I would like to learn gradient based optimization for multivariate data.
For example, assume the data I have is $X = (x_0, ..., x_n)$ where $x_i$ are some random variables and $f$ a function measuring (Pearson, if you like) correlation. Then, I would like to minimize the value of $f(X)$ i.e. make the variables $x_0, ..., x_n$ uncorrelated. How could this be achieved using gradient based methods?
After I have learnt this, the next thing is that I would like to implement the procedure in MATLAB. If you have any tips for that, I would like to hear those as well.