I have this matrix of dimension mx2. What I need is a mx1 matrix such that each element of the mx1 matrix is taken as the maximum value from each 1x2 row of the mx2 matrix. I can do by iteration I know but is there a direct way?
Yes, you can do it directly. the max function in matlab lets you specify the dimension over which you want to take max on:
max(data_m_by_two, [], 2)
should give you what you want, the 2 in there says you want to take max over the second dimension of the matrix, which is over the columns.
Related
Assume there is a data matrix (MATLAB)
X = [0.8147, 0.9134, 0.2785, 0.9649, 0.9572;
0.9058, 0.6324, 0.5469, 0.1576, 0.4854;
0.1270, 0.0975, 0.9575, 0.9706, 0.8003]
Each column represent a feature vector for a sample.
What is the fastest way to get the pairwise consine similarity measure in X in MATLAB? such as we want to compute the symmetric S is 5X5 matrix, the element in S(3,4) is the consine between the third column and fourth column.
Note: The consine measurment cos(a,b) means the angle bettween vector a and b.
If you have the Statistics Toolbox, use pdist with the 'cosine' option, followed by squareform. Note that:
pdist considers rows, not columns, as observations. So you need to transpose the input.
The output is 1 minus the cosine similarity. So you need to subtract the result from 1.
To get the result in the form of a symmetric matrix apply squareform.
So, you can use
S = 1 - squareform(pdist(X.', 'cosine'));
In Matlab, I have created a matrix A with size (244x2014723)
and a matrix B with size (244x1)
I was able to calculate the correlation matrix using corr(A,B) which yielded in a matrix of size 2014723x1. So, every column of matrix A correlates with matrix B and gives one row value in the matrix of size 2014723x1.
My question is when I ask for a covariance matrix using cov(A,B), I get an error saying A and B should be of same sizes. Why do I get this error? How is the method to find corr(A,B) any different from cov(A,B)?
The answer is pretty clear if you read the documentation:
cov:
If A and B are matrices of observations, cov(A,B) treats A and B as vectors and is equivalent to cov(A(:),B(:)). A and B must have equal size.
corr
corr(X,Y) returns a p1-by-p2 matrix containing the pairwise correlation coefficient between each pair of columns in the n-by-p1 and n-by-p2 matrices X and Y.
The difference between corr(X,Y) and the MATLAB® function corrcoef(X,Y) is that corrcoef(X,Y) returns a matrix of correlation coefficients for the two column vectors X and Y. If X and Y are not column vectors, corrcoef(X,Y) converts them to column vectors.
One way you could get the covariances of your vector with each column of you matrix is to use a loop. Another way (might be in-efficient depending on the size) is
C = cov([B,A])
and then look at the first row (or column) or C.
See link
In the more about section, the equation describing how cov is computed for cov(A,B) makes it clear why they need to be the same size. The summation is over only one variable which enumerates the elements of A,B.
I have a matrix like
x = [randn(30,1); 5+randn(30,1)];
It has 60 rows. How could I reduce the number of rows without disturbing the density?
use reshape function to change the dimensions of your matrix without changing the contents:
x=reshape(x,m,n)
yields an m x n matrix. The number of entries must not change, so m*n must be equal 60 in your case.
I have two 50 x 6 matrices, say A and B. I want to assign weights to each element of columns in matrix - more weight to elements occurring earlier in a column and less weight to elements occurring later in the same column...likewise for all 6 columns. Something like this:
cumsum(weight(row)*(A(row,col)-B(row,col)); % cumsum is for cumulative sum of matrix
How can we do it efficiently without using loops?
If you have your weight vector w as a 50x1 vector, then you can rewrite your code as
cumsum(repmat(w,1,6).*(A-B))
BTW, I don't know why you have the cumsum operating on a scalar in a loop... it has no effect. I'm assuming that you meant that's what you wanted to do with the entire matrix. Calling cumsum on a matrix will operate along each column by default. If you need to operate along the rows, you should call it with the optional dimension argument as cumsum(x,2), where x is whatever matrix you have.
Is there a way in Octave to compute and store only the diagonal of a matrix product?
Basically like doing: vector = diag(A*B);
I don't care about any of the values of A*B except those on the diagonal. The matrix sizes are around 80k x 12 and 12 x 80k, so even if I didn't care about the speed/extra memory it simply wont fit in RAM.
Strange, since Octave is a package for huge data sets and diagonals are very important, so it should be possible.
The first element in the diagonal is the scalar product of the first row of A with the first column of B. The second element in the diagonal is the scalar product of the second row of A with the second column of B.
In other words:
vector = sum(A.*B',2);
This is how you could do it in MATLAB (probably similar to Octave syntax):
vector = sum(A.*B',2);
This will compute only the resulting diagonal of the operation A*B as a column vector vector.
actually I think it's the dot product of the first row of A with the first column of B... the second diagonal element is the dot product of the second row and the second column... etc