Pattern Recognition - Computational Assignment

University: University of Piraeus Department: Informatics Academic Year: 2022–2023 Semester: 5th

Course: Pattern Recognition Assignment: Computational Course Assignment

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📖 Introduction

This project was developed in Python using Visual Studio Code and several key libraries that greatly supported our work:

• pandas
• matplotlib
• scikit-learn
• keras
• seaborn
• numpy

These libraries were installed through the terminal using standard pip commands (see bibliography in the report).

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🏗️ Data Preprocessing

1. Data Loading: We begin by loading the dataset and verifying its structure using the .head() function.

2. Feature Separation: The target feature is median_house_value.

   • X: all features except median_house_value
   • z: only median_house_value

3. Numerical vs. Categorical Features: Using .info(), we identify data types:

   • ocean_proximity: categorical
   • All others: numerical

4. Scaling Data: We apply Min-Max Scaling to bring numerical features into the 0–1 range:

   scaler = MinMaxScaler()
   X_scaled = pd.DataFrame(scaler.fit_transform(X[numerical]), columns=numerical)
   X_temp = X.drop(numerical, axis=1)
   X = pd.concat([X_temp, X_scaled], axis=1)

   Similar scaling is applied to z.

5. One-Hot Encoding: We one-hot encode the categorical feature:

   encoder = OneHotEncoder(handle_unknown='ignore', sparse=False)
   X_enc = pd.DataFrame(encoder.fit_transform(X[categorical]), columns=oc_prox)
   X_temp = X.drop(categorical, axis=1)
   X = pd.concat([X_temp, X_enc], axis=1)

6. Handling Missing Values: Using SimpleImputer(strategy='median'), we fill missing values (e.g., in total_bedrooms) with the median.

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📊 Data Visualization

• Histograms: With Seaborn, we visualize distributions:

  sns.histplot(data[column], bins=50, kde=True, lw=2)

• Scatter Plots: Using Pandas and Seaborn:

  dataset.plot(kind='scatter', x='longitude', y='median_house_value')
  sns.scatterplot(x=data['median_income'], y=data['median_house_value'], hue=data['NEAR OCEAN'])

These plots reveal correlations (e.g., between median_income and median_house_value) and geographic patterns.

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🔧 Regression Models

Least Squares Regression

We implemented two core functions:

def least_squares_train(X, y):
    mul1 = X.T.dot(X)
    inv1 = np.linalg.pinv(mul1)
    mul2 = X.T.dot(y)
    weight = np.matmul(inv1, mul2)
    return weight

def least_squares_predict(X, w):
    return np.matmul(X, w)

• Evaluation: We applied 10-fold cross-validation using scikit-learn’s KFold, calculating:

  • Mean Squared Error (MSE)
  • Mean Absolute Error (MAE)

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🤖 Multilayer Neural Network

We used Keras Sequential to build a neural network with:

• Four dense layers
• relu and softmax activations
• Optimizer: adam
• Loss: mean_squared_error
• Metrics: mae

We applied K-Fold Cross-Validation for performance evaluation.

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📎 Project Files

• main.py: Main script for data processing and model execution
• report.pdf: Detailed report with screenshots, visualizations, and analysis
• requirements.txt: List of required Python libraries

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✅ How to Run

1. Install dependencies:

   pip install -r requirements.txt

2. Run the main script:

   python main.py

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If you want, I can also generate the full README.md file in markdown format ready for copy-paste. Would you like me to prepare that for you?