector. You can do this by enforcing that a be a column vector and performing matrix-vector multiplication.
out = term2*a(:);
Matrix-vector multiplication is the dot product between the column vector a with each row in the 2D matrix we created before. This exactly corresponds to the summation of your equation for each value in x. As such, this achieves the Gaussian summation for each value in x and places this into a n x 1 vector where n is the total number of elements in x. Putting this all together gives us:
out = exp(-(x(:).^2)*b(:).')*a(:);
To finally abstract this into an anonymous function, do:
N_gauss = #(a,b,x) exp(-(x(:).^2)*b(:).')*a(:);
This function takes in the vectors a, b and x as per your problem.

Matlab-Select particular values in a matrix

I am a beginner in matlab and I have a particular z matrix of size m×1 with values 0,1,3,5,2 etc..with above values repeating. Now I have 4 other column matrix x1,x2,x3 and y and I want to do regression.
I have used lm = LinearModel.fit(x,y,'linear') specifying columns.Now I want to do regression only for values in matrix x1,x2,x3 and y for those corresponding to z matrix with value of 1 and neglect the other rows.How do I do it?
That's very simple. I'm going to assume that your matrix of predictor variables and outputs are also of size m (number of samples). All you have to do is find the locations within z that are 1, subset your 3 column matrix of x1,x2,x3 and y, then use LinearModel.fit to fit your data. Assuming your matrix of predictors is stored in X, and your outputs are stored in y, you would do this:
ind = z == 1;
xOut = X(ind,:);
yOut = y(ind);
lm1 = LinearModel.fit(xOut, yOut, 'linear');
BTW, these are very simple subsetting operations in MATLAB. Suggest you read a tutorial before asking any further questions here.

Plotting a Matrix in matlab with float elements

I have results of an experiment which is parameter optimization of support vector regression. I have the first three columns the parameters and the last column the MSE so I have about 24,646 X 4 matrix. I would like to get the parameters corresponding to the smallest MSE. How can I plot this on Matlab? the elements of the matrix are float numbers. Thank you for your help.
Use second output of min to obtain the index of the minimum value in the fourth columns; and then use that to get the parameters:
[~, ind] = min(matrix(:,4));
params = matrix(ind,1:3);

Find the minimum difference between any pair of elements between two vectors

Which of the following statements will find the minimum difference between any pair of elements (a,b) where a is from the vector A and b is from the vector B.
A. [X,Y] = meshgrid(A,B);
min(abs(X-Y))
B. [X,Y] = meshgrid(A,B);
min(abs(min(Y-X)))
C. min(abs(A-B))
D. [X,Y] = meshgrid(A,B);
min(min(abs(X-Y)))
Can someone please explain to me?
By saying "minimum difference between any pair of elements(a,b)", I presume you mean that you are treating A and B as sets and you intend to find the absolute difference in any possible pair of elements from these two sets. So in this case you should use your option D
[X,Y] = meshgrid(A,B);
min(min(abs(X-Y)))
Explanation: Meshgrid turns a pair of 1-D vectors into 2-D grids. This link can explain what I mean to say:
http://www.mathworks.com/help/matlab/ref/meshgrid.html?s_tid=gn_loc_drop
Hence (X-Y) will give the difference in all possible pairs (a,b) such that a belongs to A and b belongs to B. Note that this will be a 2-D matrix.
abs(X-Y) would return the absolute values of all elements in this matrix (the absolute difference in each pair).
To find the smallest element in this matrix you will have to use min(min(abs(X-Y))). This is because if Z is a matrix, min(Z) treats the columns of Z as vectors, returning a row vector containing the minimum element from each column. So a single min command will give a row vector with each element being the min of the elements of that column. Using min for a second time returns the min of this row vector. This would be the smallest element in the entire matrix.
This can help:
http://www.mathworks.com/help/matlab/ref/min.html?searchHighlight=min
Options C is correct if you treat A and B as vectors and not sets. In this case you won't be considering all possible pairs. You'll end up finding the minimum of (a-b) where a,b are both in the same position in their corresponding vectors (pair-wise difference).
D. [X,Y] = meshgrid(A,B);
min(min(abs(X-Y)))
meshgrid will generate two grids - X and Y - from the vectors, which are arranged so that X-Y will generate all combinations of ax-bx where ax is in a and bx is in b.
The rest of the expression just gets the minimum absolute value from the array resulting from the subtraction, which is the value you want.
CORRECT ANSWER IS D
Let m = size(A) and n = size(B)
You want to subtract each pair of (a,b) such that a is from vector A and b is from vector B.
meshgrid(A,B) creates two matrices X Y both of size nxm where X have rows sames have vector A while Yhas columns same as vector B .
Hence , Z = X-Y will give you a matrix with n*m values corresponding to the difference between each pair of values taken from A and B . Now all you have to do is to find the absolute minimum among all values of Z.
You can do that by
req_min = min(min(abs(z)))
The whole code is
[X Y ] = meshgrid(A,B);
Z= X-Y;
Z = abs(Z);
req_min = min(min(Z));
You could also use bsxfun instead of meshgrid:
min(min(abs(bsxfun(#minus, A(:), B(:).'))))
Or use pdist2:
min(min(pdist2(A(:),B(:))))

How to select values with the higher occurences from several matrices having the same size in matlab?

I would like to have a program that makes the following actions:
Read several matrices having the same size (1126x1440 double)
Select the most occuring value in each cell (same i,j of the matrices)
write this value in an output matrix having the same size 1126x1440 in the corresponding i,j position, so that this output matrix will have in each cell the most occurent value from the same position of all the input matrices.
Building on #angainor 's answer, I think there is a simpler method using the mode function.
nmatrices - number of matrices
n, m - dimensions of a single matrix
maxval - maximum value of an entry (99)
First organize data into a 3-D matrix with dimensions [n X m X nmatrices]. As an example, we can just generate the following random data in a 3-D form:
CC = round(rand(n, m, nmatrices)*maxval);
and then the computation of the most frequent values is one line:
B = mode(CC,3); %compute the mode along the 3rd dimension
Here is the code you need. I have introduced a number of constants:
nmatrices - number of matrices
n, m - dimensions of a single matrix
maxval - maximum value of an entry (99)
I first generate example matrices with rand. Matrices are changed to vectors and concatenated in the CC matrix. Hence, the dimensions of CC are [m*n, nmatrices]. Every row of CC holds individual (i,j) values for all matrices - those you want to analyze.
CC = [];
% concatenate all matrices into CC
for i=1:nmatrices
% generate some example matrices
% A = round(rand(m, n)*maxval);
A = eval(['neurone' num2str(i)]);
% flatten matrix to a vector, concatenate vectors
CC = [CC A(:)];
end
Now we do the real work. I have to transpose CC, because matlab works on column-based matrices, so I want to analyze individual columns of CC, not rows. Next, using histc I find the most frequently occuring values in every column of CC, i.e. in (i,j) entries of all matrices. histc counts the values that fall into given bins (in your case - 1:maxval) in every column of CC.
% CC is of dimension [nmatrices, m*n]
% transpose it for better histc and sort performance
CC = CC';
% count values from 1 to maxval in every column of CC
counts = histc(CC, 1:maxval);
counts have dimensions [maxval, m*n] - for every (i,j) of your original matrices you know the number of times a given value from 1:maxval is represented. The last thing to do now is to sort the counts and find out, which is the most frequently occuring one. I do not need the sorted counts, I need the permutation that will tell me, which entry from counts has the highest value. That is exactly what you want to find out.
% sort the counts. Last row of the permutation will tell us,
% which entry is most frequently found in columns of CC
[~,perm] = sort(counts);
% the result is a reshaped last row of the permutation
B = reshape(perm(end,:)', m, n);
B is what you want.