Unsupervised Machine Learning for Osteoporosis Diagnosis Using Singh Index Clustering on Hip Radiographs

1. Problem Statement

Osteoporosis is a global health crisis characterized by diminished bone mass and increased fracture risk. The current gold standard for diagnosis is Dual-energy X-ray Absorptiometry (DXA), which measures Bone Mineral Density (BMD). However, DXA is expensive, not universally available (especially in rural/developing regions), and prone to inter-device variability.

An alternative, cost-effective method is the Singh Index (SI), a semi-quantitative grading system (Grades 1–6) based on the trabecular patterns visible in plain hip radiographs. Grades 1–3 indicate osteoporosis, while 4–6 indicate normal bone structure.

• The Challenge: Manual SI grading is time-consuming, requires expert radiologists, and is subjective.
• The Gap: While Deep Learning (DL) has been applied to DXA images, there is a lack of research on automating SI grading using unlabelled plain hip X-ray images. Most existing ML models require large, labelled datasets, which are difficult to obtain for this specific task.

2. Methodology

The study employs an Unsupervised Machine Learning approach to cluster unlabelled hip X-ray images into the six SI grades without prior manual annotation.

A. Dataset

• Source: 838 hip X-ray images from Indian adults (ages 20–70) collected from SRM Medical College Hospital.
• Characteristics: The dataset is unlabelled. It contains a significant class imbalance, with a higher prevalence of normal bone images (Grades 4–6) compared to osteoporotic images (Grades 1–3).
• Pre-processing: Images were cropped to focus on the proximal femur region, resized to uniform dimensions, and converted to NumPy arrays.

B. Feature Extraction

The authors evaluated multiple approaches for feature extraction:

1. Transfer Learning: Initially tested pre-trained models (DenseNet-201, InceptionV3, EfficientNetB0) trained on ImageNet.
2. Custom CNN: A custom Convolutional Neural Network architecture was developed and ultimately selected for its superior performance.
   • Architecture: Four convolutional layers (64, 64, 128, 128 filters) followed by 2D Max Pooling.
   • Activation: ReLU with 0.5 Dropout.
   • Dense Layers: Two fully connected layers (64 and 16 nodes) to flatten and compress features.

C. Clustering Algorithms

The extracted features were fed into various unsupervised clustering algorithms to group images into 2 through 6 clusters (corresponding to SI grades). The algorithms tested included:

• K-Means
• Mini-Batch K-Means
• Spectral Clustering
• Agglomerative Clustering (Ward and Average linkage)
• Birch Clustering
• Gaussian Mixture Models (Tied, Diag, Full covariance)

D. Evaluation Metric

The Silhouette Score was used as the primary metric to evaluate cluster quality. A higher score (closer to 1) indicates better-defined, distinct clusters. The goal was to determine if the algorithms could naturally separate the images into the 6 distinct SI grades.

3. Key Contributions

1. Novel Application of Unsupervised Learning: This is one of the first studies to attempt automating the 6-grade Singh Index classification using unlabelled hip radiographs, bypassing the need for expensive manual annotation.
2. Custom Architecture Development: The authors developed a custom CNN that outperformed established transfer learning models (InceptionV3, DenseNet) in generating features suitable for clustering, evidenced by higher Silhouette Scores.
3. Comparative Analysis of Clustering: A comprehensive benchmark of nine different clustering algorithms on medical imaging data, revealing that while some algorithms work well for binary separation (Normal vs. Osteoporotic), they struggle with fine-grained 6-class separation.
4. Identification of Data Limitations: The study highlights the critical impact of dataset imbalance and image quality on unsupervised clustering performance in medical diagnostics.

4. Results and Discussion

• Cluster Performance:
  • 2-Cluster Separation: Most algorithms performed exceptionally well when grouping images into just two categories (likely separating "Normal" vs. "Osteoporotic").
    • Agglomerative Average: 0.9360 Silhouette Score.
    • Birch: 0.9234.
    • Mini-Batch K-Means: 0.8691.
  • 6-Cluster Separation (Target SI Grades): Performance dropped significantly as the number of clusters increased to 6.
    • Agglomerative Average: 0.8565.
    • K-Means: 0.6560.
    • Mini-Batch K-Means: 0.3877 (Poor performance).
• Key Findings:
  • No single algorithm successfully achieved high-fidelity separation into all 6 SI grades.
  • The Agglomerative (Average) and Birch algorithms showed the most promise for higher cluster counts.
  • Imbalance Issue: The dataset contained significantly more "healthy" (Grade 4+) images than osteoporotic ones, skewing the clustering centroids.
  • Image Quality: Variations in X-ray intensity and contrast hindered the CNN's ability to extract consistent trabecular patterns.

5. Significance and Future Directions

• Clinical Impact: The study demonstrates the feasibility of using plain X-rays (widely available) combined with ML for osteoporosis screening, potentially reducing reliance on costly DXA scans in resource-limited settings.
• Limitations: The current unsupervised model cannot yet reliably distinguish between all 6 SI grades due to data imbalance and lack of ground truth labels.
• Future Work Recommendations:
  • Data Augmentation: Incorporating reference images (centroids) for each SI grade to guide clustering.
  • Semi-Supervised Learning: Utilizing a small set of expert-labelled data to guide the unsupervised process.
  • Multi-modal Input: Integrating patient metadata (age, sex, clinical history) with image data to improve prediction accuracy.
  • Image Pre-processing: Advanced filtering to enhance trabecular visibility before feature extraction.

In conclusion, while the study did not achieve perfect 6-grade classification, it successfully validated that unsupervised learning can effectively separate general osteoporosis risk from normal bone density using plain radiographs, providing a foundation for more advanced, semi-supervised diagnostic tools.