Hierarchical Multi-label Classification I would like to make a classifier, where I can classify individuals from one hand, and from the other hand, understanding the data better, meaning figuring out which feature, is the most contributing.
I have two datasets, which are comparable; However, the labels for these datasets are somewhat different. Both datasets have samples with NO (healthy) and Yes(Cancer) labels; But one of the main factor, that makes them different is the inter medium labels; Dataset, has one class in between called (medium) while the other dataset has two intermediate labels ( Small risk, High Risk). 
Of course, small risk, is just a risk and can lead to cancer, but also can stay healthy; and high risk has more chance to become cancer but might stay just as a risk; Last but not the list, in the other hand, medium in dataset one is basically a combination of small and high risk !
One can arbitrary group high risk together with cancer, and small risk with healthy; or some other way, and exclude samples from the other dataset ...
my question is here; Can I construct a hierarchical model on the response variable and let the classifier share these information among the group WITHOUT any additional grouping ?
I assume here is an example where Bayesian can gives some real help !
 A: At this point, I think I can answer your final question in the affirmative. Yes, a hierarchical Bayesian model would be highly efficient at sharing whatever information exists in these heavily interval-censored data. (It is through the latent variables in these models that this sharing would be accomplished.) A Bayesian approach would be especially fruitful if your priors embody a substantial amount of additional information about the disease process, or even about the vagaries of the data collection process.
It's altogether possible that such a modeling exercise will demonstrate that, even with your best efforts to provide strongly informative priors, your data are too heavily censored to tell you much. That would be a very useful finding, however, as it would allow you to abandon other, less efficient modeling methods in favor of devoting resources to searching for new data of higher quality--or perhaps recovering some of the underlying detail lost in your current data by going back to the pathologists' original notes. I find it hard to believe a pathologist would ever set eyes on an excised tumor sample without producing (somewhere!) an exquisite description of it. (The same holds for radiologists, if your data come from MRI or CT imaging.)
A: First of all, you are converting the multi-class classification problem into a binary classification problem by labelling them as 0 and 1 (i.e. No risk and Sick). So one possible approach might be labeling them as 1,2,3,4 where 1=No, 2=SmallRisk etc. , then you have 4 classes and you can try to tackle 4-class classification.
Another approach can be regression. So labelling your 4 classes as [0, 0.33, 0.66, 1] then from the features, you estimate a number between 0 and 1. And you decide the class which is closest to one of those 4 numbers.

I would like to do feature selection and find those paramteres that can returns me the best result under this setup.

I suggest linear discriminant analysis for this. Simply give your labels as the first example (i.e. 1 to 4) and it will give you 4-1=3 features per sample, that have the minimum intra-class variance and the most inter-class variance. With those features, you can try to do 4-class classification.
