Structural Analysis of urban thermal comfort Data with Linear Discriminant Analysis

Project info

• Field of studyMeteorology and Climate
• LevelMaster's thesis (S2)
• Method typeDimensionality Reduction
• Estimated build time± 5 working days
• Toolsscikit-learn LinearDiscriminantAnalysis, train_test_split, accuracy_score
• PriceUS$22 - US$147

Research goal

Summarise air temperature and air humidity as drivers of thermal comfort index using Linear Discriminant Analysis, then interpret the resulting components or features.

Variables

Example result

• 0.675Test accuracy
• 0.685CV accuracy
• 0.685Macro F1 (CV)
• 85.817LD1 variance %
• 14.183LD2 variance %
• 6Features

LDA separates three groups with a test accuracy of 0.675 (cross-validated 0.685); LD1 explains 85.8% of the between-group separation.

Computed from illustrative synthetic data, not from a real study.

About Linear Discriminant Analysis

Linear Discriminant Analysis finds linear combinations of features that best separate classes and can also act as a classifier. It suits supervised dimensionality reduction and classification with reasonably separated classes.

Steps

1. 1Prepare numeric features and class labels
2. 2Split into stratified training and test sets
3. 3Fit LinearDiscriminantAnalysis
4. 4Project the data onto discriminant axes
5. 5Evaluate accuracy and confusion matrix on the test set
6. 6Plot the projection by class

Assumptions to check

• Features in each class are close to multivariate normal
• Class covariance matrices are roughly equal
• At most classes minus one discriminant components exist

Reading and reporting the results

Report accuracy, the explained variance ratio of each discriminant axis, and the features that discriminate most. Discuss covariance assumption violations if any.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, confusion_matrix

X, thermal_comfort_index = make_blobs(n_samples=450, n_features=4, centers=3, cluster_std=2.0, random_state=21)
air_temperature = X[:, 0]
air_humidity = X[:, 1]

X_tr, X_te, y_tr, y_te = train_test_split(X, thermal_comfort_index, test_size=0.3, stratify=thermal_comfort_index, random_state=21)
lda = LinearDiscriminantAnalysis(n_components=2).fit(X_tr, y_tr)
pred = lda.predict(X_te)
print("Accuracy:", round(accuracy_score(y_te, pred), 3))
print("Confusion matrix:\n", confusion_matrix(y_te, pred))
print("Explained variance ratio:", lda.explained_variance_ratio_.round(3))

Z = lda.transform(X_te)
for c in np.unique(y_te):
    plt.scatter(Z[y_te == c, 0], Z[y_te == c, 1], label=f"Class {c}", s=15)
plt.xlabel("LD1"); plt.ylabel("LD2"); plt.legend()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions