# sine, cosine transformed cyclical features - am I losing information?

If I use sine, cosine transformation for cyclical features (e.g. weekday or hour of the day), do I lose information if the first ordinal value was 0 respectively?

Assume hours of the day are encoded as follows: 0, 1, ..., 23

If I apply the sine, cosine transformation, I get 23 data points instead of 24 (cf. plot)

Am I losing information on the first ordinal value (0)?

Many thanks in advance!

## 1 Answer

Are 0 and 23 supposed to be the same?

If not then you should use $$( \sin(2i\pi/24),\cos(2i\pi/24) )$$ instead of $$( \sin(2i\pi/23),\cos(2i\pi/23) )$$ with $$i \in \{0,...,23\}$$

• no they are not the same. 0 aggregates the time between 00:00 and 00:59 am, while 23 aggregates the time between 23:00 and 23:59 so the solution you provided is perfect! thank you! – jacobumland Nov 22 '20 at 15:31