Add features other than coordinates #1

Add features other than coordinates, try to understand how to use the algorithm with $(x, y, z, f_1, f_2, \ldots, f_k)$ as input, where $(x,y,z)$ are the coordinates, and $f_i$ are additional features. There are (at least) two possible ways:

1. Multiply each coordinate triple by a positive function $h(f_1, \ldots, f_n)$. We may need monotonous in the feature variables. Here $h$ should also be "hashing" the features (not sure how close it needs to be to an actual hash function). Also, $h$ should keep the importance of the features (again, not sure by how much, as certain features are less important than others).
2. Use some sort of dimension reduction from $3+k$ to $3$. However, any reasonable dimension reduction has to be $O(3)$-invariant, for the action of $O(3)$ on the first 3 coordinates. PCA definitely is. This means we won't be able to recover the transformation.