Cluster Prominence

Cluster Prominence is calculated as the sum over all matrix elements of the cubed difference between the element's intensity pair and the matrix mean, weighted by the co-occurrence probability. The formula is:

Σᵢ Σⱼ (i + j - μₓ - μᵧ)³ · P(i,j)

• Cubing the difference makes the metric highly sensitive to outliers and extreme values
• A high positive value indicates a matrix skewed toward high-intensity pairs, suggesting dominant bright clusters
• A low or negative value indicates a matrix skewed toward low-intensity pairs, suggesting dominant dark clusters
• The metric is unsigned in most implementations, with the absolute value indicating the degree of asymmetry

In oncological imaging, Cluster Prominence correlates with tumoral heterogeneity and aggressive phenotypes:

• High Cluster Prominence in CT or MRI often indicates a tumor with a dense, high-attenuation core surrounded by less dense tissue, a pattern associated with necrosis and hypoxia
• Studies have linked elevated Cluster Prominence values to poorer prognosis in non-small cell lung cancer and glioblastoma
• The metric is sensitive to calcifications and contrast uptake patterns, making it valuable for characterizing suspicious lesions
• Unlike simpler first-order statistics, it captures spatial relationships between intensity values, providing texture information invisible to the naked eye

Cluster Prominence belongs to the cluster family of Haralick features, which also includes:

• Cluster Shade: Uses the same formula but with a squared difference term, measuring symmetry rather than tailedness. Cluster Shade indicates whether the matrix is skewed above or below the mean
• Cluster Tendency: Uses an unsquared difference term, measuring the overall grouping of similar intensity pairs
• Together, these three features provide a hierarchical description of matrix shape: Tendency (linear), Shade (quadratic), and Prominence (cubic)
• A high Cluster Prominence with a near-zero Cluster Shade suggests extreme outliers without overall skew, a pattern seen in heterogeneous tumors with isolated bright foci

Cluster Prominence is highly sensitive to image preprocessing parameters, requiring careful standardization:

• Intensity discretization: The number of gray levels (bin count) directly impacts the GLCM size and the resulting feature value. IBSI guidelines recommend fixed bin number or fixed bin width approaches
• Dynamic range: Window/level settings in CT or signal normalization in MRI must be consistent across scans to avoid introducing technical variance
• ComBat harmonization is often applied to correct for scanner-specific effects before Cluster Prominence calculation in multi-center studies
• Test-retest reliability as measured by ICC should be reported; Cluster Prominence often shows moderate reproducibility due to its cubic sensitivity to outliers

Cluster Prominence is frequently selected in multivariate radiomic signatures for its independent predictive power:

• Often survives LASSO regularization and mRMR feature selection due to its low correlation with first-order and shape features
• Combined with Entropy and Zone Percentage, it forms a powerful texture triplet for characterizing tumor heterogeneity
• In delta-radiomics studies, changes in Cluster Prominence over time can indicate treatment response earlier than changes in tumor volume
• The feature is included in the IBSI benchmark dataset, with reference values available for validation of custom implementations