💡 Problem Formulation: The Iris dataset from scikit-learn is a popular multivariate dataset with four features. However, you might face situations where a 2-feature dataset is required, for example, for visualization purposes or simplistic modeling. This article showcases how to transform the original four-feature Iris dataset into a dataset with just two features while retaining as much of the valuable information as possible.
Method 1: Principal Component Analysis (PCA)
Principal Component Analysis is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. This method helps in reducing the dimensionality while keeping the maximum variance within the data.
Here’s an example:
from sklearn import datasets from sklearn.decomposition import PCA # Load Iris dataset iris = datasets.load_iris() X = iris.data # Apply PCA to transform the dataset into 2 components pca = PCA(n_components=2) X_r = pca.fit_transform(X)
Output of the code snippet would be:
X_r[:5] – This would display the first five rows of the transformed dataset with two features.
Using PCA, the Iris dataset is transformed into two principal components that represent the directions of maximum variance. We fit the PCA model with the original data and then apply the transform method to get the dataset with reduced features.
Method 2: Linear Discriminant Analysis (LDA)
Linear Discriminant Analysis is a dimensionality reduction technique that is commonly used for the task of pattern classification. LDA is quite similar to PCA, but in addition to finding the component axes that maximize the variance of the data, it also aims to maximize the separation between multiple classes.
Here’s an example:
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA # Load Iris dataset iris = datasets.load_iris() X = iris.data y = iris.target # Apply LDA to transform the dataset into 2 components lda = LDA(n_components=2) X_r2 = lda.fit_transform(X, y)
Output of the code snippet would be:
X_r2[:5] – This would display the first five rows of the dataset transformed by LDA into two features.
LDA is particularly helpful when you are working with a labeled dataset and the goal is to maximize the class separability along with dimensionality reduction. This example demonstrates how to apply LDA on the Iris dataset by fitting the LDA model to the data and the corresponding labels, thus obtaining a reduced two-feature dataset.
Method 3: Feature Agglomeration
Feature Agglomeration is a bottom-up approach where each feature represents a leaf of the tree and features are merged iteratively by considering the one that minimally increases a given linkage distance. It’s a type of hierarchical clustering used for grouping features that are similar to each other.
Here’s an example:
from sklearn.cluster import FeatureAgglomeration # Load Iris dataset iris = datasets.load_iris() X = iris.data # Apply Feature Agglomeration to reduce to 2 features agglo = FeatureAgglomeration(n_clusters=2) X_reduced = agglo.fit_transform(X)
Output of the code snippet would be:
X_reduced[:5] – This would display the first five rows of the dataset after feature agglomeration.
This code snippet demonstrates how to employ Feature Agglomeration to reduce the number of features in the Iris dataset. The FeatureAgglomeration class from scikit-learn helps to cluster original features into a specified number of clusters, in this case, two.
Method 4: Manual Feature Selection
Manual Feature Selection involves selecting the most informative features based on domain knowledge and feature importance. For the Iris dataset, based on existing literature or preliminary exploratory data analysis, one might choose to keep the features that show the most significant differences when plotting or statistically comparing.
Here’s an example:
# Load Iris dataset iris = datasets.load_iris() X = iris.data # Manually select the first two features X_selected = X[:, :2]
Output of the code snippet would be:
X_selected[:5] – This would display the first five rows of the dataset with only the first two selected features.
In scenarios where computation time or resources are limited, manual feature selection can be an effective way of reducing dimensionality. In this code snippet, the first two features of the Iris dataset are selected manually, based on the assumption that they are the most informative.
Bonus One-Liner Method 5: Random Projection
Random Projection is a technique that projects the data into a lower-dimensional space using a random matrix, which can serve as an alternative to PCA or LDA when dimensionality reduction needs to be done quickly and with relatively low computational cost, especially in very high-dimensional spaces.
Here’s an example:
from sklearn import random_projection # Load Iris dataset iris = datasets.load_iris() X = iris.data # Apply Random Projection to reduce to 2 features transformer = random_projection.GaussianRandomProjection(n_components=2) X_new = transformer.fit_transform(X)
Output of the code snippet would be:
X_new[:5] – This displays the first five rows of the dataset after random projection.
This concise one-liner randomly projects the original feature space onto a smaller space with the specified number of dimensions, offering a quick and simple alternative to other more complex methods of dimensionality reduction.
Summary/Discussion
- Method 1: PCA. Maintains maximum variance. May not retain class separation if that’s a requirement.
- Method 2: LDA. Optimizes class separability. Assumes linear boundaries between classes and requires labels.
- Method 3: Feature Agglomeration. Captures feature similarity. May not keep the most discriminative features if not correlated.
- Method 4: Manual Feature Selection. Straightforward and domain-specific. Risks discarding valuable information if not carefully done.
- Bonus Method 5: Random Projection. Fast for high-dimensional data. The randomness implies a lack of determinism in feature selection, which might be less accurate.