Intensive and Extensive Features in Data Science. Intensive variables tell us much more about a system than extensive variables.
In physics, an extensive variable is one that depends on system size (like mass or volume). On the other hand, an intensive variable is one which does not depend on system size (like temperature, pressure, or density). While it may not be immediately obvious, intensive variables tell us much more about the system than extensive variables.
Comparing features based on an extensive scale is called absolute comparison. Likewise, comparing features based on an intensive scale is called** relative comparison**.
To illustrate the difference between extensive and intensive variables, let us consider two hypothetical players in the National Basketball Association (NBA) league. We shall refer to these players as Player A and Player B. Table 1 below shows the statistics for players A and B at the end of the regular season.
Table 1. Comparing the season of two hypothetical NBA players. Image by Benjamin O. Tayo
We will also assume that Players A and B played a total of 75 and 60 games during the season, respectively. Player B played 15 games less than player A due to injuries. We will also assume that when both players are healthy, they play on average the same amount of minutes per game.
We observe from Table 1 that based on the extensive feature (Total Points), Player A performed better than Player B. Given that Total Points scored during a season is proportional to the number of games played, it makes no sense to compare players A and B based on Total Points only. A more meaningful feature is the intensive feature called points per game (PPG). We see that in terms of PPG, player B is a better scorer with 23.3 PPG compared to player A (with an average of 21.0 PPG).
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