Performing PCA on a Real Dataset
Perform PCA on a real dataset using scikit-learn. Use the Iris dataset, a classic in machine learning, and follow these steps:
- Load the data;
- Prepare it for analysis;
- Standardize features;
- Apply
PCAto reduce its dimensionality.
This process demonstrates how to implement dimensionality reduction in practical scenarios.
12345678910111213141516171819202122import numpy as np import pandas as pd from sklearn.datasets import load_iris from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA # Load the Iris dataset data = load_iris() X = data.data feature_names = data.feature_names # Standardize features (important for PCA) scaler = StandardScaler() X_scaled = scaler.fit_transform(X) # Apply PCA to reduce to 2 components pca = PCA(n_components=2) X_pca = pca.fit_transform(X_scaled) print("Original shape:", X.shape) print("Transformed shape:", X_pca.shape) # Each row in X_pca is a sample projected onto the first two principal components
The code above performs PCA on the Iris dataset by following several key steps:
1. Loading the Data
The Iris dataset is loaded using load_iris() from scikit-learn. This dataset contains 150 samples of iris flowers, each described by four features: sepal length, sepal width, petal length, petal width.
2. Standardizing Features
Standardization ensures each feature has mean 0 and variance 1:
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
This step is essential because PCA is sensitive to the variance of each feature. Without standardization, features with larger scales would dominate the principal components, leading to misleading results.
3. Applying PCA
PCA(n_components=2) reduces the dataset from four dimensions to two:
pca = PCA(n_components=2)
X_pca = pca.fit_transform(X_scaled)
Principal components are new axes that capture the directions of maximum variance in the data. Each sample is projected onto these axes, resulting in a compact representation that retains as much information as possible.
4. Interpreting PCA Output
You can check how much variance each principal component explains:
print(pca.explained_variance_ratio_)
This outputs an array, such as [0.7277, 0.2303], meaning the first component explains about 73% of the variance and the second about 23%. Together, they capture most of the information from the original data.
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Perform PCA on a real dataset using scikit-learn. Use the Iris dataset, a classic in machine learning, and follow these steps:
- Load the data;
- Prepare it for analysis;
- Standardize features;
- Apply
PCAto reduce its dimensionality.
This process demonstrates how to implement dimensionality reduction in practical scenarios.
12345678910111213141516171819202122import numpy as np import pandas as pd from sklearn.datasets import load_iris from sklearn.preprocessing import StandardScaler from sklearn.decomposition import PCA # Load the Iris dataset data = load_iris() X = data.data feature_names = data.feature_names # Standardize features (important for PCA) scaler = StandardScaler() X_scaled = scaler.fit_transform(X) # Apply PCA to reduce to 2 components pca = PCA(n_components=2) X_pca = pca.fit_transform(X_scaled) print("Original shape:", X.shape) print("Transformed shape:", X_pca.shape) # Each row in X_pca is a sample projected onto the first two principal components
The code above performs PCA on the Iris dataset by following several key steps:
1. Loading the Data
The Iris dataset is loaded using load_iris() from scikit-learn. This dataset contains 150 samples of iris flowers, each described by four features: sepal length, sepal width, petal length, petal width.
2. Standardizing Features
Standardization ensures each feature has mean 0 and variance 1:
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
This step is essential because PCA is sensitive to the variance of each feature. Without standardization, features with larger scales would dominate the principal components, leading to misleading results.
3. Applying PCA
PCA(n_components=2) reduces the dataset from four dimensions to two:
pca = PCA(n_components=2)
X_pca = pca.fit_transform(X_scaled)
Principal components are new axes that capture the directions of maximum variance in the data. Each sample is projected onto these axes, resulting in a compact representation that retains as much information as possible.
4. Interpreting PCA Output
You can check how much variance each principal component explains:
print(pca.explained_variance_ratio_)
This outputs an array, such as [0.7277, 0.2303], meaning the first component explains about 73% of the variance and the second about 23%. Together, they capture most of the information from the original data.
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