Introduction to Dimensionality Reduction

When working with machine learning models, datasets with too many features can cause issues like slow computation and overfitting. Dimensionality reduction helps by reducing the number of features while retaining key information.

Techniques like principal component analysis (PCA), singular value decomposition (SVD) and linear discriminant analysis (LDA) project data onto a lower-dimensional space, preserving important details.

Example:

when you are building a model to predict house prices with features like bedrooms, square footage, and location. If you add too many features, such as room condition or flooring type, the dataset becomes large and complex.

Before Dimensionality Reduction

With too many features, training can slow down and the model may focus on irrelevant details, like flooring type, which could lead to inaccurate predictions.

How Dimensionality Reduction Works?

Lets understand how dimensionality Reduction is used with the help of the figure below:

• On the left, data points exist in a 3D space (X, Y, Z), but the Z-dimension appears unnecessary since the data primarily varies along the X and Y axes. The goal of dimensionality reduction is to remove less important dimensions without losing valuable information.
• On the right, after reducing the dimensionality, the data is represented in lower-dimensional spaces. The top plot (X-Y) maintains the meaningful structure, while the bottom plot (Z-Y) shows that the Z-dimension contributed little useful information.

This process makes data analysis more efficient, improving computation speed and visualization while minimizing redundancy

Dimensionality Reduction Techniques

Dimensionality reduction techniques can be broadly divided into two categories:

Feature Selection

Feature selection chooses the most relevant features from the dataset without altering them. It helps remove redundant or irrelevant features, improving model efficiency. There are several methods for feature selection including filter methods, wrapper methods and embedded methods.

• Filter methods rank the features based on their relevance to the target variable.
• Wrapper methods use the model performance as the criteria for selecting features.
• Embedded methods combine feature selection with the model training process.

Please refer to Feature Selection Techniques for better in depth understanding about the techniques.

Feature Extraction

Feature extraction involves creating new features by combining or transforming the original features. There are several methods for feature extraction stated above in the introductory part which is responsible for creating and transforming the features. PCA is a popular technique that projects the original features onto a lower-dimensional space while preserving as much of the variance as possible.

Although one can perform dimensionality reduction with several techniques, the following are the most commonly used ones: 

1. Principal Component Analysis (PCA): Converts correlated variables into uncorrelated ‘principal components,’ reducing dimensionality while maintaining as much variance as possible, enabling more efficient analysis.
2. Missing Value Ratio: Variables with missing data beyond a set threshold are removed, improving dataset reliability.
3. Backward Feature Elimination: Starts with all features and removes the least significant ones in each iteration. The process continues until only the most impactful features remain, optimizing model performance.
4. Forward Feature Selection: Forward Feature Selection Begins with one feature, adds others incrementally, and keeps those improving model performance.
5. Random Forest: Random forest Uses decision trees to evaluate feature importance, automatically selecting the most relevant features without the need for manual coding, enhancing model accuracy.
6. Factor Analysis: Groups variables by correlation and keeps the most relevant ones for further analysis.
7. Independent Component Analysis (ICA): Identifies statistically independent components, ideal for applications like ‘blind source separation’ where traditional correlation-based methods fall short.

Dimensionality Reduction Examples

Dimensionality reduction plays a crucial role in many real-world applications, such as text categorization, image retrieval, gene expression analysis, and more. Here are a few examples:

1. Text Categorization: With vast amounts of online data, dimensionality reduction helps classify text documents into predefined categories by reducing the feature space (like word or phrase features) while maintaining accuracy.
2. Image Retrieval: As image data grows, indexing based on visual content (color, texture, shape) rather than just text descriptions has become essential. This allows for better retrieval of images from large databases.
3. Gene Expression Analysis: Dimensionality reduction accelerates gene expression analysis, helping classify samples (e.g., leukemia) by identifying key features, improving both speed and accuracy.
4. Intrusion Detection: In cybersecurity, dimensionality reduction helps analyze user activity patterns to detect suspicious behaviors and intrusions by identifying optimal features for network monitoring.

Advantages of Dimensionality Reduction

As seen earlier, high dimensionality makes models inefficient. Let’s now summarize the key advantages of reducing dimensionality.

• Faster Computation: With fewer features, machine learning algorithms can process data more quickly. This results in faster model training and testing, which is particularly useful when working with large datasets.
• Better Visualization: As we saw in the earlier figure, reducing dimensions makes it easier to visualize data, revealing hidden patterns.
• Prevent Overfitting: With fewer features, models are less likely to memorize the training data and overfit. This helps the model generalize better to new, unseen data, improving its ability to make accurate predictions.

Disadvantages of Dimensionality Reduction

• Data Loss & Reduced Accuracy – Some important information may be lost during dimensionality reduction, potentially affecting model performance.
• Choosing the Right Components – Deciding how many dimensions to keep is difficult, as keeping too few may lose valuable information, while keeping too many can lead to overfitting.