You can for example use an objective function. Let say you want to maximize a function of the Expenses, Profits and Turnover. In the objective function, give a negative weight to Expenses and Turnover and a positive one to Profits. I don’t know if this will work for your problem, but that would be my first guess.

Another question:
If I want to compute an index where not only the units and scales are different, but also the input metrics into the index have different interpretations – specifically, one metric is better if the values are higher and another one is better if the values are lower, how can I compute an index that represents all numbers concisely and meaningfully?
Let’s say I have Expenses ($), Profits($) and Turnover (%). Expenses and Turnover are better if lower, but Profits are better if higher.
If comparing two companies on these metrics, and I want to compute one index to show the “best” performing company on these parameters, how can I do this?
Sorry, not strictly data-mining relevant, but thought someone here might have an answer!

Tried using z-scores and normalizing but doesnt work due to different hi-low interpretations.
Eventually used a reverse-rank for Expenses and Turnover so that all have same order. However, rank does not show quantity difference between the two companies, just their ranks!

this is a great blog, thanks to all for helpful comments.

This is similar to trimming the data, except that instead of discarding data: values greater than the specified upper limit are replaced with the upper limit, and those below the lower limit are replace with the lower limit. Often, the specified range is indicate in terms of percentiles of the original distribution (like the 5th and 95th percentile).

This process is sometimes used to make conventional measures more robust, as in the Winsorized variance.

Will, your suggestions seem very interesting. I don’t know the “winsorize” technique, but it seems it could be used in addition to normalization.

1. Monotonic scaling of the data (assuming that distinct values are not collapsed) will have no affect on the most common logical learning algorithms (tree- and rule-induction algorithms).

2. There are robust alternatives, such as: subtract the median and divide by the IQR, or scale linearly so that the 5th and 95th percentiles meet some standard range.

3. Outliers (technically, and high leverage points) present an interesting challenge. One possibility is to Winsorize the data after scaling it.