Suppose one hase a data matrix A with size n-by-m, n denotes the number of trials and m denotes the variables, and one intends to find some ways to reduce the matrix A, say, reducing the size of n.
One way is to first centralize the column vectors to each of its column mean, respectively, and then deteremine the matrix of variances, transpose(A)*A.
Next, one can find the eigenpairs of the aforementioned variance matrix and then one can set a cut off criterion based on the magnitudes of the eigenvalues. By projecting A onto the eigenvectors corresponding to the remaining eigenvalues, one has a way to reduce A.
An issue to above approach is that, often times one would increase the size of n by conducting new trials. Each time adding a new trial, or rows of A, one has to recalcuate each of the column mean and re-construct the variances matrix all over again.
Are there formula that allows one to "correct" the new variance matrix or directly correct the eigenpairs of the variance matrix from previously calculated ones?