15 Key Techniques for Dimensionality Reduction in Machine Learning

Think of dimensionality reduction in machine learning like navigating through a crowded city using the shortest, most efficient route. By avoiding unnecessary detours and focusing on the essential streets, you save time and energy.

In machine learning, dimensionality reduction works similarly: it simplifies complex data by keeping the most important features and discarding the unnecessary ones. 

But do you know why dimensionality reduction is crucial in machine learning? By reducing the size of the dataset, algorithms have to process less information, which speeds up both the training and prediction phases of machine learning models. 

Are you curious to learn about the concept of dimensionality reduction in machine learning? This blog will help you discover different techniques for optimizing machine learning. 

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What Is Dimensionality Reduction in Machine Learning?

Dimensionality reduction in machine learning is the process of simplifying a dataset by reducing its number of features (or dimensions) while keeping the most critical information. It's like packing for a trip: instead of carrying your entire wardrobe, you carefully choose just a few useful outfits.

From a technical perspective, consider a photograph with millions of pixels. Dimensionality reduction resizes the photo to a smaller resolution so that the photo's size reduces but still serves its purpose.

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 chooses a subset of the original features without altering or combining them. It retains the relevant features and discards the redundant ones.

Here are the different feature selection techniques.

1. Filter Methods

Filter methods check the relevance of each feature based on statistical tests and rank them according to their importance.

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.

2. Wrapper Methods

Wrapper methods evaluate subsets by training a machine learning model and measuring performance.

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.

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

3. Embedded Methods

Embedded methods select features during the model training process itself. The learning process itself is used to identify the most relevant features.

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.

What Are Feature Extraction Techniques?

Feature extraction techniques transform the original features into a new set of features by combining or summarizing them. The most important information from the original ones is captured, leading to fewer dimensions.

Here are some popular feature extraction techniques.

1. Linear Methods

Linear methods assume that a linear relationship exists between the features and the target variable. They are easy to interpret and 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. 

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.

How Do Linear and Non-Linear Techniques Compare?

Dimensionality reduction in machine learning can be divided into linear and non-linear techniques based on the relationship between features. 

Here’s how linear and non-linear methods are differentiated.

Key Differences Between Linear and Non-Linear Methods

Linear reduction is based on the assumption of linear relationships between features.  It is suitable for data that lies on or near a linear subspace.  Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) are examples of linear reduction techniques.

Non-linear method is based on complex relationships between features. It is suitable for data that lies on a non-linear subspace. t-SNE and Kernel PCA are some examples of non-linear methods.

Here’s a comparison between linear and non-linear methods.

Are you confused about choosing the appropriate dimensionality reduction for machine learning? The following section will provide you with essential tips.

Also Read: Linear Vs. Non-Linear Data Structure

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. 

What Factors Should You Consider?

Consider the following factors while choosing different feature reduction techniques in machine learning.

• 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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Want to learn how to reduce data dimensions in machine learning? Read on.

How Is Dimensionality Reduction Applied in Machine Learning?

Dimensionality reduction is used for tasks such as compressing high-dimensional image data, improving model performance, and speeding up computations in large-scale problems. 

These advantages highlight the versatility of dimensionality reduction techniques across various domains in machine learning.

Here are some of the details of the applications of dimensionality reduction in machine learning.

What Are the Applications of Dimensionality Reduction?

Dimensionality reduction extends its utility beyond preprocessing, shaping how models handle complexity and scale efficiently. Its applications span practical solutions that transform raw data into actionable insights. A few are mentioned below. 

• Data visualization for exploratory analysis

Dimensional reduction allows the conversion of high-dimensional data into 2D or 3D for easy visualization, allowing analysts to identify clusters, patterns, or anomalies.

Example: t-SNE reduction is used in the marketing sector to visualize customer segmentation based on purchasing behavior.

• Preprocessing for supervised learning models

Dimensionality reduction removes irrelevant or redundant features, thus improving the model's performance, reducing overfitting, and speeding up the training process.

Example: The PCA reduction technique preprocesses stock market data, enabling predictive models to identify factors driving stock prices.

• Noise reduction in signal processing

Dimensionality reduction can remove noise from signals while retaining essential information.

Example: PCA technique can remove unwanted background noise in audio recordings.

• Gene expression data analysis in genomics

You can identify key genes responsible for specific traits or diseases by using dimensionality reduction.

Example: PCA technique can analyze genomic datasets to detect biomarkers for diseases like cancer. 

Also Read: Top 10 Dimensionality Reduction Techniques in Machine Learning

Dimensionality Reduction Examples

Dimensionality reduction in machine learning is a valuable tool to improve model performance, visualization, and noise elimination. 

Here are examples of how dimensionality reduction can be applied in various scenarios.

• Iris Dataset

Principal Component Analysis (PCA) can reduce the four original features (sepal length, sepal width, petal length, and petal width) into two principal components while preserving most of the data variance.

• MNIST Dataset

You can use t-SNE or UMAP to project high-dimensional handwritten digit data into a 2D space, visualizing clusters of similar digits.

• Custom Dataset

Autoencoders can denoise data by encoding it into a lower-dimensional representation and reconstructing it to remove noise.

Also Read: Top 10 Machine Learning Datasets Project Ideas for Beginners

Now that you’ve covered the basics of dimensionality reduction in machine learning, let’s explore how you can apply this technique to Python.

How to Implement Dimensionality Reduction in Python?

Python offers you powerful libraries for implementing dimensionality reduction techniques. Libraries like sci-kit-learn, matplotlib, and TensorFlow provide easy-to-use tools for applying methods such as t-SNE, PCA, and autoencoders. 

Here’s how you can use dimensionality reduction in Python.

Python Code Examples for Dimensionality Reduction

Each dimensionality reduction technique has its strengths and is applied based on dataset characteristics, problem type, and computational requirements.

Here are some examples of using Python libraries for different dimensionality reduction techniques.

1. PCA

PCA technique can reduce dimensions by projecting data into a smaller space while retaining maximum variance.

Here’s how Python’s Scikit-learn library uses PCA dimensionality reduction for an Iris dataset.

Code snippet:

from sklearn.decomposition import PCA
from sklearn.datasets import load_iris
import matplotlib.pyplot as plt

# Load the Iris dataset
data = load_iris()
X = data.data
y = data.target

# Apply PCA
pca = PCA(n_components=2)  # Reduce to 2 dimensions
X_pca = pca.fit_transform(X)

# Plot the results
plt.scatter(X_pca[:, 0], X_pca[:, 1], c=y, cmap='viridis', edgecolor='k')
plt.xlabel('Principal Component 1')
plt.ylabel('Principal Component 2')
plt.title('PCA on Iris Dataset')
plt.colorbar(label='Class')
plt.show()

2. t-SNE

t-SNE (t-Distributed Stochastic Neighbor Embedding) uses a non-linear method for visualizing high-dimensional data.

Here’s how Python’s Scikit-learn library uses t-SNE dimensionality reduction for a high-dimensional digits dataset.

Code snippet:

from sklearn.manifold import TSNE
from sklearn.datasets import load_digits
import matplotlib.pyplot as plt

# Load the Digits dataset
digits = load_digits()
X = digits.data
y = digits.target

# Apply t-SNE
tsne = TSNE(n_components=2, random_state=42, perplexity=30)
X_tsne = tsne.fit_transform(X)

# Plot the results
plt.scatter(X_tsne[:, 0], X_tsne[:, 1], c=y, cmap='tab10', s=15)
plt.xlabel('t-SNE Component 1')
plt.ylabel('t-SNE Component 2')
plt.title('t-SNE on Digits Dataset')
plt.colorbar(label='Digit Label')
plt.show()

3. Autoencoders

Autoencoders learn a compressed representation of the input data. 

Here’s how Python’s NumPy library uses autoencoder dimensionality reduction for a high-dimensional digits dataset.

Code snippet:

import numpy as np
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Input, Dense
from sklearn.preprocessing import MinMaxScaler

# Generate sample data
np.random.seed(42)
data = np.random.rand(1000, 20)  # 1000 samples, 20 features
scaler = MinMaxScaler()
data_scaled = scaler.fit_transform(data)

# Build the autoencoder
input_dim = data_scaled.shape[1]
encoding_dim = 5  # Reduced dimension

# Encoder
input_layer = Input(shape=(input_dim,))
encoded = Dense(encoding_dim, activation='relu')(input_layer)

# Decoder
decoded = Dense(input_dim, activation='sigmoid')(encoded)

# Autoencoder model
autoencoder = Model(input_layer, decoded)
autoencoder.compile(optimizer='adam', loss='mse')

# Train the autoencoder
autoencoder.fit(data_scaled, data_scaled, epochs=50, batch_size=32, shuffle=True, verbose=0)

# Extract the encoder part for dimensionality reduction
encoder = Model(input_layer, encoded)
reduced_data = encoder.predict(data_scaled)

print(f"Original shape: {data_scaled.shape}, Reduced shape: {reduced_data.shape}")

Best Practices for Dimensionality Reduction

Following the best practices while applying dimensionality reduction can improve the performance and interpretability of your machine learning workflows.

Here are some best practices for dimensionality reduction.

1. Normalize data before applying PCA or t-SNE

Always normalize your dataset before applying dimensionality reduction techniques. Without normalization, you may get biased results.

Code snippet:

from sklearn.preprocessing import StandardScaler

# Sample data
data = [[100, 0.1], [200, 0.2], [300, 0.3]]

# Normalize data
scaler = StandardScaler()
normalized_data = scaler.fit_transform(data)
print("Normalized Data:", normalized_data)

2. Choose the number of dimensions based on the explained variance

Decide the optimal number of dimensions to retain based on metrics like explained variance ratio (for PCA).

Code snippet:

from sklearn.decomposition import PCA

# Apply PCA
pca = PCA()
pca.fit(normalized_data)

# Explained variance ratio
print("Explained Variance Ratio:", pca.explained_variance_ratio_)

3. Test multiple techniques to find the best fit for your dataset

Experiment with various methods (PCA or Autoencoders) to find the best technique for your dataset and problem.

Code snippet:

from sklearn.decomposition import PCA
from sklearn.manifold import TSNE

# Apply PCA
pca = PCA(n_components=2)
reduced_pca = pca.fit_transform(normalized_data)

# Apply t-SNE
tsne = TSNE(n_components=2, random_state=42)
reduced_tsne = tsne.fit_transform(normalized_data)

print("PCA Reduced:", reduced_pca)
print("t-SNE Reduced:", reduced_tsne)

4. Beware of Overfitting

Avoid keeping too many dimensions, as it can negate the benefits of dimensionality reduction, leading to overfitting.

Code snippet:

# Retain components with explained variance > 0.90
pca = PCA(n_components=0.90)
reduced_data = pca.fit_transform(normalized_data)
print("Reduced Data Shape:", reduced_data.shape)

5. Consider computational resources

Choose methods that suit your hardware and time constraints for large datasets. Computationally Intensive techniques like t-SNE can be avoided.

Code snippet: 

from sklearn.decomposition import TruncatedSVD

# Apply Truncated SVD for sparse, high-dimensional data
svd = TruncatedSVD(n_components=2)
reduced_data = svd.fit_transform(normalized_data)
print("SVD Reduced Data:", reduced_data)

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Why Do We Need Dimensionality Reduction?

Dimensionality reduction is incredibly useful in data analysis and machine learning because it makes complex data manageable, accurate, and fast to work with. 

Here’s a detailed breakdown of the need for dimensionality reduction.

• Simplifies complex datasets

Dimensionality reduction simplifies complex datasets by reducing the number of features, making the data more accessible for work.

Example: Consider a dataset with 100 features (like height, weight, age). You can use dimensionality reduction to keep just a few key features that still capture the essence of the data.

• Mitigates the curse of dimensionality

As the number of features in a dataset increases, the space's volume grows exponentially, making it difficult to find meaningful patterns.

Example: Reducing dimensions shrinks the search space, making it easier to spot patterns and relationships.

• Improves model performance and reduces overfitting

Reducing dimensions in large datasets helps the model focus on the most essential features, improving its ability to generalize.

Example: For a model trying to predict house prices, too many irrelevant features (like the color of the window) can affect its ability to spot patterns.

• Enhances data visualization in 2D or 3D

Dimensionality reduction converts high-dimensional data into 2D or 3D, making it easier to plot and see trends. 

Example: Visualizing data with 50 features can be complex. By reducing the features to 2 or 3, you can create a simple scatter plot.

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Now, one of the key challenges with large datasets is addressing the curse of dimensionality, which is explored in the section below.

What Is the Curse of Dimensionality?

The curse of dimensionality arises when you are working with high-dimensional data, where the number of features (or dimensions) in a dataset becomes large. The rise in data dimensions leads to the growth of data space, which can cause several problems that affect the functioning of machine learning.

Dimensionality reduction techniques, like PCA (Principal Component Analysis), reduce the number of features while preserving important information.

Here’s how the curse of dimensionality impacts models.

How Does the Curse of Dimensionality Impact Models?

The curse of dimensionality can mainly affect the reliability of distance-based algorithms, which work on the concept of proximity or similarity between data points. Check how the curse of dimensionality affects distance-based algorithms.

• Diminishing predictive power in high-dimensional spaces

Distance-based algorithms find meaningful patterns and relationships between data points. As the number of dimensions increases, the distance between any two points becomes more similar, making it difficult for the algorithm to distinguish between them.

• Inefficiency of distance metrics 

Distance metrics like Euclidean distance work well in low-dimensional spaces. Most of the data points in high-dimensional space tend to be almost equidistant from each other, making it difficult for the model to distinguish.

• Overfitting in models with too many features

The rise in features makes the model capture irrelevant patterns rather than the underlying relationships. This leads to poor generalization when the model is applied to new data.

• Sparse Data

As the number of dimensions increases, the data points become increasingly sparse. This makes it hard for the algorithm to learn meaningful patterns from the data.

Now that you have identified the curse of dimensionality in machine learning, let’s examine the different techniques of dimensionality reduction in machine learning.

Also Read: 45+ Best Machine Learning Project Ideas for Beginners