from scipy.spatial import KDTree

K = 10

# Function to estimate core distances and PDF
def estimate_pdf_using_core_distances(data, K):
    tree = KDTree(data)
    core_distances = []
    
    for point in data:
    
        # k+1 because the point itself is included
        distances, _ = tree.query(point, k=K + 1) 
        
        # The k-th nearest neighbor distance
        core_distance = distances[-1] 
        
        core_distances.append(core_distance)
    
    core_distances = np.array(core_distances)
    estimated_pdf = 1 / core_distances
    
    # Normalize to make it a PDF
    estimated_pdf /= np.sum(estimated_pdf)  
    return estimated_pdf
hdbscan
