Models Implemented
- Hopsital Data -

Models Implemented

1. KMeans Clustering

   • Objective: We perform pattern discovery and classification analysis using KMeans clustering for the distribution of hospitals by ZIP code in Colorado (CO) and Utah (UT).

   • Why chosen: Suitable for uncovering structure in unlabeled ZIP-level hospital data (CO & UT).

   • Assumptions: Numeric, standardized data; spherical and equally-sized clusters; predefined k.

   • Hyperparameter tuning: Tried k = 2–10; selected k = 5 using silhouette score (best score = 0.904).

   • Challenges & solutions:

     1. ZIP codes lack spatial meaning → used PCA with state & hospital count

     2. Windows MKL warning → set OMP_NUM_THREADS = 1 and suppressed warnings

2. Regression (Linear & Ridge)

   • Objective: We will test whether it is possible to predict the number of hospitals (Hospital_Count) for each ZIP code from the ZIP code and state information.

   • Why chosen: Suitable for small, numeric, tabular data; Ridge helps prevent overfitting.

   • Assumptions: Linearity, numeric input, homoscedasticity; Ridge assumes regularization improves generalization.

   • Hyperparameter tuning: GridSearchCV used for Ridge (alpha = 1000).

   • Challenges & solutions:

     1. Low R² → added Ridge regularization

     2. Limited features → used ZIP (numeric) + state (one-hot)

3. Apriori Analysis

   • Objective: What are the most common attribute patterns among the characteristics (type and ownership structure) of hospitals?

   • Why chosen: Ideal for discovering frequent patterns in categorical data (Hospital Type, Ownership).

   • Assumptions: Requires binary, one-hot encoded transactions; assumes frequent subsets imply frequent supersets.

   • Hyperparameter tuning: Grid search on min_support and lift to balance rule quantity and relevance.

   • Challenges & solutions:

     1. Raw data not suitable → applied TransactionEncoder

     2. Too many weak rules → filtered with support/lift thresholds

4. Random Forest

   • Objective: Predicting a specific class based on the attributes of a hospital.

   • Why chosen: Handles mixed data types and imbalanced classes well; robust and non-linear.

   • Assumptions: Non-parametric; no assumptions on data distribution or linearity.

   • Hyperparameter tuning: GridSearchCV on n_estimators, max_depth, min_samples_split, with class_weight='balanced'.

   • Challenges & solutions:

     1. Imbalanced classes → used class_weight='balanced'

     2. Missing/invalid values → cleaned with pd.to_numeric and dropna

     3. Unseen classes in test set → used labels= and zero_division=0

Performance Evaluation

1. KMeans Clustering

   • Evaluation Metrics: Silhouette Score and Davies-Bouldin Index are used.

   • Results: See this page.

2. Regression (Linear & Ridge)

   • Evaluation Metrics: RMSE, MSE, and R² are used.

   • Results: See this page.

3. Apriori Analysis

   • Evaluation Metrics: Rules assessed using Support, Confidence, and Lift; sorted by Lift.

   • Results: See this page.

4. Random Forest

   • Evaluation Metrics: Precision, recall, F1-score (macro & weighted)

   • Results: See this page.

5. Conclusion

   • Best Model for Comparing Colorado and Utah

KMeans Clustering is best aligned with the goal.
→ It identifies geographic patterns in hospital distribution across ZIP codes, enabling structural comparison of facility availability between the two states.

• Other Models

Linear/Ridge Regression: Poor predictive power; not useful for comparison.

Apriori: Reveals ownership/type patterns, but not suitable for state-level comparison.

Random Forest: Good for prediction, but focuses on ownership classification, not availability.

• Conclusion

KMeans provides the most relevant insights for comparing the distribution and concentration of hospitals in Colorado and Utah.

Data Formatting for Models

1. KMeans Clustering

   • Data Formatting: Features are scaled.

   • Before-and-after data transformation snapshots: See this page.

2. Regression (Linear & Ridge)

   • Data formatting: Categorical variables one-hot encoded; no scaling required for these models.

   • Before-and-after data transformation snapshots: See this page.

3. Apriori Analysis

   • Data formatting: Converted attributes to one-hot transactions for Apriori compatibility.

   • Before-and-after data transformation snapshots: See this page.

4. Random Forest

   • Data formatting: One-hot encoding for categories; label encoding for target

   • Before-and-after data transformation snapshots: See this page.