Andrew Ng scaling and normalizing expression I'm involved in the design of a recommender system and I'm using a mixture expression of z-score and min-max scaling for scaling and normalizing data:
$X_{norm} = \frac{X - \mu}{X_{max} - X_{min}}$
Andrew Ng has used it in some of his videos, e.g.: https://class.coursera.org/ml-003/lecture/21
I would like to get further information about that expression and some papers where it's used I can cite.
 A: It's not particularly innovative. It's simply an inlined version of two transformations:


*

*Scale to [0;1] (give equal weight to all features, assuming a linear distribution of values and no significant outliers)

*Shift mean to 0 (to center the data set; this will not affect the output at all for most algorithms.)


No need to cite or give credit for such basic linear algebra.
A: To me it looks like you are mixing two different kinds of normalization/standardization techniques.
You typed
$$X_{norm} = \frac{x - \mu}{x_{max} - x_{min}},$$
and it looks like a mix of standardization:
$$X_{stand} = \frac{X -\mu}{\sigma},$$
where you subtract the mean from each observation and divide by the standard deviation,
and unity-based normalization:
$$X_{norm} = \frac{X - min(X)}{max(X)-min(X)},$$
where you transform your observation so that each $X_{norm} \in [0,1]$.
Look at this code and its output:
x <- rnorm(100, 1, 2)
# raw data
plot(density(x))

# standardization
x1 <- (x - mean(x)) / sd(x)
plot(density(x1))

# unity-based
x2 <- (x - min(x)) / (max(x) - min(x))
plot(density(x2))

# Andrew Ng
x3 <- (x - mean(x)) /(max(x) - min(x) )
plot(density(x3))

plot(density(x), ylim = c(0,2))
lines(density(x1), col = "blue") # standardization
lines(density(x2), col = "red") # unity-based normalization
lines(density(x3), col = "purple") # Andrew Ng


Each of such techniques are pretty common in data analysis, and if you want to use them you don't need to cite any specific paper. Just explain and motivate your choice.
However, when you have to transform your data you must choose the technique that best fits your needs, and not just simply because a great researcher like Andrew Ng applied it. So, why do you need to transform your data? Answer such a question and then choose the most appropriate transformation.
A: As I see this transformation is similar to a uniform transformation, $\frac{x-\min_x}{\max_x-\min_x}$. the only bit that is added to this transformation is replacing $\min_x$ with $\mu$ in the numerator and the goal is getting zero mean, $\mathbb{E}X_{norm}=0$. Maybe you can find some references in machine learning journals(but I am not completely sure)
