Multi-label Kernel Construction for 3-Class MKL Problem

[mehrankhosrojerdi]

Hi!

Thank you very much for this great repository and your hard work. I'm currently working on a project involving multiple quantum phases and I had a question regarding kernel construction and label alignment in the context of multi-kernel learning (MKL).

In this project, I have two distinct kernels:

• The first kernel is a $20 \times 20$ symmetric matrix corresponding to 20 samples labeled as paramagnetic (-1) and ferromagnetic (0).
• The second kernel is a $12 \times 12$ matrix built from a different set of 12 samples, labeled as ferromagnetic (-1) and antiphase (+1).

My goal is to combine these two kernels to train a model capable of distinguishing three phases in total: paramagnetic, ferromagnetic, and antiphase. However, I’ve encountered the following issue:

Since the two kernels are built over disjoint sets of samples (20 and 12), the total number of labels is 32, but each individual kernel is only defined for a subset. From my understanding, MKLpy requires the target Y to match the shape of each individual kernel, i.e., len(Y) == K.shape[0] for all kernels in KL.

My Questions:

1. How should I construct the input kernel list and label vector Y for this kind of partially overlapping or disjoint kernel scenario?

2. Is there a recommended way to combine these kernels when they are computed on different subsets, or should I recompute both kernels over a shared set of samples covering all three classes?

3. How would you suggest constructing the test kernel matrix, especially in cases where the two base kernels were computed on different sample sets?

Thank you in advance for your time and help — I really appreciate any guidance you can provide!

Best regards,
Mehran