# How to solve a multi-class and multi-label problem?

I have a following classification problem with somewhere around 2000 examples.

For each example, there is a feature vector $\bf{x}$ of size $N$ and a label vector $\bf{y}$ of size $L$. Each label entry can take 3 values from a label-set $S\in\{-1,0,1\}$. The label vector has some structure to it such as there could be up to 3 entries with -1 and maximum one entry with 1 etc etc.

so for example y could be [-1, -1, 0, 1, 0, 0] for L=6

How to approach this kind of problem? Any hints/suggestions?

• You can use the simple binary relevance method that is also used in normal multi-label problems. Dec 10 '17 at 8:36

I don't know if this is a good idea, but if you regard each entry in your vector as a variable -- which I assume it actually is -- say A, B, C, ... F in your example, you can encode the values as M1, 0 and P1 (for -1, 0, and +1, respectively) and combine the two to create actual labels. Your example's labels would thus be: [AM1, BM1, C0, DP1, E0, F1].

I believe this would work with standard multi-label algorithms. The problem would be that prediction would not constrain the labels to follow your other rules (3 minus, 1 plus, etc).

But I don't think that thinking of your S as labels is going to work in the multi-label literature/paradigm since they are not really labels.