implementing K-Means Clustering Convergence in Python - Unexpected Empty Clusters
I'm implementing the K-Means clustering algorithm using Python and the `scikit-learn` library (version 1.0.2), but I've run into an scenario where the algorithm sometimes converges with empty clusters, leading to an behavior. Specifically, when I call `kmeans.fit(data)`, I occasionally get the warning: `ConvergenceWarning: Number of distinct clusters (k) found smaller than n_clusters (3)`. This happens particularly when my dataset contains outliers or when the initial centroids are poorly chosen. I've tried several approaches to mitigate this. First, I set the `n_init` parameter to 10 to ensure multiple initializations of the centroids. I also attempted to preprocess the data by applying Min-Max scaling and using the `StandardScaler` from `sklearn.preprocessing` to normalize the features. However, the scenario continues. Here’s a snippet of my code: ```python import numpy as np import pandas as pd from sklearn.preprocessing import StandardScaler from sklearn.cluster import KMeans # Sample dataset np.random.seed(42) data = np.random.rand(100, 2) outliers = np.array([[3, 3], [4, 4], [5, 5]]) data = np.vstack((data, outliers)) # Preprocessing scaler = StandardScaler() data_scaled = scaler.fit_transform(data) # K-Means clustering kmeans = KMeans(n_clusters=3, n_init=10, random_state=42) # Fitting the model kmeans.fit(data_scaled) print("Cluster centers:", kmeans.cluster_centers_) ``` Despite my attempts to handle the outliers and scale the data, I'm still working with the empty cluster scenario, which halts my analysis. Is there any additional preprocessing I should consider, or strategies within `KMeans` that can help avoid this question? Any insights or best practices would be greatly appreciated!