Help creating an amplification transformation

[trinker]

I'm attempting to apply a transformation to set of values between -1 and 1 (values are already between -1 and 1). I'm not a mathematician and so I know what I want but I don't know how to represent it mathematically. The basic idea is that in language there are some words that amplify meaning such as really. If I measure the polarity of a sentence say:

"This burger is really crappy."

The polarity may be assessed at -.4 using techniques similar to those by Jeffery Breen found here (LINK). Anyway the word "really" amplifies the negative word crappy.

This may be done already in linguistics but I've yet to find it. So I'm attempting to make this amplification similar to a fisherz transformation for correlations. The data is already between 1 and -1 and is similar to a correlation coefficient. I don't want to lose that meaning.

I need a math transformation that will do the following.

Rules:
1. I want to amplify the current value (-.4 in this case)
2. The amplification can not exceed -1 or 1 (so if the polarity score is already 1 it will stay at 1)

Not certain rules:
3. I'm not sure if it makes sense to have the amplification increase exponentially or at a constant rate with larger polarity scores amplifying more (ie does the really in "really stinks" [polarity score= -.2] weight or amplified as much as "really sucks the big one I hate this" [polarity score= -.4].

I'm thinking this is somewhat similar to the problem with log odds in logistic regression and a transformation similar to the one that reduces scores to between 1 and 0 but extending this to 1 and -1.

I'm thinking a vector of polity scores that are to be amplified may look like this:

     ps    aps
1  -1.0 -1.000
2  -0.8 -0.950
3  -0.6 -0.700
4  -0.4 -0.450
5  -0.2 -0.225
6   0.0  0.000
7   0.2  0.225
8   0.4  0.450
9   0.6  0.700
10  0.8  0.950
11  1.0  1.000

ps=polarity score; aps=amplified polarity score

If this is not clear or doesn't make sense please ask and I'll clarify.

[Dason]

A power transformation (with exponent between 0 and 1) might work. The problem with that is that it would shift smaller values more than it shifts larger values which is sort of the opposite of the effect that you have displayed in your examples.