Summary
Intrinsic dimensionality of a space is the number of required* pieces of information that we need to describe each object in a space.
Extrinsic dimensionality of a space is the number of pieces we are using to describe the space.
Definitions
- Space: set of object with some structure.
- 3D space: set of all points in a 3 dimensions.
- Dimensions: D-dimension space is one in which a D information required to describe each object in the space.
Example
- Although the space below is 3D, we can represent each point on the paper with only 2 pieces of information (in red).
- We can infer the the 3D coordinate from the 2D point.
Related: Low-rank Adaption (LoRA)