Similarity Network Fusion: Multi-Omics Patient Subtyping

Omics Layers (patient similarity networks)

Genomic (SNP)

Transcriptomic (RNA-seq)

Proteomic (noisy)

Fusion Controls

Fusion iterations T 0

KNN neighborhood K 8

Detected subtypes k 3

Live Readouts

Fusion iteration

0 / 20

Active layers

Cluster separation

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Subtype purity

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How it works

Each of N patients has a feature vector in every omics layer v (genomic, transcriptomic, proteomic). Within a layer, pairwise similarity uses a self-tuning Gaussian kernel on the Euclidean distance d_ij:

W(v)_ij = exp( -d_ij² / (μ · ε_i · ε_j) )
ε_i = mean distance from patient i to its K nearest neighbors

Two matrices are derived per layer: a fully normalized affinity P(v) (global) and a KNN-sparsified, row-normalized S(v) (local). Similarity Network Fusion (Wang et al., 2014) then iteratively projects each view through the *others'* status:

P(v)_{t+1} = S(v) · [ (1/(V-1)) Σ_{u≠v} P(u)_t ] · S(v)ᵀ
P_fused    = (1/V) Σ_v P(v)_T

Each round, a weak or noisy layer (e.g. a proteomic assay with more measurement noise) is "corrected" by the consensus structure of the other views — signal that is real in ≥2 layers survives and strengthens; layer-specific noise that appears in only one view is washed out. After T iterations, spring-embedding the fused network pulls its true subtypes into visibly separated clusters, something no single layer shows on its own.

Layer toggles — remove a view from the fusion sum entirely, to see how much a layer contributes (or hurts) the final subtype separation.
Fusion iterations T — advances the cross-diffusion above; edges are re-weighted from P_fused at the chosen T and the node layout relaxes toward the new structure.
KNN neighborhood K — controls how many neighbors define each patient's local affinity S(v); too small loses structure, too large blurs cluster boundaries.
Detected subtypes k — runs k-means on the fused similarity layout to color-code the discovered patient subtypes.

Real-world relevance: this is the actual algorithm behind cancer-subtype discovery projects such as TCGA Pan-Cancer, where SNF combined mRNA, miRNA and DNA-methylation similarity networks to reveal tumor subtypes invisible to any single molecular layer.

Subtype A Subtype B Subtype C+

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