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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