# Combining multiple observation weights for classification

Let's say you have multiple sources of observation weights for a dataset. For example, you have a $$[0,1]$$ weight coming from the label's certainty ($$w_c$$) and another one coming from its recency ($$w_t$$). What would be the best way to combine those into a single number to be used when training a classifier?

Some options I have considered:

• Product: $$w_cw_t$$
• Arithmetic mean: $$\frac{w_c+w_t}{2}$$
• Geometric mean: $$\sqrt{w_cw_t}$$
• Harmonic mean: $$\frac{2w_cw_t}{w_c+w_t}$$

All of the above make (intuitive) sense on some level. Any ideas as to what is best practice or at least some pointers to literature on the topic?