# Questions tagged [normalization]

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

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### 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 ...
251k views

### 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, ...
102k views

### Is it a good practice to always scale/normalize data for machine learning? [duplicate]

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 ...
3k views

### Ridge\Lasso — Standardization of dummy indicators

Say I have a data set with say 5000 rows and about 150 columns (5000 samples, 150 predictors/features) and I'm interested in a applying a ridge or lasso regression. (Let us assume using a logit link ...
103k views

### 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. ...
109k views

### 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 ...
212k views

### Why do we need to normalize data before principal component analysis (PCA)? [duplicate]

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? ...
68k views

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

What are the best (recommended) pre-processing steps before performing k-means?
108k views

### 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. ...
18k views

### whether to rescale indicator / binary / dummy predictors for LASSO

For the LASSO (and other model selecting procedures) it is crucial to rescale the predictors. The general recommendation I follow is simply to use a 0 mean, 1 standard deviation normalization for ...
28k views

### 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 ...
36k views

### 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 ...
73k views

### What does “normalization” mean and how to verify that a sample or a distribution is normalized?

I have a question in which it asks to verify whether if the Uniform distribution (${\rm Uniform}(a,b)$) is normalized. For one, what does it mean for any distribution to be normalized? And two, how ...
110k views

### 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.
12k views

### Converting (normalizing) very small likelihood values to probability

I am writing an algorithm where, given a model, I compute likelihoods for a list of datasets and then need to normalize (to probability) each one of the likelihood. So something like [0.00043, 0.00004,...
999 views

### Neural Networks input data normalization and centering

I'm learning Neural Networks and I grasped the algebra behind them. I'm now interested in understanding how normalization and centering of the input data affect them. In my personal learning project (...
43k views

### 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 ...
22k views

### “Normalizing” variables for SVD / PCA

Suppose we have $N$ measurable variables, $(a_1, a_2, \ldots, a_N)$, we do a number $M > N$ of measurements, and then wish to perform singular value decomposition on the results to find the axes of ...
1k views

### scaling for SVM destroys my results [duplicate]

I'm applying standard 0-1 scaling of features before SVM classification for financial data but the results are worse. This is the results before scaling ...
879 views

### Is the normal distribution a better approximation to the binomial distribution with proportions near or far from 0.5?

From the Online Stat Book: I don't understand this: The accuracy of the approximation depends on the values of N and π. A rule of thumb is that the approximation is good if both Nπ and N(1-π) ...
41k views

### How to represent an unbounded variable as number between 0 and 1

I want to represent a variable as a number between 0 and 1. The variable is a non-negative integer with no inherent bound. I map 0 to 0 but what can I map to 1 or numbers between 0 and 1? I could use ...
12k views

### Standardizing features when using LDA as a pre-processing step

If a multi-class Linear Discriminant Analysis (or I also read Multiple Discriminant Analysis sometimes) is used for dimensionality reduction (or transformation after dimensionality reduction via PCA), ...
1k views

### In Machine learning, how does normalization help in convergence of gradient descent?

I have read in an article that normalization helps gradient descent to converge faster in machine learning. But I cannot understand why is that. Any idea?
325 views

### Effect of rescaling of inputs on loss for a simple neural network

I've been trying out a simple neural network on the fashion_mnist dataset using keras. Regarding normalization, I've watched this video explaining why it's necessary to normalize input features, but ...
31k views

### 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 ...
9k views

### Normalization prior to cross-validation

Does normalizing data (to have zero mean and unity standard deviation) prior to performing a repeated k-fold cross-validation have any negative conquences such as overfitting? Note: this is for a ...
7k views

### De normalize predicted value

Alright so i have found this really good answer on how to normalize my data. I implemented @user25658 's code into my own project successfully, trained a linear model and used it to make a ...
6k views

### With the Naive Bayes classifier, why do we have to normalize the probabilities after calculating the probabilities of each hypothesis?

In the Naive Bayes classifier, why do we have to normalize the probabilities after calculating the probabilities of each hypothesis?
2k views

### Raw data outperforms Z-score transformed data in SVM classification

I've been trying to perform a binary classification using an SVM classifier (scikit-learn's SVC with RBF kernel). I have a sample size of about 100, with about 70 features each. The features are of ...
46k views

### When should I apply feature scaling for my data [duplicate]

I had a discussion with a colleague and we started to wonder, when should one apply feature normalization / scaling to the data? Let's say we have a set of features with some of the features having a ...
36k views

### Is cosine similarity identical to l2-normalized euclidean distance?

Identical meaning, that it will produce identical results for a similarity ranking between a vector u and a set of vectors V. I have a vector space model which has distance measure (euclidean ...
58k views

### When to normalize data in regression? [duplicate]

Under what circumstances should the data be normalized/standardized when building a regression model. When i asked this question to a stats major, he gave me an ambiguous answer "depends on the data". ...
38k views

### Is it essential to do normalization for SVM and Random Forest?

My features' every dimension has different range of value. I want to know if it is essential to normalize this dataset.
14k views

### A robust (non-parametric) measure like Coefficient of Variation — IQR/median, or alternative?

For a given set of data, spread is often calculated either as the standard deviation or as the IQR (inter-quartile range). Whereas a standard deviation is ...
13k views

### How does quantile normalization work?

In gene expression studies using microarrays, intensity data has to be normalized so that intensities can be compared between individuals, between genes. Conceptually, and algorithmically, how does "...
17k views

### Standardization vs. Normalization for Lasso/Ridge Regression

I am aware it is common practice to standardize the features for ridge and lasso regression, however, would it ever be more practical to normalize the features on a (0,1) scale as an alternative to z-...
7k views

### In general, does normalization mean to normalize the samples or features?

I'm just getting into machine learning, and I have seen two conflicting practices for normalization. To be concrete, let's suppose that we have a $n \times d$ matrix containing our training data, ...
26k views

### Logistic regression and scaling of features

I was under the belief that scaling of features should not affect the result of logistic regression. However, in the example below, when I scale the second feature by uncommenting the commented line, ...
8k views

### Dynamic Time Warping and normalization

I'm using Dynamic Time Warping to match a "query" and a "template" curve and having reasonable success thus far, but I have some basic questions: I'm assessing a "match" by assessing whether the DTW ...
8k views

### Min-Max scaling on Z-score standardizd data?

For a specific task of score fusion I need to test my data on some different normalization techniques like typical Z-normalization or Sigmoid-normalization. This is my first step to do. For a second ...
8k views

### Should I ever standardise/normalise the target data/ dependent variables in regression models?

After standardising the explanatory variables the difference in magnitude between the explanatory variables and the target data is ~3 orders of magnitudes. I want to know if transformation of the ...
5k views

### Scaling/Normalization not need for tree based models

I could not find a good answer/reference that can explain why rf/decision trees/gbm are not susceptible to the scale of values of numerical variables. My sense is that since boosting methods ...
1k views

### Random matrices with constraints on row and column length

I need to generate random non-square matrices with $R$ rows and $C$ columns, elements randomly distributed with zero mean, and constrained such that the length ($L_2$ norm) of each row is $1$ and the ...
22k views

### What are the primary differences between z-scores and t-scores, and are they both considered standard scores?

We are currently converting student test scores in this manner : ( ScaledScore - ScaledScore Mean ) / StdDeviation ) * 15 + 100 I was referring to this ...
36k views

### What does it mean to use a normalizing factor to “sum to unity”?

Would you also be able to provide an example? I have very little mathematical/statistical knowledge and have never understood normalization.
9k views

### How to standardize data for hierarchical clustering?

When running hierarchical clustering analysis of a matrix of individuals x samples (e.g., employee performances across different days), there are several ...
17k views

### How to transform negative data to be homoscedastic

I have a bunch of data that's both positive and negative. Its calculated from the residuals of an ANOVA (i.e. specific leaf area calculated as the residuals of an ANOVA of leaf area with leaf blade ...
368 views

### Follow-up question: When should you center your data & when should you standardize?

I have a follow up question to MånsT's reply to the "When should you center your data & when should you standardize"-question. ( I cannot leave a comment as I am below the magic "50 ...