Last Updated on August 20, 2020

**Feature selection** is the process of reducing the number of input variables when developing a predictive model.

It is desirable to reduce the number of input variables to both reduce the computational cost of modeling and, in some cases, to improve the performance of the model.

Statistical-based feature selection methods involve evaluating the relationship between each input variable and the target variable using statistics and selecting those input variables that have the strongest relationship with the target variable. These methods can be fast and effective, although the choice of statistical measures depends on the data type of both the input and output variables.

As such, it can be challenging for a machine learning practitioner to select an appropriate statistical measure for a dataset when performing filter-based feature selection.

In this post, you will discover how to choose statistical measures for filter-based feature selection with numerical and categorical data.

After reading this post, you will know:

- There are two main types of feature selection techniques: supervised and unsupervised, and supervised methods may be divided into wrapper, filter and intrinsic.
- Filter-based feature selection methods use statistical measures to score the correlation or dependence between input variables that can be filtered to choose the most relevant features.
- Statistical measures for feature selection must be carefully chosen based on the data type of the input variable and the output or response variable.

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**Update Nov/2019**: Added some worked examples for classification and regression.**Update May/2020**: Expanded and added references. Added pictures.

## Overview

This tutorial is divided into 4 parts; they are:

- Feature Selection Methods
- Statistics for Filter Feature Selection Methods
- Numerical Input, Numerical Output
- Numerical Input, Categorical Output
- Categorical Input, Numerical Output
- Categorical Input, Categorical Output

- Tips and Tricks for Feature Selection
- Correlation Statistics
- Selection Method
- Transform Variables
- What Is the Best Method?

- Worked Examples
- Regression Feature Selection
- Classification Feature Selection

## 1. Feature Selection Methods

**Feature selection** methods are intended to reduce the number of input variables to those that are believed to be most useful to a model in order to predict the target variable.

Feature selection is primarily focused on removing non-informative or redundant predictors from the model.

— Page 488, Applied Predictive Modeling, 2013.

Some predictive modeling problems have a large number of variables that can slow the development and training of models and require a large amount of system memory. Additionally, the performance of some models can degrade when including input variables that are not relevant to the target variable.

Many models, especially those based on regression slopes and intercepts, will estimate parameters for every term in the model. Because of this, the presence of non-informative variables can add uncertainty to the predictions and reduce the overall effectiveness of the model.

— Page 488, Applied Predictive Modeling, 2013.

One way to think about feature selection methods are in terms of **supervised** and **unsupervised** methods.

An important distinction to be made in feature selection is that of supervised and unsupervised methods. When the outcome is ignored during the elimination of predictors, the technique is unsupervised.

— Page 488, Applied Predictive Modeling, 2013.

The difference has to do with whether features are selected based on the target variable or not. Unsupervised feature selection techniques ignores the target variable, such as methods that remove redundant variables using correlation. Supervised feature selection techniques use the target variable, such as methods that remove irrelevant variables..

Another way to consider the mechanism used to select features which may be divided into **wrapper** and **filter** methods. These methods are almost always supervised and are evaluated based on the performance of a resulting model on a hold out dataset.

Wrapper feature selection methods create many models with different subsets of input features and select those features that result in the best performing model according to a performance metric. These methods are unconcerned with the variable types, although they can be computationally expensive. RFE is a good example of a wrapper feature selection method.

Wrapper methods evaluate multiple models using procedures that add and/or remove predictors to find the optimal combination that maximizes model performance.

— Page 490, Applied Predictive Modeling, 2013.

Filter feature selection methods use statistical techniques to evaluate the relationship between each input variable and the target variable, and these scores are used as the basis to choose (filter) those input variables that will be used in the model.

Filter methods evaluate the relevance of the predictors outside of the predictive models and subsequently model only the predictors that pass some criterion.

— Page 490, Applied Predictive Modeling, 2013.

Finally, there are some machine learning algorithms that perform feature selection automatically as part of learning the model. We might refer to these techniques as **intrinsic** feature selection methods.

… some models contain built-in feature selection, meaning that the model will only include predictors that help maximize accuracy. In these cases, the model can pick and choose which representation of the data is best.

— Page 28, Applied Predictive Modeling, 2013.

This includes algorithms such as penalized regression models like Lasso and decision trees, including ensembles of decision trees like random forest.

Some models are naturally resistant to non-informative predictors. Tree- and rule-based models, MARS and the lasso, for example, intrinsically conduct feature selection.

— Page 487, Applied Predictive Modeling, 2013.

Feature selection is also related to dimensionally reduction techniques in that both methods seek fewer input variables to a predictive model. The difference is that feature selection select features to keep or remove from the dataset, whereas dimensionality reduction create a projection of the data resulting in entirely new input features. As such, dimensionality reduction is an alternate to feature selection rather than a type of feature selection.

We can summarize feature selection as follows.

**Feature Selection**: Select a subset of input features from the dataset.**Unsupervised**: Do not use the target variable (e.g. remove redundant variables).- Correlation

**Supervised**: Use the target variable (e.g. remove irrelevant variables).**Wrapper**: Search for well-performing subsets of features.- RFE

**Filter**: Select subsets of features based on their relationship with the target.- Statistical Methods
- Feature Importance Methods

**Intrinsic**: Algorithms that perform automatic feature selection during training.- Decision Trees

**Dimensionality Reduction**: Project input data into a lower-dimensional feature space.

The image below provides a summary of this hierarchy of feature selection techniques.

In the next section, we will review some of the statistical measures that may be used for filter-based feature selection with different input and output variable data types.

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## 2. Statistics for Filter-Based Feature Selection Methods

It is common to use correlation type statistical measures between input and output variables as the basis for filter feature selection.

As such, the choice of statistical measures is highly dependent upon the variable data types.

Common data types include numerical (such as height) and categorical (such as a label), although each may be further subdivided such as integer and floating point for numerical variables, and boolean, ordinal, or nominal for categorical variables.

Common input variable data types:

**Numerical Variables**- Integer Variables.
- Floating Point Variables.

**Categorical Variables**.- Boolean Variables (dichotomous).
- Ordinal Variables.
- Nominal Variables.

The more that is known about the data type of a variable, the easier it is to choose an appropriate statistical measure for a filter-based feature selection method.

In this section, we will consider two broad categories of variable types: numerical and categorical; also, the two main groups of variables to consider: input and output.

Input variables are those that are provided as input to a model. In feature selection, it is this group of variables that we wish to reduce in size. Output variables are those for which a model is intended to predict, often called the response variable.

The type of response variable typically indicates the type of predictive modeling problem being performed. For example, a numerical output variable indicates a regression predictive modeling problem, and a categorical output variable indicates a classification predictive modeling problem.

**Numerical Output**: Regression predictive modeling problem.**Categorical Output**: Classification predictive modeling problem.

The statistical measures used in filter-based feature selection are generally calculated one input variable at a time with the target variable. As such, they are referred to as univariate statistical measures. This may mean that any interaction between input variables is not considered in the filtering process.

Most of these techniques are univariate, meaning that they evaluate each predictor in isolation. In this case, the existence of correlated predictors makes it possible to select important, but redundant, predictors. The obvious consequences of this issue are that too many predictors are chosen and, as a result, collinearity problems arise.

— Page 499, Applied Predictive Modeling, 2013.

With this framework, let’s review some univariate statistical measures that can be used for filter-based feature selection.

### Numerical Input, Numerical Output

This is a regression predictive modeling problem with numerical input variables.

The most common techniques are to use a correlation coefficient, such as Pearson’s for a linear correlation, or rank-based methods for a nonlinear correlation.

- Pearson’s correlation coefficient (linear).
- Spearman’s rank coefficient (nonlinear)

### Numerical Input, Categorical Output

This is a classification predictive modeling problem with numerical input variables.

This might be the most common example of a classification problem,

Again, the most common techniques are correlation based, although in this case, they must take the categorical target into account.

- ANOVA correlation coefficient (linear).
- Kendall’s rank coefficient (nonlinear).

Kendall does assume that the categorical variable is ordinal.

### Categorical Input, Numerical Output

This is a regression predictive modeling problem with categorical input variables.

This is a strange example of a regression problem (e.g. you would not encounter it often).

Nevertheless, you can use the same “*Numerical Input, Categorical Output*” methods (described above), but in reverse.

### Categorical Input, Categorical Output

This is a classification predictive modeling problem with categorical input variables.

The most common correlation measure for categorical data is the chi-squared test. You can also use mutual information (information gain) from the field of information theory.

- Chi-Squared test (contingency tables).
- Mutual Information.

In fact, mutual information is a powerful method that may prove useful for both categorical and numerical data, e.g. it is agnostic to the data types.

## 3. Tips and Tricks for Feature Selection

This section provides some additional considerations when using filter-based feature selection.

### Correlation Statistics

The scikit-learn library provides an implementation of most of the useful statistical measures.

For example:

- Pearson’s Correlation Coefficient: f_regression()
- ANOVA: f_classif()
- Chi-Squared: chi2()
- Mutual Information: mutual_info_classif() and mutual_info_regression()

Also, the SciPy library provides an implementation of many more statistics, such as Kendall’s tau (kendalltau) and Spearman’s rank correlation (spearmanr).

### Selection Method

The scikit-learn library also provides many different filtering methods once statistics have been calculated for each input variable with the target.

Two of the more popular methods include:

- Select the top k variables: SelectKBest
- Select the top percentile variables: SelectPercentile

I often use *SelectKBest* myself.

### Transform Variables

Consider transforming the variables in order to access different statistical methods.

For example, you can transform a categorical variable to ordinal, even if it is not, and see if any interesting results come out.

You can also make a numerical variable discrete (e.g. bins); try categorical-based measures.

Some statistical measures assume properties of the variables, such as Pearson’s that assumes a Gaussian probability distribution to the observations and a linear relationship. You can transform the data to meet the expectations of the test and try the test regardless of the expectations and compare results.

### What Is the Best Method?

There is no best feature selection method.

Just like there is no best set of input variables or best machine learning algorithm. At least not universally.

Instead, you must discover what works best for your specific problem using careful systematic experimentation.

Try a range of different models fit on different subsets of features chosen via different statistical measures and discover what works best for your specific problem.

## 4. Worked Examples of Feature Selection

It can be helpful to have some worked examples that you can copy-and-paste and adapt for your own project.

This section provides worked examples of feature selection cases that you can use as a starting point.

### Regression Feature Selection:

(*Numerical Input, Numerical Output*)

This section demonstrates feature selection for a regression problem that as numerical inputs and numerical outputs.

A test regression problem is prepared using the make_regression() function.

Feature selection is performed using Pearson’s Correlation Coefficient via the f_regression() function.

1 2 3 4 5 6 7 8 9 10 11 |
# pearson's correlation feature selection for numeric input and numeric output from sklearn.datasets import make_regression from sklearn.feature_selection import SelectKBest from sklearn.feature_selection import f_regression # generate dataset X, y = make_regression(n_samples=100, n_features=100, n_informative=10) # define feature selection fs = SelectKBest(score_func=f_regression, k=10) # apply feature selection X_selected = fs.fit_transform(X, y) print(X_selected.shape) |

Running the example first creates the regression dataset, then defines the feature selection and applies the feature selection procedure to the dataset, returning a subset of the selected input features.

1 |
(100, 10) |

### Classification Feature Selection:

(*Numerical Input, Categorical Output*)

This section demonstrates feature selection for a classification problem that as numerical inputs and categorical outputs.

A test regression problem is prepared using the make_classification() function.

Feature selection is performed using ANOVA F measure via the f_classif() function.

1 2 3 4 5 6 7 8 9 10 11 |
# ANOVA feature selection for numeric input and categorical output from sklearn.datasets import make_classification from sklearn.feature_selection import SelectKBest from sklearn.feature_selection import f_classif # generate dataset X, y = make_classification(n_samples=100, n_features=20, n_informative=2) # define feature selection fs = SelectKBest(score_func=f_classif, k=2) # apply feature selection X_selected = fs.fit_transform(X, y) print(X_selected.shape) |

Running the example first creates the classification dataset, then defines the feature selection and applies the feature selection procedure to the dataset, returning a subset of the selected input features.

1 |
(100, 2) |

### Classification Feature Selection:

(*Categorical Input, Categorical Output*)

For examples of feature selection with categorical inputs and categorical outputs, see the tutorial:

## Further Reading

This section provides more resources on the topic if you are looking to go deeper.

### Tutorials

- How to Calculate Nonparametric Rank Correlation in Python
- How to Calculate Correlation Between Variables in Python
- Feature Selection For Machine Learning in Python
- An Introduction to Feature Selection

### Books

- Applied Predictive Modeling, 2013.
- Feature Engineering and Selection, 2019.
- Feature Engineering for Machine Learning, 2018.

### Articles

- Feature selection, scikit-learn API.
- What are the feature selection options for categorical data? Quora.

## Summary

In this post, you discovered how to choose statistical measures for filter-based feature selection with numerical and categorical data.

Specifically, you learned:

- There are two main types of feature selection techniques: supervised and unsupervised, and supervised methods may be divided into wrapper, filter and intrinsic.
- Filter-based feature selection methods use statistical measures to score the correlation or dependence between input variables that can be filtered to choose the most relevant features.
- Statistical measures for feature selection must be carefully chosen based on the data type of the input variable and the output or response variable.

**Do you have any questions?**

Ask your questions in the comments below and I will do my best to answer.

Hi Jason,

Thank you for the nice blog. Do you have a summary of unsupervised feature selection methods?

All of the statistical methods listed in the post are unsupervised.

Hi

Actually I’ve got the same question like Mehmet above. Please correct me if I’m wrong, the talk in this article is about input variables and target variables. With that I understand features and labels of a given supervised learning problem.

But in your answer it says unsupervised! I’m a bit confused.

Thanks.

They are statistical tests applied to two variables, there is no supervised learning model involved.

I think by unsupervised you mean no target variable. In that case you cannot do feature selection. But you can do other things, like dimensionality reduction, e.g. SVM and PCA.

But the two code samples you’re providing for feature selection _are_ from the area of supervised learning:

– Regression Feature Selection (Numerical Input, Numerical Output)

– Classification Feature Selection (Numerical Input, Categorical Output)

Do you maybe mean that supervised learning is _one_ possible area one can make use of for feature selection BUTthis is not necessarily the only field of using it?

Perhaps I am saying that this type of feature selection only makes sense on supervised learning, but it is not a supervised learning type algorithm – the procedure is applied in an unsupervised manner.

OK I guess know I understand what you mean.

Feature selection methods are used by the supervised learning problems to reduce the numer of input features (or as you call them “the input variables”), however ALL of these methods themself work in an unsupervised manner to do so.

That is my understanding.

What do you mean by unsupervised – like feature selection for clustering?

Hello Sir,

If we have no target variable, can we apply feature selection before the clustering of a numerical dataset?

No. Feature selection requires a target – at least all of the supervised methods do.

You can use unsupervised methods to remove redundant inputs. I don’t have an example of this yet.

Hi jason, thanks for the post!

I have used pearson selection as a filter method between target and variables. My target is binary however, and my variables can either be categorical or continuous. Is the Pearson correlation still a valid option for feature selection? If not, could you tell me what other filter methods there are whenever the target is binary and the variable either categorical or continuous?

No, Pearson’s is not appropriate. Consider anova f.

Thanks again for short and excellent post. How about Lasso, RF, XGBoost and PCA? These can also be used to identify best features.

Yes, but in this post we are focused on univariate statistical methods, so-called filter feature selection methods.

Thanks for your time for the clarification.

Thanks for sharing. Actually I was looking for such a great blog since a long time.

Thanks!

I hope it helps.

Pleasegivetworeasonswhyitmaybedesirabletoperformfeatureselectioninconnection with document classification.

What would feature selection for document classification look like exactly? Do you mean reducing the size of the vocab?

quite an informative article with great content

Thanks!

Hi Jason! Thanks for this informative post! I’m trying to apply this knowledge to the Housing Price prediction problem where the regressors include both numeric features and categorical features. In your graph, (Categorical Inputs, Numerical Output) also points to ANOVA. To use ANOVA correctly in this Housing Price case, do I have to encode my Categorical Inputs before SelectKBest?

Yes, categorical variables will need to be label/integer encoded at the least.

Hi Jason! I have dataset with both numerical and categorical features. The label is categorical in nature. Which is the best possible approach to find feature importance? Should I OneHotEncode my categorical features before applying ANOVA/Kendall’s?

Use separate statistical feature selection methods for different variable types.

Or try RFE.

Hey Jason,

Thanks a lot for this detailed article.

I have a question, after one hot encoding my categorical feature, the created columns just have 0 and 1. My output variable is numerical and all other predictors are also numerical. Can i use pearson/spearman correlation for feature selection here (and for removing multicollinearity as well) ??

Now since one hot encoded column has some ordinality (0 – Absence, 1- Presence) i guess correlation matrix will be useful.

I tried this and the output is making sense business wise. Just wanted to know your thoughts on this, is this fundamentally correct ??

No, spearman/pearson correlation on binary attributes does not make sense.

You perform feature selection on the categorical variables directly.

Thanks a lot for your nice post. I’m way new to ML so I have a really rudimentary question. Suppose I have a set of tweets which labeled as negative and positive. I want to perform some sentiment analysis. I extracted 3 basic features: 1. Emotion icons 2.Exclamation marks 3. Intensity words(very, really). My question is: How should I use these features with SVM or other ML algorithms? In other words, how should I apply the extracted features in SVM algorithm?

should I train my dataset each time with one feature? I read several articles and they are just saying: we should extract features and deploy them in our algorithms but HOW?

Help me, please

The text will need a numeric representation, such as a bag of words.

This is called natural language processing, you can get started here:

https://machinelearningmastery.com/start-here/#nlp

Thank you sir

You’re welcome.

Hey jason,

Can you please say why should we use univariate selection method for feature selection?

Cause we should use correlation matrix which gives correlation between each dependent feature and independent feature,as well as correlation between two independent features.

So, using correlation matrix we can remove collinear or redundant features also.

So can you please say when should we use univariate selection over correlation matrix?

Yes, filter methods like statistical test are fast and easy to test.

You can move on to wrapper methods like RFE later.

hi Jason

thnx for your helpful post

i want to know which method to use?

input vairables are

1. age

2.sex(but it has numbers as 1 for males and 2 for females)

3. working hours-

4. school attainment (also numbers)

the output is numeric

could you plz help

Perhaps note whether each variable is numeric or categorical then follow the above guide.

Hi, Jason!

Do you mean you need to perform feature selection for each variable according to input and output parameters as illustrated above? Is there any shortcuts where I just feed the data and produce feature scores without worrying on the type of input and output data?

Yes, different feature selection for diffrent variable types.

A short cut would be to use a different approach, like RFE, or an algorithm that does feature selection for you like xgboost/random forest.

Hello Jason,

Thank you for your nice blogs, I read several and find them truly helpful.

I have a quick question related to feature selection:

if I want to select some features via VarianceThreshold, does this method only apply to numerical inputs?

Can I encode categorical inputs and apply VarianceThreshold to them as well?

Many thanks!

Thanks!

Yes, numerical only as far as I would expect.

Hi Jason!

Is there any way to display the names of the features that were selected by SelectKBest?

In your example it just returns a numpy array with no column names.

Yes, you can loop through the list of column names and the features and print whether they were selected or not using information from the attributes on the SelectKBest class.

Hi Jason,

Many thanks for this detailed blog. A quick question on the intuition of the f_classif method.

Why do we select feature with high F value? Say if y takes two classes [0,1], and feature1 was selected because it has high F-statistic in a univariate ANOVA with y, does it mean that the mean of feature11 when y = 0, is statistically different from the mean of feature 1 when y = 1? and therefore feature 1 likely to be useful in predicting y?

Yes, large values. But don’t do it manually use a built-in selection method.

See the worked examples at the end of the tutorial as a template.

hi jason,

so im working with more than 100 thousand samples dota2 dataset which consist of the winner and the “hero” composition from each match. I was trying to build winner of the match prediction model similiar to this [http://jmcauley.ucsd.edu/cse255/projects/fa15/018.pdf]. so the vector input is

Xi= 1 if hero i on radiant side, 0 otherwise.

X(119+i) = 1 if hero i on dire side, 0 otherwise

The vector X consist 238 entri since there are 119 kind of heroes. Each vector represent the composition of the heroes that is played within each match. Each match always consist of exactly 10 heroes (5 radiant side 5 dire side).

From this set up i would have a binary matrix of 100k times (222 + 1) dimension with row represent how many samples and columns represent features, +1 columns for the label vector (0 and 1, 1 meaning radiant side win)

so if i dot product between two column vector of my matrix, i can get how many times hero i played with hero j on all the samples.

so if i hadamard product between two column vector of my matrix and the result of that we dot product to the vector column label i can get how many times hero i played with hero j and win.

with this i can calculate the total weight of each entri per samples that corresponding to the vector label. i could get very high coorelation between this “new features” to the label vector. but i cant find any references to this problem in statistics textbook on binary data.

Not sure I can offer good advice off the cuff, sorry.

Hi Jason, Thanks for this article. I totally understand this different methodologies. I have one question.

If lets say. I have 3 variables. X,Y,Z

X= categorical

Y= Numerical

Z= Categorical, Dependent(Value I want to predict)

Now, I did not get any relationship between Y and Z and I got the Relationship between Y and Z. Is it possible that if we include X, Y both together to predict Z, Y might get the relationship with Z.

If is there any statistical method or research around please do mention them. Thanks

I would recommend simply testing reach combination of input variables and use the combination that results in the best performance for predicting the target – it’s a lot simpler than multivariate statistics.

One recommendation is to use the DSD (Definitive Screening Design), a type of statistical Design of Experiments (DoE), which can “estimate of main effects that are unbiased by any second-order effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order effects” [1]

The DSD can also be augmented with two-level categorical factors “where the experiment can estimate quadratic effects, the estimation of which decreases as more categorical factors are added” [2]

We use this method to assist in feature selection in CNNs intended for industrial process applications.

[1] B. Jones and C. J. Nachtsheim, “A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects,” Journal of Quality Technology, vol. 43, no. 1, pp. 1-15, 2011

[2] B. Jones and C. J. Nachtsheim, “Definitive Screening Designs with Added Two-Level Categorical Factors,” Journal of Quality Technology, vol. 45, no. 2, pp. 121-129, 2013

Great suggestion, thanks for sharing George!

When having a dataset that contains only categorical variables including nominal, ordinal & dichotomous variables, is it incorrect if I use either Cramér’s V or Theil’s U (Uncertainty Coefficient) to get the correlation between features?

Thanks

San

I don’t know off-hand, sorry.

Very good article.

I have detected outliers and wondering how can I estimate contribution of each feature on a single outlier?

We are talking about only one observation and it’s label, not whole dataset.

I couldn’t find any reference for that.

This sounds like an open question.

Perhaps explore distance measures from a centroid or to inliers?

Or univariate distribution measures for each feature?

Thank you for quick response.

That’s one class multivalve application.

For a single observation, I need to find out the first n features that have the most impact on being in that class.

From most articles, I can find the most important features over all observations, but here I need to know that over a selected observations.

Simply fit the model on your subset of instances.

1) In case of feature selection algorithm (XGBosst, GA, and PCA) what kind of method we can consider wrapper or filter?

2) what is the difference between feature selection and dimension reduction?

XGBoost would be used as a filter, GA would be a wrapper, PCA is not a feature selection method.

Feature selection chooses features in the data. Dimensionality reduction like PCA transforms or projects the features into lower dimensional space.

Technically deleting features could be considered dimensionality reduction.

Thank you so much for your time to respond. Would you like to share some of the material on the same (so I can use it for my thesis as a reference)?

In addition, I am excited to know the advantages and disadvantaged in this respect; I mean when I use XGBoost as a filter feature selection and GA as a wrapper feature selection and PCA as a dimensional reduction, Then what may be the possible advantages and disadvantages?

best regards!

If you need theory of feature selection, I recommend performing a literature review.

I cannot help you with advantages/disadvantages – it’s mostly a waste of time. I recommend using what “does” work best on a specific dataset, not what “might” work best.

I didn’t get your point.

I have 1 record which is outlier. and wanted to know which features had the most contribution on that record to get outlier.

Thank you and sorry if question is confusing

I suggested that it is an open question – as in, there are no obvious answers.

I suggested to take it on as a research project and discover what works best.

Does that help, which part is confusing – perhaps I can elaborate?

Thank you

Should research on that

Thanks for the suggestion.

Do the above algorithms keep track of ‘which’ features have been selected, or only selects the ‘best’ feature data? Aafter having identified the ‘best k features’, how do we extract those features, ideally only those, from new inputs?

Yes, you can discover which features are selected according to their column index.

Hi Jason,

thanks again you for the nice overview. Here is relatively new package introducing the Phi_K correlation coefficient that claims that it can be used across categorical, ordinal and numerical features. It is also said to capture non-linear dependency.

https://phik.readthedocs.io/en/latest/#

best wishes

Oliver

Thanks for sharing.

Hi Jason, Thanks for the amazing article.

A question on using ANOVA. Given Categorical variables and a Numerical Target, would you not have to assume homogeneity of variance between the samples of each categorical value. From what I learned, ANOVA require the assumption of equal variance.

Perhaps.

Often the methods fail gracefully rather than abruptly, which means you can use them reliably when when assumptions are violated.

Hello Jason,

Thank you for your explanation and for sharing great articles with us!

You have clearly explained how to perform feature selection in different variations in the “How to Choose Feature Selection Methods For Machine Learning” table.

+ Numerical Input, Numerical Output:

Pearson’s correlation coefficient (linear). Spearman’s rank coefficient (nonlinear)

+ Numerical Input, Categorical Output:

ANOVA correlation coefficient (linear). Kendall’s rank coefficient (nonlinear).

+ Categorical Input, Numerical Output:

ANOVA correlation coefficient (linear). Kendall’s rank coefficient (nonlinear).

+ Categorical Input, Categorical Output:

Chi-Squared test (contingency tables). Mutual Information.

I would like to ask some questions about the dataset that contains a combination of numerical and categorical inputs.

1- Which methods should we apply when we have a dataset that has a combination of numerical and categorical inputs? (e.g: Total Input: 50; Numerical:25 and Categorical:25. Task: Classification problem with the categorical values)

2- Should I apply one of the label encoding methods (encoding depending on the labels in the feature let’s say I applied one-hot, target encoding). Get the numerical values from the categorical input. Then, my problem becomes into the Numerical Input, Categorical Output. In this time, should I apply to the ANOVA correlation coefficient (linear) and Kendall’s rank coefficient (nonlinear) techniques?

3- OR, What would be the better approaches to apply feature selection techniques to the classification (Categorical Output) problem that includes a combination of numerical and categorical input?

Thank you.

You’re welcome.

You would use a separate method for each data type or a wrapper method that supports all inputs at once.

I have a mixture of numeric, ordinal, and nominal attributes.

For the first two, Pearson is used to determine the correlation with the target.

For the nominal type, I still cannot find a good reference on how we should handle it for correlation. Encode it to numeric doesn’t seem correct as the numeric values would probably suggest some ordinal relationship but it should not for nominal attributes.

Any advice?

I also tested the model performance based on the transformed attribute that gives higher correlation with the target, but however, the model performance did not improve as expected. any suggestions what can i explore further?

Nominal is “Categorical” now follow the above advice based on the type of the output variable.

Hi Jason, when the output, i.e. the label is 0 or 1 meant to represent Bad and Good, is this considered as numeric output or categorical output?

It is a number that we can map to a category in our application.

So this response variable should be considered as categorical target or numeric target.

Categorical.

Jason you have not shown the example of categorical input and numerical output.

You can reverse the case for: Numerical Input, Categorical Output

Sir,

In my dataset, 29 attributes are yes/no values(binary) and the rest is numeric(float)type attributes. Class has 7 values(multiclass). I want to try this dataset for classification. Which techniques of feature selections are suitable? Please give me a hand!

With respect!

Thaung

Some ideas:

Perhaps establish a baseline performance with all features?

Perhaps try separate feature selection methods for each input type?

Perhaps try a wrapper method like RFE that is agnostic to input type?

Hi Jason and thanks a lot for this wonderful and so helpful work.

1- wrapper methods : does the model get rid of irrelevant features or it just assigns small weights.?

2-filter methods: when using univariate techniques, how to detect or prevent redundant among the selected variables ?

3- What about t-statistic ?

Thanks in advance.

Wrapper tests different subsets of features and chooses a subset that gives best skill.

Deleting redundant features is performed without the target. e.g. highly correlated features can be dropped.

Yes, I have read this. I don’t have an example.

Thanks a lot.

You’re welcome.

Hello Sir,

I am new to this subject, I want to apply UNSUPERVISED MTL NN model for prediction on a dataset, for that I have to first apply clustering to get the target value. I want to apply some feature selection methods for the better result of clustering as well as MTL NN methods, which are the feature selection methods I can apply on my numerical dataset.

The above tutorial explains exactly, perhaps re-read it?

So we train the final ML model on the features selected in the feature selection process??

We fit_transform() xtrain, so do we need to transform() xtest beforr evaluation???

Yes, you can call fit_transform to select the features then fit a model.

Ideally, you would use feature selection within a modeling Pipeline.

So what I can ask after this knowledgeable post.

I have dataset in which

I am having more than 80 features in which one feature is categorical( IP address)(will convert it to numeric using get_dummies))) and all other are numerical. The response variable is 1(Good) and -1(Bad)

What i am going to do is remove constant variable using variance threshold in sklearn. then remove correleated features using corr() function.

After doing all this want to apply kbest with Pearson Correlation Coefficient and fisher to get a set of ten good performing features.

So am I doing it in right way??

And Can I use pearson in case of my dataset, as my dataset having both categorical ( which will be converted to numeric using get_dummies) and numeric features. And my response variable is 1 and -1

If the target is a label, then the problem is classification and Pearson’s correlation is inappropriate.

Hi Jason,

Thanks a lot for the article.

I have both numerical and categorical features. Should I normalize/scale numerical features before doing filter methods or wrapper methods?

Perhaps try it and see if it makes a difference with your choice of data and model.

Hi Jason, can you kindly provide the reference (paper/book) of the Figure flow chart 3: How to Choose Feature Selection Methods For Machine Learning, which I can use for my thesis paper citation? That would be great.

You can cite this web page directly. This will help:

https://machinelearningmastery.com/faq/single-faq/how-do-i-reference-or-cite-a-book-or-blog-post

Good article.

My data has thousand features. Out of which 10 percent features are categorical and the rest features are continuous. The output is a categorical.

Will RFE take both categorical and continuous input

For feature selection. If yes can I add a cutoff value for selecting features ?

Yes, it supports both feature types:

https://machinelearningmastery.com/rfe-feature-selection-in-python/

Yes, you can specify the number of features to select.

Thank’s for the link and response

You’re welcome.

Hi,

Great article.

I have features based on time.

What is the best methods to run feature selection over time series data?

Thanks!

ACF and PACF for lag inputs:

https://machinelearningmastery.com/gentle-introduction-autocorrelation-partial-autocorrelation/

Is it appropriate or useful to use a Chi-squared test with (a) numeric input and numeric output; (b) categorical input and numeric output? I also understood from the article that you gave the most common and most suited tests for these cases but not an absolute list of tests for each case. Am I correct?

It can be done, but my understanding is that it is intended for categorical inputs and a categorical output variable:

https://machinelearningmastery.com/chi-squared-test-for-machine-learning/

Hi, Great article! I have a question regarding how RFE rank their feature importances beforehand, as far I understood its based on how high the absolute of coef is (for linear regression), correct me me if i’m wrong because sometimes when I manually rank feature’s coef after fitting linear regression, it doesn’t match with RFE.ranking_

Thanks!

Good question, you can learn more about RFE here:

https://machinelearningmastery.com/rfe-feature-selection-in-python/

Thanks for the informative article Jason.

I understand that this post is concentrating on supervised methods – ie we are considering the dtypes for each distinct pairing of input variable and the target output variable that we wish to predict and then select the appropriate statistical method(s) to evaluate the relationship based on the input/output variable dtype combinations, as listed in your article.

I wish to better understand what you call unsupervised ie removing redundant variables (eg to prevent multicollinearity issues).

If I am not thinking about the problem in terms of input variable and output variable, but rather I just want to know how any 2 variables in my dataset are related then I know that first I need to check if the scatterplot for the 2 variables shows a linear or monotonic relation.

I think the logic is then, if the 2 attributes show a linear relationship then use Pearson correlation to evaluate the relationship between the 2 attributes. If the 2 attributes show a monotonic relationship (but not linear) then use a rank correlation method eg Spearman, Kendall.

My question is, how does the dtype of each attribute in the attribute pair factor in in this non input/output variable context? Is the “How to Choose Feature Selection Methods For Machine Learning” decision tree only applicable in an input/output variable context, or do the combinations of dtypes also factor in to the situation that I describe?

For example, I want to know if attribute 1 & 2 in my dataset are correlated with one and other. Neither attribute is an output variable, ie I am not trying to make a predicition. If attribute 1 is a categorical attribute and attribute 2 is a numerical attribute then I should use one of ANOVA or Kendal as per your decision tree? Or is this decision tree not applicable for my situation?

A lot of the online examples I see just seem to use Pearson correlation to represent the bivariate relationship, but I know from reading your articles that this is often inappropriate. I’m really struggling to understand the rules for each distinct situation, including which assumptions can be ignored in real world contexts and which can’t, so that I know which type of correlation is appropriate to use in which situation.

If you could provide any clarity or pointers to a topic for me to research further myself then that would be hugely helpful, thank you

Removing low variance or highly correlated inputs is a different step, prior to feature selection described above.

The same types of correlation measure can be used, although I would personally stick to pearson/spearmans for numerical and chi squared for categorical. E.g. type with type, not across type. Keep it very simple.

Hi, Why did you say Kendhall and not Kruskal-Wallis for non-parametric instead of ANOVA?

By the way, your articles are my bible! Really thanks in advance

Thanks!

Kendall’s is commonly used for non-parametric estimation of correlation (rank correlation).

Kruskal-Wallis is commonly used for non-parametric comparison of sample means

Hi!! as we know to make a more robust model we try to check it by doing cross-validation, So while doing cross-validation in each fold suppose I get different results, how should I proceed?

By different results I mean we get different useful feature each time in the fold.

Yes, the cross-validation procedure evaluates your modeling pipeline.

It is not about what specific features are chosen for each run, it is about how does the pipeline perform on average.

Once you have an estimate of performance, you can proceed to use it on your data and select those features that will be part of your final model.

Does that help?

Hi, thanks for the article!

For input numerical, output categorical:

Interestingly the references are not straight forward, and they almost don’t intersect (apart from ROC).

1) Feature Engineering and Selection, 2019: http://www.feat.engineering/greedy-simple-filters.html#

->It doesn’t comment about Kendall, only about Anova F-Test (slightly)

->t-test and ROC are mentioned as options, but not in this article

2) Applied Predictive Modeling, 2013. Chapter 18

->Anova is mentioned once, pg. 467 (slightly) -> but not in the categorical chapter (18.2)

->Chi2 in feature selection, not found

-> ROC mentioned, but not in this article

Would it be possible to explain why Kendall, for example or even ANOVA are not given as options?

Many thanks!

Sure, there’s lots of approaches that can be used.

You can use any correlation technique you like, I have listed the ones that are easy to access in Python for common use cases.

Thank you, and I really appreciate you mentioning good academic references. It definitely makes your articles outstand if compared to the vastly majority of other articles, which are basically applying methods in already developed Python packages and referencing it to the package documentation itself or non-academic websites.

Thanks!

Hi Jason,

Thank you for your precious article. Can you please explain to me if it’s reasonable to use feature selection approaches like “Pearson’s correlation coefficient” or “Spearman’s rank coefficient” to select the best subset of data for a Deep Neural Network, Random Forest or adaptive neuro-fuzzy inference system (ANFIS)?

Thanks,

Masoud

It depends on the specific data and model.

I recommend testing a suite of techniques and discover what works best for your specific project.

Thank you for your comment.

You’re welcome.

Thank you for the post. I would like to know that when you do the scoring, you get the number of features. But how do you know which features they are? Sometimes machine makes mistake and we have to use logic to see if it makes sense or not.

You’re welcome.

Good question, this tutorial shows you how to list the selected features:

https://machinelearningmastery.com/feature-selection-with-numerical-input-data/

Great article. Just one comment, spearman correlation is not really nonlinear right? it describes the monotonicity of the relationship. If there is non-linear relationship of order greater than 1 then Spearman correlation might even read as 0.

It is nonparametric.

Thanks Jason for the article..

I just realized spearman correlation test is for the numeric variables and doesn’t support categorical variables.

Is there any NON-PARAMETRIC test for the categorical variables?

I don’t think “nonlinear” makes sense for discrete probability distributions.

Thanks Jason for the clarification.

Yes, the data is categorical and its discrete probability distribution.

Does it mean that there is an underlying hypothesis/assumption that non-parametric approaches means assuming non-linear relationship?

Sorry, to ask questions. But I really like your articles and the way you give an overview and hence developed a lot on interest in your articles.

No, it’s just that the concept of “linear” or “nonlinear” is not valid for discrete distributions.

Great Article Jason!!

Just a few questions, please-

1)Is it better to do SelectKBest & mutual_info_classif, before dummification of categorical variables or post dummification?

2) If the relationship is non-linear would Chi-square and the other measure you described in the article, gives zero, because it failed to identify the linear relationship? Or are there any measures which would account to even the non-linear relationship between the input and output?

Perhaps experiment before and after and see what works best for your dataset (e.g. results in the best performing models).

No, not zero, but perhaps a misleading score.

Refer to an interesting article on Feature selection here.

https://www.analyticsvidhya.com/blog/2020/10/a-comprehensive-guide-to-feature-selection-using-wrapper-methods-in-python/

Thanks for sharing. That site is COVERED in ads. Yuck!

Loved the article!!!

But I have a doubt!

suppose we select 10 best features using univariate analysis(pearson correlation and SelectKBest).

But What will we do, if the selected features are strongly correlated.?

for example, if there are two features with strong positive correlation, then should we remove or not remove one of them? How will we decide which to remove and which to keep?

Thanks!

Some models are not bothered by correlated features.

Also, compare results to other feature selection methods, like RFE.

Hi Jason Brownlee thanks for the nice article. i am v new in ML. i want to work in unsupervised ML or DL.

I have data of human navigation and want to work on step detection. i want to extract features as many as possible from the data. Could you guide me that how i can do it with your algorithm. Looking for the kind response. Thanks

Perhaps start here:

https://machinelearningmastery.com/start-here/#dataprep

Hi

It is not clear for me how to proceed in case of a mix of categorical and numerical fetaures.

One approach is to select numerical and categorical features separately and combine the results.

Another approach is to use a wrapper methods like RFE to select all features at once.

https://machinelearningmastery.com/rfe-feature-selection-in-python/

Hi Jason, Thanks again for these precious tutorials.

When using the f_regression(), I check the score for each feature (given by the attribute scores_), does it represent the strength of the pearson’s correlation ?

Thanks in advance.

Juste a complement to my last question:

Because I read somewhere that the pearson’s coefficient that’s usually between -1 and 1 is converted to F-score .

Not quite (if I recall correctly), but you can interpret as a relative importance score so variables can be compared to each other.

Thanks Jason.

You’re welcome.

Thanks Jason, I refer to this article often. For an ensemble of models (not just a random forest, say a random forest + logistic reg + Naive bayes), would you try separate supervised feature selection for each model, with the result being different inputs for each model? Thanks!

Thanks.

Yes, I tried that, you can see an example here:

https://machinelearningmastery.com/feature-selection-subspace-ensemble-in-python/

Hello Jason,

Thank you for this great article. I would like to ask you about a problem I have been dealing with recently. I am working with a data that has become high dimentional data (116 input) as a result of one hot encoding. In this data, all input variables are categorical except one variable . The output variable is also categorical. What feature selection technique would you recommend for this kind of problem?

Thanks!

Perhaps try RFE on the integer encoded inputs as a first step:

https://machinelearningmastery.com/rfe-feature-selection-in-python/

Hi Jason,

thanks for this post.

I am running through a binary classification problem in which I used a Logistic Regression with L1 penalty for feature selection stage.

Now after this I have plotted the correlation matrix (pearson as my ifeature are all numerical) between the features and I still see quite a bit of multicollinearity off-diagonal.

So my question is: can this be acceptable or the multicollinearity (high correlation between features) is such a strong assumption that maybe I should use another approach for feature selection?

Many thanks

Luigi

Not sure Pearson’s correlation coefficient is appropriate when the target is binary.

Removing colinear inputs can improve the performance of linear models like logistic regression, it’s a good idea.

Hello Jason,

What should i do if i have both numerical and categorical data as input?

Can i test the numerical and categorical variables separately and merge the best variables from both tests?

Great question!

You can select from each type separately and aggregate the results. It’s not perfect, but a starting point.

Alternately, you can use an approach like RFE:

https://machinelearningmastery.com/rfe-feature-selection-in-python/

Thank you.

Doing a filter method test on mixed type data should be avoided then. Right?

I would not go that far. I would say it is a challenge and must be handled carefully.

Hi Jason,

my dataset has about 340 numerical features and there are lots of correlations between them. Of course I can calculate the correlation matrix using Pearson’s or Spearman’s correlation.

But then, what are strategies for feature selection based on that?

Thanks

Frank

Remove the features with the largest sum correlation across all pairs.

Or just trial different feature selection methods / algorithms that perform auto feature selection and discover what works best empirically for your dataset. I strongly recommend the approach for fast and useful outcomes.

Thanks, I’ll try using the sum of correlations (sum of absolute values, I guess).

If there was a group of features which were all highly correlated with each other, those features would get a high sum of correlations and would all get removed. But I should keep at least one of them.

I’m somehow thinking about clustering the features based on their correlation for a while now. Has this been done before? Whould it be possible to do that with sklearn?

Yes. There is probably a standard algorithm for the approach, I recommend checking the literature. I don’t have a tutorial on the topic.

No this approach is not available in sklearn. Instead, sklearn provide statistical correlation as a feature importance metric that can then be used for filter-based feature selection. A very successful approach.

Is there any feature selection method that can deal with missing data? I tried a few things with sklearn, but it was always complaining about NaN. If I drop all the rows that have no missing values then there is little left to work with. I’m hoping that I need to this step only after the feature selection.

There may be. Generally, it is a good idea to address the missing data first.