Assume we have 3 variables for 3 countries as shown below:
| Country | GDP | Child Mortality | Health Expenditure | | X | 5 | 8 | 4 | | Y | 7 | 3 | 1 | | Z | 12 | 4 | 9 |
Now if GDP and health expenditure increase, it is a better country. While if child mortality increases it is a worse country.
Q1. How does PCA and clustering take care of these type of predictors appropriately without having the intelligence of knowing which set of predictors makes it a better country as value increases and which set of predictors make it a worse country as value increases?
Q2. Do we need to translate some predictors like child mortality with some inverse values (eg: divide by 1 or something else on scaled data), so that even for that column an increase in value signifies a better country, so the behavior is similar to columns like GDP / Health Spend etc, so our PCA and clustering algorithms are better able to model and provide good clusters ? Note, that there is no y in the model, we just have a list of countries which we need to cluster.
Anything of this sort is done in modelling and any techniques for these ?
OR what I am seeing here is invalid, and we just dont need to care about any translation (other than simple feature scaling) and directly run PCA/clustering algorithms ? And if we do this how does it take care to create appropriate clusters mathematically ?