Hi Adam Rish,
To address your first question,
Yes, both Cosine Similarity and Spectral Angle Mapper share some mathematical similarities, but they also have distinct characteristics such as:
- Range of values: Cosine Similarity ranges from -1 to 1, whereas for Spectral Angle Mapper, the values range typically between 0 and π/2 (0 to 90 degrees).
- Dimensionality: Cosine Similarity operates on the entire vector space, comparing the similarity of all spectral bands. Spectral Angle Mapper, on the other hand, operates on the angle between vectors in a high-dimensional space.
To address your second question,
Yes, both Cosine Similarity and Spectral Angle Mapper are intended to be insensitive to magnitude variations as Cosine Similarity focuses on the similarity of spectral reflectance values, while Spectral Angle Mapper considers the angles between spectral vectors in a high-dimensional space.
And in the case, you mentioned, where Z = kX , CS(ZY) should indeed be equal to CS(XY). This is because Cosine Similarity measures the angle between vectors, which is independent of their magnitudes.
I hope this helps!
