how to find cosine similarity in a pre-computed matrix with a new vector?
Since cosine similarity is symmetric. You can compute the similarity meassure with the old data matrix, that is similarity between the new sample (1,2048) and old matrix (5000,2048) this will give you a vector of (5000,1) you can append this vector into the column dimension of the pre-computed cosine matrix making it (5000,5001) now since you know the cosine similarity of the new sample to itself. you can append this similarity to itself, back into the previously computed vector making it of size (5001,1), this vector you can append in the row dimension of the new cosine matrix that will make it (5001,5001)
I have a dataframe with 5000 items(rows) and 2048 features(columns). 
Shape of my dataframe is (5000, 2048).
when I calculate cosine matrix using pairwise distance in sklearn, I get (5000,5000) matrix. 
Here I can compare each other. 
But now If I have a new vector shape of (1,2048), how can find cosine similarity of this item with early dataframe which I had, using (5000,5000) cosine matrix which I have already calculated? 
EDIT 
PS: I can append this new vector to my dataframe and calculate again cosine similarity. But for large amount of data it gets slow. Or is there any other fast and accurate distance metrics?