EDOtrans

EDOtrans applies an EDO-transformation to adapt Euclidean distance calculations for scale non-invariance, improving clustering of multimodal and high-dimensional biological data.

Key Features:

• Scale non-invariance correction: Addresses the scale non-invariance of Euclidean distance caused by squaring differences between data points, which can distort within- and between-cluster distances.
• Breakpoint at 1 adjustment: Modifies the implicit Euclidean breakpoint at 1 to change how distances are calculated and interpreted for cluster differentiation.
• EDO-transformation for multimodal variability: Applies a transformation tailored to datasets with multimodal distributions and nontrivial variability to produce more appropriate variable representations for clustering.
• Gaussian mixture modeling of standard deviation: Models variable standard deviations using a mixture of Gaussian distributions and identifies dominant modes through item categorization.
• Comparative performance metrics: Evaluated against untransformed data, z-transformed data, and pooled variable scaling with improvements reported in cluster accuracy, adjusted Rand index, and Dunn's index on artificial and biomedical datasets.
• Application to high-dimensional genomic data: Demonstrated superior clustering performance on gene expression datasets from breast cancer tissues compared with established methods.

Scientific Applications:

• Clustering and data projection: Improves clustering and projection tasks where traditional Euclidean metrics lack scale invariance.
• Genomic studies: Applied to gene expression analysis, including breast cancer tissue datasets, to enhance cluster differentiation.
• Proteomics and other omics: Applicable to proteomics and other high-dimensional biological data requiring precise cluster separation.

Methodology:

Implemented in the "EDOtrans" R package; variables are transformed using a model that accounts for scale non-invariance and the method employs Gaussian mixture modeling of standard deviations with item categorization to select dominant modes.