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data [2012/10/18 14:12]
melancon
data [2013/10/08 10:29] (current)
bpinaud [Normalization]
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 There are a number of ways normalization can be accomplished. Values spreading over an interval $[a, b]$ may be brought down to $[0, 1]$ linearly using the formula $f(x) = (x - a)/(b-a)$. The comparison then relies on the fact that values spread over the same interval. That is, considering the column $X_i$ as a random variable, we compute a new variable $Y_i = (X_i - a)/(b - a)$ by applying a linear (affine) transform to $X_i$. It does not however take the distribution of values into account: although values sit in the same interval, their mean value might well differ (and most importantly their standard deviation). There are a number of ways normalization can be accomplished. Values spreading over an interval $[a, b]$ may be brought down to $[0, 1]$ linearly using the formula $f(x) = (x - a)/(b-a)$. The comparison then relies on the fact that values spread over the same interval. That is, considering the column $X_i$ as a random variable, we compute a new variable $Y_i = (X_i - a)/(b - a)$ by applying a linear (affine) transform to $X_i$. It does not however take the distribution of values into account: although values sit in the same interval, their mean value might well differ (and most importantly their standard deviation).
  
-Another way to go with normalization is to make sure the mean value sits at the origin while values all spread more or less the same way around ​tis mean value: in other words, bring the mean value to 0 and normalize the variance of the data sample to 1. This is accomplished the following way. Let $x_1, \ldots, x_N$ be data samples (real numbers or integers):+Another way to go with normalization is to make sure the mean value sits at the origin while values all spread more or less the same way around ​this mean value: in other words, bring the mean value to 0 and normalize the variance of the data sample to 1. This is accomplished the following way. Let $x_1, \ldots, x_N$ be data samples (real numbers or integers):
  
   * The mean $\mu$ is equal to $\mu = \frac{1}{N} \sum_i x_i$   * The mean $\mu$ is equal to $\mu = \frac{1}{N} \sum_i x_i$
/net/html/perso/melancon/Visual_Analytics_Course/data/pages/data.txt · Last modified: 2013/10/08 10:29 by bpinaud