Cyclical Encoding for Time Features

Time-of-day, day-of-week, and month all wrap around: hour 23 is followed by hour 0, December is followed by January. Encoding them as plain integers (0–23 for hour, 1–12 for month) hides this wraparound — a model sees 23 and 0 as maximally far apart on the number line, even though 11pm and midnight are one hour apart in reality.

Cyclical encoding fixes this by mapping each time value onto a circle using a pair of sine and cosine features: $x_{sin} = \sin(2\pi \cdot h / 24)$ and $x_{cos} = \cos(2\pi \cdot h / 24)$ for an hour $h$. In words: rescale the hour so a full day maps to one trip around a circle, then read off that point's horizontal and vertical coordinates. Now hour 23 and hour 0 land right next to each other on the circle, exactly as they should, and the model can learn smooth, continuous patterns across the wraparound point instead of a false discontinuity.

Worked example

Hour 23 encodes to $(\sin(2\pi \cdot 23/24), \cos(2\pi \cdot 23/24)) \approx (-0.26, 0.97)$. Hour 0 encodes to $(0, 1)$. These two points sit close together on the unit circle, correctly reflecting that they're one hour apart — unlike raw integers 23 and 0, which sit 23 units apart on a number line despite being adjacent in real time.