15 Key Techniques for Dimensionality Reduction in Machine Learning

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A powerful new technique blends deep learning with diffusion maps, cutting computational costs and boosting generalization. It enables efficient nonlinear dimensionality reduction, without the need for traditional spectral decomposition, transforming how we process complex data!

Dimensionality reduction is a crucial technique in machine learning, designed to reduce the number of features in a dataset while retaining its essential patterns and information. This process helps improve the efficiency of models, reduces computational costs, and enhances their interpretability, especially when dealing with high-dimensional data.

In this blog, we’ll explore 15 essential dimensionality reduction techniques, from classic methods like PCA to advanced deep learning approaches. These techniques can help you optimize models and simplify complex data efficiently.

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Top 15 Dimensionality Reduction Techniques for Machine Learning?

Feature Selection and Feature Extraction are the two methods used for dimensionality reduction in machine learning. Both techniques aim to reduce the number of features (or dimensions) in a dataset while retaining as much helpful information as possible.

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Here’s a brief idea of how feature reduction techniques work in machine learning.

What Are Feature Selection Techniques?

Feature selection is a technique used in machine learning to identify and select a subset of the original features in the dataset without altering or combining them. The aim is to retain only the most relevant and significant features while discarding redundant or irrelevant ones. This step is crucial in building efficient machine learning models, as it reduces overfitting, improves model accuracy, and minimizes computational cost.

Feature selection techniques can be broadly classified into three categories: Filter Methods, Wrapper Methods, and Embedded Methods. Each approach uses a different mechanism to assess the importance of features.

1. Filter Methods

Filter methods assess the relevance of features using statistical techniques independently of any machine learning model. These methods typically rank the features based on their individual importance or correlation with the target variable and discard the least relevant ones.

Here are some examples of filter methods.

• Correlation coefficient analysis

Correlation coefficient analysis measures the strength and direction of the linear relationship between two variables. The correlation coefficient (usually Pearson’s r) ranges from -1 to 1, where values close to 1 or -1 indicate strong relationships and 0 indicates no relationship.

It helps identify highly correlated features that may be redundant in machine learning models.

• Chi-square test

The chi-square test determines if there is a significant association between two categorical variables. The technique compares observed frequencies with expected frequencies under the assumption of independence. A high chi-square value indicates a significant relationship between the variables.

It is used in categorical data analysis, such as selecting features in classification problems.

• Information gain

The information gain technique measures the effectiveness of an attribute in classifying a dataset based on the reduction in entropy. The feature that has the highest information gain (or greatest reduction in uncertainty) is considered the most important.

It is mainly used in decision trees to select the most informative features for splitting nodes.

Strengths of Filter Methods:

• Computationally inexpensive and fast.
• Independent of any learning model, which makes them versatile.
• Effective for large datasets with many features.

Limitations of Filter Methods:

• They may miss interactions between features that are only revealed when considered together in a model.

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2. Wrapper Methods

Wrapper methods evaluate the performance of a feature subset by actually training a machine learning model and assessing its accuracy. These methods are more computationally expensive but tend to provide better performance as they consider feature interactions and model performance during the selection process.

Here are some important wrapper methods.

• Recursive Feature Elimination (RFE)

The RFE technique recursively removes the least important features and builds the model again to identify the most significant features. RFE trains a model, ranks the features, removes the least important one, and repeats the process until the desired number of features is selected.

It is used with any machine learning model, typically regression or classification models, to maximize model performance.

• Sequential Feature Selection

It selects features by sequentially adding (forward selection) or removing (backward elimination) features based on model performance. In forward selection, one feature is added at a time and then evaluated. In backward elimination, features are removed one by one based on the model’s performance.

It is mainly used to find the best subset of features, balancing performance and simplicity.

Strengths of Wrapper Methods:

• More accurate in selecting the right features since they are tailored to the specific model.
• Can capture interactions between features.

Limitations of Wrapper Methods:

• Highly computationally intensive, especially for large datasets.
• Can lead to overfitting if the model performance is not properly validated.

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Also Read: How to Choose a Feature Selection Method for Machine Learning?

3. Embedded Methods

Embedded methods perform feature selection as part of the model training process. These methods take into account the relationship between features and the target during the learning phase, making them both efficient and effective.

You can check these important embedded methods.

• Lasso Regression

Lasso regression performs both feature selection and regularization to improve the model’s accuracy and interpretability. Lasso adds a penalty term to the linear regression cost function, forcing some feature coefficients to be zero, thus performing automatic feature selection.

It is mainly used in linear models for feature selection, especially when dealing with high-dimensional data.

• Tree-based feature selection

The tree-based models (like decision trees and random forests) rank and select important features based on their contribution to reducing model error.

Tree-based models measure feature importance based on how well features split the data to remove impurities. Features with higher importance scores are selected.

It is commonly used in classification and regression tasks, particularly when working with structured data.

Strengths of Embedded Methods:

• Computationally efficient as feature selection happens during model training.
• Captures feature interactions effectively.
• Produces robust models with fewer hyperparameters to tune.

Limitations of Embedded Methods:

• May not work well with models that don’t naturally provide feature importance (e.g., KNN, SVM).
• Tends to be model-specific, meaning the selected features may not generalize well to other models.

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What Are Feature Extraction Techniques?

eature extraction involves transforming the original features into a new set of features by combining or summarizing them. The goal is to capture the most important information while reducing the number of dimensions. Feature extraction is especially useful when you need to reduce complexity while preserving essential patterns in the data.

Feature extraction techniques are categorized into linear methods (which assume linear relationships between features) and non-linear methods (which capture more complex, non-linear relationships).

Here are some popular feature extraction techniques.

1. Linear Methods

Linear methods work by projecting the data into a new space where the relationship between the features and the target variable can be captured in a linear manner. These methods are easy to interpret and computationally efficient.

Here are some of the examples of linear methods.

• Principal Component Analysis (PCA)

The PCA dimensionality reduction technique reduces the number of features in a dataset while preserving as much variance (information) as possible. 

It identifies the directions (principal components) in which the data has the highest variation and projects the data onto a smaller set of dimensions along these directions. It is mainly used in unsupervised learning tasks.

It is used in cases such as image compression to reduce the complexity of datasets with many features.

• Linear Discriminant Analysis (LDA)

LDA technique simplifies data by focusing on the features that best distinguish different categories. It helps in better classification by highlighting the most important differences. 

LDA projects data onto a lower-dimensional space by maximizing the distance between class means and minimizing the variance within each class.

LDA is mainly used in pattern recognition, especially in face recognition and speech recognition.

• Singular Value Decomposition (SVD)

It is a matrix factorization technique that decomposes a matrix into the product of three matrices.

It is mainly used in fields like signal processing, machine learning, and natural language processing. 

Strengths of Linear Methods:

• Easy to interpret and computationally efficient.
• Works well for datasets where features have linear relationships.

Limitations of Linear Methods:

• Limited in capturing complex non-linear relationships.
• May not perform well when the data lies on a non-linear manifold.

2. Non-Linear Methods

Non-linear methods identify complex patterns and relationships in the data that linear methods can miss. They are more powerful but expensive to implement.

Here are some of the examples of non-linear methods.

• t-SNE

t-SNE is a non-linear dimensionality reduction technique that visualizes high-dimensional data in 2D or 3D. It reduces the divergence between probability distributions of pairwise similarities in the original high-dimensional space and the lower-dimensional space. It preserves local structures but not global structures.

t-SNE is usually used in visualizing clusters in high-dimensional datasets like image or text data.

• UMAP

UMAP technique is similar to t-SNE but is faster and better at preserving both local and global structures. UMAP models the data as a fuzzy topological structure and makes a low-dimensional representation by optimizing the preservation of these structures. 

It is used in cases such as manifold learning and data visualization.

• Autoencoders:

Autoencoders compress and then reconstruct data, effectively reducing dimensionality. It consists of an encoder, which compresses the input data into a smaller representation (latent space), and a decoder, which reconstructs the data from the compressed form.

The autoencoder technique is usually used for feature extraction in images and text data.

• Kernel PCA

Kernel PCa uses kernel methods to perform non-linear dimensionality reduction. Kernel PCA maps the data to a higher-dimensional space where linear separation is easier and then performs PCA in this new space.

It is suitable for use in datasets with complex, non-linear structures like images or time series.

• Isomap

The isomap technique generalizes Multi-dimensional Scaling (MDS) by incorporating geodesic distances to preserve the global structure. 

Isomap first computes the shortest path between all pairs of points in a graph and then performs classical MDS on these distances to obtain a lower-dimensional embedding.

It is mainly used in non-linear datasets, such as in image or 3D shape analysis.

Also Read: Feature Extraction in Image Processing

After a brief understanding of linear and non-linear techniques, let’s explore the difference between the two.

Strengths of Non-Linear Methods:

• Can capture complex, non-linear relationships that linear methods miss.
• Ideal for high-dimensional data with intricate patterns.

Limitations of Non-Linear Methods:

• Computationally expensive and often slower than linear methods.
• More challenging to interpret and requires careful tuning.

Also Read: Feature Extraction in Image Processing

After a brief understanding of linear and non-linear techniques, let’s explore the difference between the two.

How to Choose the Right Dimensionality Reduction Technique?

Before selecting a dimensionality reduction technique, you must consider factors like the complexity of your data, the goals of your analysis, and the resources available for computation.

Below, you will read about some critical factors to consider. 

• Linear vs Non-Linear Data

If your data has linear relationships, PCA or LDA are appropriate as they reduce dimensions while preserving linear structures. In the case of non-linear data (consisting of complex patterns or interactions), methods like t-SNE or Isomap are effective.

• Visualization Goals

If visualizing your high-dimensional data in 2D or 3D is your goal, t-SNE and PCA are popular choices. 

• Computational Resources

Linear methods like PCA are more efficient for large datasets with many features. Non-linear techniques, such as autoencoders, require more computational resources.

• Interpretability

Methods like filtering based on statistical tests offer better interpretability since they retain the original features.

When Should You Use Feature Selection vs Feature Extraction?

Both feature selection and feature extraction are valuable techniques for dimensionality reduction in machine learning, but each is suited to specific scenarios. 

Here's how to determine when to use feature selection and feature extraction.

1. Feature Selection

You can use feature selection when you want to retain original features and eliminate irrelevant ones. It is ideal when you have a small data with a moderate number of features. 

For example, datasets with a lot of redundant features can be reduced using this technique.

2. Feature Extraction

Apply this technique to transform your original data into a smaller set of new features that capture the key patterns. It is beneficial for high-dimensional data.

For example, you can use feature selection to preserve important patterns in image or text data.

What Are Common Scenarios and Recommended Techniques?

When dealing with scenarios such as high-dimensional data, you may have to use specific dimensionality reduction techniques. These techniques will ensure that you choose the correct technique for the situation.

Here’s how to navigate some common scenarios.

• High-Dimensional Image Data

For high-dimensional image data, you can use PCA or Autoencoders. Both these techniques efficiently reduce the dimensions of image data.

• Cluster Visualization

t-SNE or UMAP techniques are suitable for visualizing clusters in high-dimensional data. The ability to capture complex and non-linear relationships makes them appropriate. 

• Classification Problems

LDA (Linear Discriminant Analysis) or PCA are the most appropriate techniques for classification problems. 

• Time-Series Data

For time-series data, you can choose PCA or Autoencoders. Both can capture the temporal patterns in time-series data. 

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Dimensionality reduction in machine learning can simplify complex datasets without affecting critical insights. It is the compass that can guide you toward a more efficient and insightful machine-learning journey.

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References:

• https://arxiv.org/abs/2505.06087