Questions tagged [normalization]

Usually "normalization" means re-expressing univariate data to make values lie within a specified range.

Tag Usage

Do not confuse normalization with or .

"Normalization" refers to several related processes:

  • ("Feature scaling") A set of numbers whose maximum is $M$ and minimum is $m$ can be converted to the range from $0$ to $1$ by means of an affine transformation (which amounts to changing their units of measurement) $x \to (x-m)/(M-m)$.

  • A set of positive numbers $\{p_i\}$ representing probabilities or weights can be uniformly rescaled to sum to unity: divide each $p_i$ by the sum of all the $p_i$.

  • Analogously, a distribution (or indeed any non-negative function with a finite nonzero integral) can be normalized to have a unit integral by dividing its values by the integral.

  • A vector in a normed linear space is normalized (to unit length) by dividing it by its norm. This is a general procedure encompassing the two preceding operations as special examples.

The range from $0$ to $1$ can be made from $0$ to any desired limit $\alpha$ by multiplying a previously unit-normalized value by $\alpha$.

Other kinds of operations exist having a similar intent of re-expressing values in a predetermined range. Many of these are nonlinear and tend to be used in specialized settings.

1239 questions
416
votes
6 answers

How to normalize data to 0-1 range?

I am lost in normalizing, could anyone guide me please. I have a minimum and maximum values, say -23.89 and 7.54990767, respectively. If I get a value of 5.6878 how can I scale this value on a scale of 0 to 1.
Angelo
  • 4,615
178
votes
5 answers

What's the difference between Normalization and Standardization?

At work we were discussing this as my boss has never heard of normalization. In Linear Algebra, Normalization seems to refer to the dividing of a vector by its length. And in statistics, Standardization seems to refer to the subtraction of a mean…
Chris
  • 1,789
124
votes
2 answers

Why do we need to normalize data before principal component analysis (PCA)?

I'm doing principal component analysis on my dataset and my professor told me that I should normalize the data before doing the analysis. Why? What would happen If I did PCA without normalization? Why do we normalize data in general? Could someone…
jjepsuomi
  • 6,067
95
votes
2 answers

How to normalize data between -1 and 1?

I have seen the min-max normalization formula but that normalizes values between 0 and 1. How would I normalize my data between -1 and 1? I have both negative and positive values in my data matrix.
covfefe
  • 1,299
84
votes
7 answers

What are good initial weights in a neural network?

I have just heard, that it's a good idea to choose initial weights of a neural network from the range $(\frac{-1}{\sqrt d} , \frac{1}{\sqrt d})$, where $d$ is the number of inputs to a given neuron. It is assumed, that the sets are normalized - mean…
elmes
  • 967
81
votes
8 answers

How and why do normalization and feature scaling work?

I see that lots of machine learning algorithms work better with mean cancellation and covariance equalization. For example, Neural Networks tend to converge faster, and K-Means generally gives better clustering with pre-processed features. I do not…
erogol
  • 1,677
75
votes
7 answers

Data normalization and standardization in neural networks

I am trying to predict the outcome of a complex system using neural networks (ANN's). The outcome (dependent) values range between 0 and 10,000. The different input variables have different ranges. All the variables have roughly normal…
Boris Gorelik
  • 2,807
69
votes
2 answers

Are mean normalization and feature scaling needed for k-means clustering?

What are the best (recommended) pre-processing steps before performing k-means?
pedrosaurio
  • 1,373
66
votes
4 answers

Perform feature normalization before or within model validation?

A common good practice in Machine Learning is to do feature normalization or data standardization of the predictor variables, that's it, center the data substracting the mean and normalize it dividing by the variance (or standard deviation too). For…
SkyWalker
  • 925
63
votes
2 answers

scale a number between a range

I have been trying to achieve a system which can scale a number down and in between two ranges. I have been stuck with the mathematical part of it. What im thinking is lets say number 200 to be normalized so it falls between a range lets say 0 to…
Saneesh B
  • 733
  • 1
  • 6
  • 5
63
votes
7 answers

Is it a good practice to always scale/normalize data for machine learning?

My understanding is that when some features have different ranges in their values (for example, imagine one feature being the age of a person and another one being their salary in USD) will affect negatively algorithms because the feature with…
Juan Antonio Gomez Moriano
  • 1,329
61
votes
1 answer

How to apply standardization/normalization to train- and testset if prediction is the goal?

Do I transform all my data or folds (if CV is applied) at the same time? e.g. (allData - mean(allData)) / sd(allData) Do I transform trainset and testset separately? e.g. (trainData - mean(trainData)) / sd(trainData) (testData - mean(testData)) /…
DerTom
  • 807
60
votes
5 answers

Should you ever standardise binary variables?

I have a data set with a set of features. Some of them are binary $(1=$ active or fired, $0=$ inactive or dormant), and the rest are real valued, e.g. $4564.342$. I want to feed this data to a machine learning algorithm, so I $z$-score all the…
siamii
  • 2,097
57
votes
4 answers

Normalization vs. scaling

What is the difference between data 'Normalization' and data 'Scaling'? Till now I thought both terms refers to same process but now I realize there is something more that I don't know/understand. Also if there is a difference between Normalization…
d.putto
  • 931
  • 2
  • 11
  • 13
52
votes
3 answers

Is standardisation before Lasso really necessary?

I have read three main reasons for standardising variables before something such as Lasso regression: 1) Interpretability of coefficients. 2) Ability to rank the coefficient importance by the relative magnitude of post-shrinkage coefficient…
Jase
  • 2,306
1
2 3
…
82 83