I have a group of metrics that have been z-scaled. All of the metrics have the property that if some entity has a larger value on a metric, that entity is "better" or "more important" in regards to the metric. Basically, the larger the value, the better.
However, I have some correlated metrics and want to remove them. I have used PCA which has allowed me to reduce the number of metrics from 10 to 6 but still retain 99% of the variance. However, after doing PCA, the reduced components no longer have the property that if some entity has a larger value on a metric, that entity is "better" or "more important". I see that entities that originally scored very highly on the non-reduced metrics, have low or even negative values on the reduced PCA metrics. If I now rank the entities using some ranking algorithm, these entities no longer rank highly. Is it possible to do PCA and retain that property?