Clustering 3D multivariate data

Question

I am looking for a clustering procedure that will group a number of 3D points on the basis of their spatial relations and multivariate dimensions. Dimensions are mostly represented with (interval) metric variables and few composed of categorical variables.
My questions:

1. Is there any clustering procedure that also factors in weighting coefficients assigned (by user) to certain dimensions or spatial relation (distance)?
2. Is there any clustering procedure that analyses both categorical and metric dimensions?
3. Is there a clustering procedure thatr fullfill these requirements and it is already implemented in any of the commonly-used statistical software such as R, MATLAB, Python?

My data looks like this:

1. 0.0303 0.0763 0.1363 0.1753 0.1916 0.2411 0.2661
2. 0.0000 0.0000 0.0000 0.0084 0.0176 0.0393 0.0482
3. 0.3287 0.3794 0.4887 0.7151 1.0220 4.8060 7.4140
4. 0.2310 0.2692 0.3563 0.4384 0.4836 0.6694 0.8040

Is there a method that considers both numerical and alphabetical values? For example if I add to this dataset a column with values such as A, B, C, AC, CF,.... Thanks

Answer 1

It would be nice show a few example data points to make sure that my answer is what you may be looking for, but anyways,

1) I think so, you may wanna look at feature weighting for k-means in this paper

3) For the libraries commonly used for this, you may wanna look at this answer or this code

2) I'm unclear what you mean here, maybe you could elaborate, or probably someone's going to pick up on it and answer you on this point.