Solving Hot-One Encoded Column Overload with PCA

Introduction
Picture this: You are working on your data science project, and you just employed one-hot encoding to handle categorical data. Suddenly your dataset explodes with numerous columns. This post will show you how to use PCA as your knight in shining armor.

The One-Hot Explosion:
The power of one-hot encoding is undeniable for tackling categorical data. Yet, it unleashes a cascade of binary columns when in operation, skyrocketing your dataset's dimension into the stratosphere. A very essential technique when it comes to machine learning, yet a challenge in terms of computational efficiency.

What is PCA:
Principal Component Analysis (PCA) is basically like a magician's wand that transforms high-dimensional data into a more manageable form while retaining critical data.

The Power of PCA:
The components created from the application of PCA are new variables that capture most of the data's variance. They are linear combinations of original features and provide insight into the most significant patterns. It's essential to note that PCA doesn't selectively retain vital features while discarding less important ones. Instead, it transforms these features into entirely new entities.

PCA in Action: Step by Step

Step 1: Standardization
Always begin by standardizing your data to ensure each feature is on a comparable scale.

from sklearn.preprocessing import StandardScaler

# Standardize the data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

Step 2: Applying PCA:
Apply PCA to the standardized data and select number of components that you would like to retain.

from sklearn.decomposition import PCA

# Create a PCA object and fit it to the data
pca = PCA(n_components=0.95)  # Retain 95% of variance
pca.fit(data_scaled)

# Transform the data using the new components
data_pca = pca.transform(data_scaled)

Step 3: Interpretation and Explained Variance
Get to know the meaning behind the principal components by examining the explained variance ratios.

# Explained variance ratios of components
explained_variance_ratio = pca.explained_variance_ratio_

# Interpretation
for i, ratio in enumerate(explained_variance_ratio):
    print(f"Principal Component {i+1}: Explained Variance = {ratio:.2f}")

Determining the Right Number of Components: Scree Plot

Choosing the Number:
Think of your data as a recipe, with various ingredients representing different pieces of information. Just like in cooking, some ingredients (data components) contribute more flavor (variance) than others.

Now, picture a "scree plot" as a taste test. You sample each ingredient (data component) separately to see how much it adds to the overall flavor (explained variance) of your dish (data analysis).

Here's the key: As you add more ingredients, there comes a point where the taste doesn't change much. It's like having all the essential flavors in your dish and adding more doesn't make it significantly better.

This moment is the "elbow point" on the graph. It signifies that you've captured the most critical elements of your data; adding more won't enhance your analysis significantly.

In data terms, the scree plot helps you find this balance. It guides you in selecting just enough data components to represent your information effectively.

import matplotlib.pyplot as plt

# Plot scree plot
plt.plot(range(1, len(explained_variance_ratio) + 1), explained_variance_ratio, marker='o')
plt.xlabel("Number of Components")
plt.ylabel("Explained Variance Ratio")
plt.title("Scree Plot")
plt.show()

The Sweet Spot:
Select the number of components that strikes a crucial balance between reduction and information retention, typically 95% of the variance is a good amount.

Conclusion:
Now by applying PCA, you can streamline your analysis while preserving crucial information and also taking control of the dimensionality.

PS: Check out projects on my GitHub repo. Your thoughts and feedback go a long way.
GitHub: https://github.com/IsmailOtukoya