I have a dataset including 100k high dimensional data (e.g. houses in LA) (dim=100, e.g. house parameters like area, distance to downtown, etc.). Below is the 2-component PCA representation of the data, colored by target value (e.g. housing price).
As you can see, price function has a stochastic behavior and changes rapidly everywhere.
- Is there a dimensionality reduction method that takes the target value into account and as a result, it aggregates low priced homes on one side and we can see a gradient of housing prices in the map?
- Can manifold learning help in anyway with this task?
I tried Backward feature extraction based on ridge regression to reduce the dimensionality based on their effect on regression results on target value, and then applied PCA and normalized it, but the output was not as desired. Here is the output: