What is Factor Analysis in Machine Learning – Its Objective, Types and Applications?

What is Factor Analysis?

According to a study published in MDPI, over 560,000 journal articles published between 2013 and 2023 used Exploratory Factor Analysis (EFA). This huge number itself stands as a testament to the fact that factor analysis is one of the most widely used techniques for making sense out of complex data.

But what exactly is it? At its core, factor analysis is about simplifying complexity. Instead of struggling with dozens of individual variables, this method groups them into a few bigger themes, or “factors.” Think of it like sorting a messy wardrobe; rather than counting every single item, you arrange them into categories like shirts, trousers, or jackets. The result is a clearer picture that helps researchers, businesses, and data scientists focus on what really matters.

Source: MDPI

The factor analysis technique is useful for minimizing a massive volume of variables into fewer numbers of factors. This particular technique can determine the maximum common variance from all variables to put them in a common score. This score can be used for deeper analysis because it is an index of all the variables.

It is a component of the general linear model. It can also lead to several assumptions like linear relationships and no multicollinearity. Dive into this article to explore more details about factor analysis.

The Importance of Factor Analysis

Why does factor analysis matter? Because it helps you see the bigger picture without drowning in details. Let us understand the importance of factor analysis by reading further:

• Makes Data Easier to Handle: Instead of getting lost in dozens of variables, factor analysis groups them into a few key themes you can actually work with.
• Helps You Focus on What Matters: By highlighting the variables with the greatest impact, it guides smarter decisions, eliminating unnecessary noise.
• Saves Time and Effort: Whether in research, psychology, or marketing, it eliminates unnecessary complexity and accelerates analysis.
• Brings Out Hidden Insights: It often uncovers patterns you might not notice at first glance, like customer preferences or personality traits.

How Does Factor Analysis Work?

At its core, factor analysis follows a few logical steps:

1. Look for Correlations: Identify which variables move together.
2. Extract Factors: Use statistical methods (like PCA or maximum likelihood) to find patterns.
3. Rotate the Factors: Apply rotations such as varimax to make results easier to interpret.
4. Check Factor Loadings: Check which variables strongly relate to each factor.
5. Build Factor Scores: Assign scores to each observation, showing how it relates to the factors.

Key Objectives of Factor Analysis

The key objectives of factor analysis can be broken down into the following pointers:

• Determining the number of factors required to explain common themes within a particular variable set.
• Determining the extent to which every variable in the dataset is connected to a common factor or theme.
• Interpreting the common factors in a dataset.
• Understanding the degree to which each observed data point is representative of a theme or factor.

Types of Factor Analysis

There are two main types: Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA). 

1. Confirmatory Factor Analysis

This type of analysis can determine whether any relationship exists between factors or a set of variables. The analysis method confirms the connection between two components of variables in a particular dataset. The purpose of CFA is to evaluate whether certain data is suitable for the requirements of a particular hypothesis. 

At the beginning of the process, the researcher formulates a hypothesis related to the lines of a certain theory. The model gets rejected when the constraints imposed on a model aren’t suitable for the data. In such a case, it gets confirmed that no relationship is present between a factor and its underlying components. 

2. Exploratory Factor Analysis

The objective of exploratory analysis is to understand the underlying latent structure of a large variable set. Exploratory factor analysis can identify the relationship between measured variables inside an entity.

Confirmatory factor analysis focuses on recognizing a connection between an observed variable set and its underlying structure. But exploratory factor analysis focuses on revealing a connection between the different variables of a given dataset.

Comparison Between EFA and CFA –

Have a look at the comparison table between EFA and CFA to know the differences:

Feature	Exploratory Factor Analysis (EFA)	Confirmatory Factor Analysis (CFA)
Purpose	Discover hidden patterns	Test a predefined model
Flexibility	High	Lower (follows a fixed model)
Hypothesis Required	No	Yes
Ideal For	Early-stage research and surveys	Theory testing and validation studies

Factor Analysis vs. FAIR

It’s important not to confuse factor analysis with FAIR (Factor Analysis of Information Risk). They sound similar, but they serve entirely different purposes.

• Factor Analysis: A statistical method for reducing data complexity and uncovering patterns.
• FAIR: A framework for quantifying cybersecurity and operational risks in financial terms.

When to use what?

• Use factor analysis when working with large datasets and looking for hidden structures.
• Use FAIR when analyzing risks, especially in business or cybersecurity, to measure financial impact.

Assumptions Before Using Factor Analysis

Before jumping in, a few conditions must be met for factor analysis to work properly:

• Sample Size: At least 5–10 observations per variable.
• Correlation Strength: Variables should correlate moderately (ideally above 0.3).
• No Multicollinearity: Variables shouldn’t overlap too heavily.
• Linearity: Relationships among variables should be linear.
• Tests for Suitability: Run the KMO (Kaiser-Meyer-Olkin) test and Bartlett’s test to confirm data readiness.

How to Decide the Number of Factors

One of the trickiest parts of factor analysis is deciding how many factors to keep. If you keep too many, things get messy; too few, and you might miss important insights. So, these tips will help you decide the right number of factors:

• Scree Plot: Keep factors before the curve levels off (“elbow”).
• Eigenvalue Rule: Retain factors with eigenvalues above 1.
• Parallel Analysis: Compare with random data and retain stronger factors.
• Theoretical Fit: Ensure factors make sense in context.

Different Methods Used for Factor Analysis

The different methods used to extract the factor from a specific data set are as follows:

• Principal Component Analysis: It involves extracting the highest variance and placing them into the first factor. Once the variance determined by the first factor is removed, it starts extracting the highest variance for the second factor. The process continues till the last factor in a dataset.
• Image Factoring: This method of extracting the factor from a given dataset is dependent on the correlation matrix. In image factoring, the OLS Regression method can help predict the factor. 
• Common Factor Analysis: This method involves removing the common variance and putting it into factors. This method is particularly useful for SEM, and it does not contain the unique variance of different variables. 
• Maximum Likelihood Factor: This is another method of extracting the factor according to the correlation metric. But this method focuses on the maximum likelihood of determining the factor.

Also Read: What is Data Scraping?

Applications of Factor Analysis

1. Marketing

Marketing strategies can significantly benefit from the statistical method of analysis. Companies can use these techniques to determine a correlation between different factors or variables of a marketing campaign. 

Furthermore, it can build connections with consequent feedback and customer satisfaction. It ensures that you verify the efficacy of a marketing campaign and its impact on the target market. 

2. Nutrition

It can build a connection between the nutritional health of an individual and their diet. To establish that, this type analysis focuses on the dietary practices of a certain population. Moreover, the nutritional intake of an individual and their consequent health status has enabled nutritionists to determine the right quantity of nutrients one individual should consume within a specific time period. 

3. Data Mining

In data mining, this analysis is as crucial as artificial intelligence. Factor analysis can classify a complex and vast dataset into filtered-out variables that have some connection with each other. It helps simplify the process of data mining. 

Data scientists have always struggled with finding connections between different variables. But data mining has become much more advanced due to factor analysis. 

4. Machine Learning

Machine Learning and data mining techniques complement one another. Maybe this explains why there are tools and methodologies for machine learning to perform factor analysis.

Factor Analysis in machine learning is used to reduce the number of variables in a given dataset to obtain a more accurate and enhanced collection of observable factors. Multiple algorithms based on machine learning are used to work in this manner. 

They are properly trained with massive amounts of data in order to lead the way to new applications. Factor analysis is an unsupervised machine learning approach that is commonly used in machine learning for dimensionality reduction. As a result, machine learning and factor analysis could be used together to create data mining approaches and make data analysis much more efficient.

Also Read: What Is Predictive Analytics?

Factor Analysis Advantages

Now that you know the different types of factor analysis and their applications, learn about some of its benefits:

• Cost-Effective: Data research and data mining algorithms are extremely expensive. But the statistical model of factor analysis is available at a surprisingly affordable cost. Moreover, you don’t need too many resources to perform factor analysis. Additionally, it can be performed by experienced professionals as well as beginners.
• Measurable: One of the major benefits of factor analysis is its measurable nature. This statistical model can be worked upon various attributes. Whether it’s subjective or objective, it works well with everything.
• Flexible: Several machine learning algorithms are limited to a single approach. But factor analysis is an exception and offers a lot of flexibility. The flexible approach of the statistical model helps determine the connections between different variables and their underlying components.

How Can You Optimize Your Survey for Factor Analysis

If you plan to perform analyse the data you collect, you will have to focus on the following:

• Target an Adequate Number of Respondents: Large datasets are more useful for factor analysis. If you want your analysis to deliver optimum results, you should have a large group of respondents. Variables like your topic of interest and population size will influence the exact number of respondents you need. But it’s better to follow the approach of “the more the respondents, the better.”
• Ask Multiple Questions: While creating a questionnaire for your survey, you must add as many questions as possible. This analysis won’t be successful if your survey consists of a few broad questions. The end goal of analysis is to simplify an extensive concept by looking at the minute and more contextual information. Therefore, asking multiple questions will help serve the purpose and provide you with the results you need.
• Avoid Open-Ended Questions: Your goal should be collecting quantitative data. Answers to open-ended questions won’t be suitable for analysis. You should provide answer options in the form of different scales.

It will help you avoid trouble while analysing data. But try to use the same scaled answer options for as many questions as possible for data consistency.

Also Read: Time Series Analysis: Techniques and Applications

Wrapping up

Research and innovations in the field of factor analysis continue to help people make better judgments in a variety of industries. Continuous refinement in methodologies makes it one of the most significant decision-making tools for all sectors in the future.

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