data

# Differences

This shows you the differences between two versions of the page.

 data [2012/10/18 14:12]melancon data [2013/10/08 10:29] (current)bpinaud [Normalization] Both sides previous revision Previous revision 2013/10/08 10:29 bpinaud [Normalization] 2012/10/18 14:12 melancon 2012/10/18 14:11 melancon [Histograms] 2012/10/18 14:10 melancon [Histograms] 2012/10/18 14:07 melancon [Histograms] 2012/10/17 15:58 melancon 2012/10/17 15:45 melancon 2012/04/19 17:51 melancon [Data] 2012/04/19 17:50 melancon [Data] 2012/04/19 17:50 melancon [Data] 2012/04/19 17:50 melancon [Data] 2012/04/19 17:49 melancon [Data] 2012/04/19 17:48 melancon [Data] 2012/02/07 23:19 melancon [Histograms] 2012/01/17 22:07 melancon [Normalization] 2012/01/17 22:02 melancon [Data] 2012/01/17 22:00 melancon [Data] 2012/01/17 21:59 melancon [Data] 2012/01/17 21:58 melancon [Data] 2012/01/17 21:53 melancon [Normalization] 2011/12/19 20:33 melancon [Normalization] 2011/12/19 20:33 melancon [Histograms] 2011/12/19 20:32 melancon [Data] 2011/12/19 19:45 melancon [Normalization] 2011/09/19 18:45 melancon 2011/09/13 20:35 melancon 2011/09/13 20:11 melancon 2013/10/08 10:29 bpinaud [Normalization] 2012/10/18 14:12 melancon 2012/10/18 14:11 melancon [Histograms] 2012/10/18 14:10 melancon [Histograms] 2012/10/18 14:07 melancon [Histograms] 2012/10/17 15:58 melancon 2012/10/17 15:45 melancon 2012/04/19 17:51 melancon [Data] 2012/04/19 17:50 melancon [Data] 2012/04/19 17:50 melancon [Data] 2012/04/19 17:50 melancon [Data] 2012/04/19 17:49 melancon [Data] 2012/04/19 17:48 melancon [Data] 2012/02/07 23:19 melancon [Histograms] 2012/01/17 22:07 melancon [Normalization] 2012/01/17 22:02 melancon [Data] 2012/01/17 22:00 melancon [Data] 2012/01/17 21:59 melancon [Data] 2012/01/17 21:58 melancon [Data] 2012/01/17 21:53 melancon [Normalization] 2011/12/19 20:33 melancon [Normalization] 2011/12/19 20:33 melancon [Histograms] 2011/12/19 20:32 melancon [Data] 2011/12/19 19:45 melancon [Normalization] 2011/09/19 18:45 melancon 2011/09/13 20:35 melancon 2011/09/13 20:11 melancon 2011/09/13 20:10 melancon 2011/09/13 18:59 melancon 2011/09/13 18:54 melancon 2011/09/13 18:53 melancon 2011/09/13 18:48 melancon 2011/09/13 18:43 melancon 2011/09/13 18:39 melancon 2011/09/13 17:25 melancon 2011/09/13 17:21 melancon 2011/09/13 17:01 melancon 2011/09/13 16:56 melancon 2011/09/13 16:48 melancon 2011/09/13 16:47 melancon created Line 87: Line 87: 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 $\mu = \frac{1}{N} \sum_i x_i$