Which algorithm to use to identify clusters with a similar value? Here, an example of my problem:
10000 observations of people with several features [age, gender, region, number of sons, ...] and a value to predict "income".
There is not a general relationship between features and income, therefore a normal regression has poor results.
Nevertheless, I want to identify specific patterns where this relationship exists. For instance:
[young, woman, 2 son] -> high income
[young, man] -> small income
...

Maybe doing a clustering on the features, and then a regression on each cluster?
Or pattern recognition? topic modeling?

Thank you in advance
What you are describing is called ordinal regression. The target variable (income) is divided into discrete groups where the relative ordering between different groups is preserved (low, middle, high).

Binning a continuous variable as the advantage of better handling noisy data.