I am conducting k-means clustering analysis. My clusters separate very well. Anova, effect size and discriminant analysis results also support this separation. But I can't get efficient results from methods such as cluster stability index, jaccard coefficient, rand coefficient. My clusters are not stable. What can I do? Is it a necessary step clusters to be stable? Can you reccomend me a scientific arcticle or book to understand this well and reference it?
Thank you in advance.
Cluster stability is an important consideration in clustering analysis. It measures the robustness of the clustering results and determines how well the clusters hold up under different conditions or perturbations. If your clusters are not stable, it indicates that they might not be reliable or generalizable, and the clustering solution could be sensitive to variations in the data or initial conditions.
Ensuring cluster stability is not always a strict requirement, but it is highly desirable because stable clusters are more likely to represent meaningful patterns in the data. When clusters are not stable, it could be due to various factors, such as noisy data, suboptimal clustering algorithm parameters, or an inherent difficulty in finding stable clusters for a specific dataset.
Here are some steps you can take to improve cluster stability:
Regarding scientific articles or books on cluster stability, here are some references that can help you gain a deeper understanding:
Remember that cluster stability is just one aspect of evaluating clustering results, and it's essential to consider other validation techniques and the practical implications of your findings in your specific research context.
import numpy as np
from sklearn.cluster import KMeans
from sklearn.metrics import adjusted_rand_score, jaccard_score
def kmeans_cluster_stability(X, n_clusters, n_bootstraps=100):
rand_scores = []
jaccard_scores = []
for _ in range(n_bootstraps):
# Create a random bootstrap sample
sample_indices = np.random.choice(X.shape[0], size=X.shape[0], replace=True)
bootstrap_sample = X[sample_indices]
# Perform k-means clustering
kmeans = KMeans(n_clusters=n_clusters, random_state=42)
labels = kmeans.fit_predict(bootstrap_sample)
# Calculate Adjusted Rand Index and Jaccard Score compared to the original labels
rand_scores.append(adjusted_rand_score(labels, kmeans.labels_))
jaccard_scores.append(jaccard_score(labels, kmeans.labels_, average='macro'))
mean_rand_score = np.mean(rand_scores)
mean_jaccard_score = np.mean(jaccard_scores)
return mean_rand_score, mean_jaccard_score
# Example usage:
if __name__ == "__main__":
# Assume you have your data in the variable X (numpy array or pandas DataFrame)
n_clusters = 4
rand_score, jaccard_score = kmeans_cluster_stability(X, n_clusters)
print(f"Mean Adjusted Rand Score: {rand_score}")
print(f"Mean Jaccard Score: {jaccard_score}")
Thank you sincerely for your detailed answer! I have two more questions, I would be very grateful if you could answer them.
1. The Coefficient of Variation (CV) values of my clusters are quite good. The clusters are quite consistent within themselves. I work in the field of social sciences and when I examine the clusters crosswise with other variables, I get meaningful results. Discriminant analysis also indicates that my clusters are classified in a meaningful way, 90% correctly. Are these included in the internal stability factors? It that enough for validity and reliability?
2. I have tried Gaussian Mixture Models (GMM) instead of K-means, I think this algorithm more flexible. But there are even fewer resources on this topic and I am a social scientist not a computer scientist. Can you suggest me some resources on GMM that can help me interpret the validity and reliability of the resulting clusters?
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