sine, cosine transformed cyclical features - am I losing information?
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16-12-2020 - |
Question
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!
Solution
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 $i \in \{0,...,23\}$
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