Refactor balanced K-Means implementation; update beta parameter default value, handle empty embeddings, and ensure proper centroid updates. Enhance UI to include beta input and adjust event handler to read beta value for clustering.

Implement balanced K-Means clustering; add new clustering type option in UI and update event handler to support balanced K-Means functionality.

Enhance cluster naming and K-Means functionality; implement random selection for cluster names, improve centroid initialization, and adjust UMAP parameters for better projection accuracy.

Refactor K-Means clustering implementation; modularize embedding and clustering logic, enhance heatmap and scatter plot functions, and improve cluster naming process.