angle calculation in high-Dim space

[ShuaiLYU]

Hi, Thanks for you work.

May I ask can I use cosine similarity to represent the angle ？ does it make sense ?

Best,
Lyus

[pdh-coder]

Cosine similarity can be used in place of the angle when all angles are smaller than π in 2D space, since cos(x) is monotonically decreasing when x is smaller than π, that means the consistency of angles is equivalent to the cosine. However, when the largest angle is larger than π, it will be invalid. For example, three angles 0, 0, 2π, their variance is 8.77; while, their consines are 1, 1, 1 respectively, the variance reach to the minimum 0. Moreover, cosine similarity cannot represent the centrality for high-dimensional data.

[ShuaiLYU]

Cosine similarity can be used in place of the angle when all angles are smaller than π in 2D space, since cos(x) is monotonically decreasing when x is smaller than π, that means the consistency of angles is equivalent to the cosine. However, when the largest angle is larger than π, it will be invalid. For example, three angles 0, 0, 2π, their variance is 8.77; while, their consines are 1, 1, 1 respectively, the variance reach to the minimum 0. Moreover, cosine similarity cannot represent the centrality for high-dimensional data.

Thanks for your explanation.

[ShuaiLYU]

Cosine similarity can be used in place of the angle when all angles are smaller than π in 2D space, since cos(x) is monotonically decreasing when x is smaller than π, that means the consistency of angles is equivalent to the cosine. However, when the largest angle is larger than π, it will be invalid. For example, three angles 0, 0, 2π, their variance is 8.77; while, their consines are 1, 1, 1 respectively, the variance reach to the minimum 0. Moreover, cosine similarity cannot represent the centrality for high-dimensional data.

I was wondering if you plan to provide a python implementation of the high-Dim angle calculation algorithm? looking forward to it