Principal Component Analysis (PCA) is a dimensionality reduction method widely used in machine learning and data science. In essence, PCA reduces the number of variables (or features) in a dataset while still preserving the most important information like major trends or patterns.
How Does PCA Work?
Standardization:
Before applying PCA, it’s essential to standardize your dataset. This process ensures that all features are on the same scale, so no single variable dominates the analysis due to its magnitude.Covariance Matrix Computation:
Next, compute the covariance matrix of your data. This matrix captures the pairwise relationships between features, helping you understand how they vary together.Eigenvectors & Eigenvalues:
From the covariance matrix, calculate the eigenvectors and eigenvalues. These mathematical tools help identify the principal components, which are the directions (or axes) that capture the most variance in your dataset.Feature Vector Formation:
Once the eigenvectors are computed, select the top principal components based on their corresponding eigenvalues. This new set of features (the feature vector) represents the reduced dimension of your data.Data Projection:
Finally, project your original dataset onto the new axes defined by the principal components. This step transforms your data into a lower-dimensional space while preserving its key properties.
Advantages of PCA
Data Visualization:
PCA simplifies the visualization of high-dimensional data. By projecting data into 2D or 3D spaces, it becomes much easier to identify patterns, clusters, or anomalies.Multicollinearity Handling:
Original features in a dataset might be highly correlated, which can cause issues in many machine learning algorithms. PCA creates new, uncorrelated variables that help address these challenges.Noise Removal:
By focusing on components that capture the most variance, PCA can help eliminate components with low variance, which are often attributed to noise thereby potentially improving model performance.
Note: While PCA is a powerful tool, it can sometimes lead to a loss of interpretability. The new features (principal components) are linear combinations of the original variables, which may not have a straightforward interpretation in the context of the original dataset.
Visualizing PCA in Action
Imagine you have 3D data characterized by features X, Y, and Z. By applying PCA, you can transform this 3D data into a 2D representation, with the new axes labeled (M, O) i.e. (PC1, PC2). This transformation retains the essence of the data's variability, making it much easier to analyze and visualize.
Liked this article? Make sure to 💜 click the like button.
Feedback or addition? Make sure to 💬 comment.
Know someone that would find this helpful? Make sure to 🔁 share this post.
Get in touch
You can find me on LinkedIn | YouTube | GitHub | X
Book an Appointment: Topmate
If you wish to make a request on particular topic you would like to read, you can send me an email to analyticalrohit.connect@gmail.com
Share this post