singular-value-decomposition-interpretation

singular-value-decomposition-interpretation

Summary

Interprets SVD output from DNA methylation data to detect and characterize batch effects and latent components using Random Matrix Theory thresholding. This skill identifies when principal components exceed the theoretical maximum and correctly applies component capping to avoid over-interpretation of technical artifacts.

When to use

After loading and normalizing a beta-valued methylation matrix (450K or EPIC array), apply SVD interpretation when you need to assess whether observed variation is driven by batch effects rather than biological signal, or when you want to determine the true dimensionality of latent technical confounders in the data.

When NOT to use

• Input beta matrix has not been quality-controlled or normalized; apply QC filtering first.
• You expect true biological dimensionality >20 in your data; the 20-component cap is a hard ceiling for reporting, not a recommendation to truncate analysis before batch correction.

Inputs

• normalized beta-valued matrix (rows: CpG probes; columns: samples)
• sample metadata table (optional, for correlating components with batch variables)

Outputs

• component count (maximum 20 when Random Matrix Theory detects >20)
• singular values and corresponding loadings
• scree plot showing variance explained per component
• component correlation summary with batch variables

How to apply

Call champ.SVD() on the normalized beta matrix to perform singular value decomposition analysis. The function automatically applies Random Matrix Theory to detect the number of latent components present in the methylation dataset. If Random Matrix Theory identifies more than 20 latent components, ChAMP implements a component capping mechanism that reports exactly 20 components as the maximum—this is by design to prevent spurious inflation of component count. Inspect the returned component count and visualize the scree plot to assess the proportion of variance explained by each component. Use the component structure to identify batch variables (e.g., processing date, array position, technician) that correlate with the principal components, indicating batch contamination.