LDA : Reducing Dimension¶
Application of LDA in Modelling¶
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import numpy as np
from sklearn.datasets import load_wine
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
1. Load the Wine dataset¶
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wine = load_wine()
X = wine.data
y = wine.target
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# (OPTIONAL) Create the base DataFrame with the 13 chemical features
import pandas as pd
df = pd.DataFrame(data=wine.data, columns=wine.feature_names)
# 3. Add the numeric target column (0, 1, or 2)
df["target_code"] = wine.target
# Display a sample containing rows from each class
print(df.sample(10))
# print(df['target_code'].value_counts())
alcohol malic_acid ash alcalinity_of_ash magnesium total_phenols \
17 13.83 1.57 2.62 20.0 115.0 2.95
114 12.08 1.39 2.50 22.5 84.0 2.56
78 12.33 0.99 1.95 14.8 136.0 1.90
165 13.73 4.36 2.26 22.5 88.0 1.28
79 12.70 3.87 2.40 23.0 101.0 2.83
8 14.83 1.64 2.17 14.0 97.0 2.80
24 13.50 1.81 2.61 20.0 96.0 2.53
132 12.81 2.31 2.40 24.0 98.0 1.15
161 13.69 3.26 2.54 20.0 107.0 1.83
7 14.06 2.15 2.61 17.6 121.0 2.60
flavanoids nonflavanoid_phenols proanthocyanins color_intensity hue \
17 3.40 0.40 1.72 6.60 1.13
114 2.29 0.43 1.04 2.90 0.93
78 1.85 0.35 2.76 3.40 1.06
165 0.47 0.52 1.15 6.62 0.78
79 2.55 0.43 1.95 2.57 1.19
8 2.98 0.29 1.98 5.20 1.08
24 2.61 0.28 1.66 3.52 1.12
132 1.09 0.27 0.83 5.70 0.66
161 0.56 0.50 0.80 5.88 0.96
7 2.51 0.31 1.25 5.05 1.06
od280/od315_of_diluted_wines proline target_code
17 2.57 1130.0 0
114 3.19 385.0 1
78 2.31 750.0 1
165 1.75 520.0 2
79 3.13 463.0 1
8 2.85 1045.0 0
24 3.82 845.0 0
132 1.36 560.0 2
161 1.82 680.0 2
7 3.58 1295.0 0
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2. Split into training and testing sets (80% train, 20% test)¶
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X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=0.2, random_state=42, stratify=y
)
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3. Scale the data manually (Crucial for teaching step-by-step workflows)¶
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scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)
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4. Apply LDA to reduce dimensions to 2D¶
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lda = LinearDiscriminantAnalysis(n_components=2)
X_train_lda = lda.fit_transform(X_train_scaled, y_train) # Needs 'y_train' because LDA is supervised
X_test_lda = lda.transform(X_test_scaled)
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import matplotlib.pyplot as plt
# 1. Create the figure
plt.figure(figsize=(7, 5))
# 2. Define distinct colors and markers for the three wine classes
colors = ["#FF4136", "#2ECC40", "#0074D9"] # Red, Green, Blue
markers = ["o", "^", "s"] # Circle, Triangle, Square
target_names = wine.target_names
# 3. Loop through each class and plot its training points
for category, color, marker in zip(range(3), colors, markers):
# Create a boolean mask to isolate the current class
class_mask = y_train == category
plt.scatter(
X_train_lda[class_mask, 0],
X_train_lda[class_mask, 1],
c=color,
marker=marker,
edgecolor="k",
alpha=0.8,
s=50, # Marker size
label=target_names[category],
)
# 4. Add labels, grid, and legend
plt.title("LDA Feature Space (Training Set Only)", fontsize=12, fontweight="bold")
plt.xlabel("Linear Discriminant 1 (LD1)", fontsize=10)
plt.ylabel("Linear Discriminant 2 (LD2)", fontsize=10)
plt.grid(True, linestyle="--", alpha=0.5)
plt.legend(title="Wine Classes", loc="best")
# 5. Render the plot
plt.tight_layout()
plt.show()
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5. Train the Logistic Regression classifier on the 2D LDA features¶
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model = LogisticRegression(random_state=42)
model.fit(X_train_lda, y_train)
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LogisticRegression(random_state=42)In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
LogisticRegression(random_state=42)
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6. Evaluate the model using the processed test data¶
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accuracy = model.score(X_test_lda, y_test)
print(f"Model Accuracy on Test Set: {accuracy * 100:.2f}%")
Model Accuracy on Test Set: 97.22%
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# Lets pick a sample
print(list(X[0]))
print(y[0])
[14.23, 1.71, 2.43, 15.6, 127.0, 2.8, 3.06, 0.28, 2.29, 5.64, 1.04, 3.92, 1065.0] 0
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new_wine_sample = np.array(
[[14.23, 1.71, 2.43, 15.6, 127.0, 2.8, 3.06, 0.28, 2.29, 5.64, 1.04, 3.92, 1065.0]]
) # =X[0], actual y[0] = 0
# Step A: Scale the new sample
new_sample_scaled = scaler.transform(new_wine_sample)
# Step B: Project the new sample into the 2D LDA space
new_sample_lda = lda.transform(new_sample_scaled)
# Step C: Make the final prediction
predicted_class = model.predict(new_sample_lda)
print(f"Predicted Cultivator: Class {predicted_class[0]} ({wine.target_names[predicted_class[0]]})")
Predicted Cultivator: Class 0 (class_0)
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