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 dij:
W(v)_ij = exp( -d_ij² / (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. The four small heatmaps show each layer's own affinity matrix (rows/columns re-ordered by true subtype), so you can watch the block-diagonal subtype structure sharpen in the fused panel as T rises even when a single noisy layer shows almost none. The line chart tracks a true-subtype affinity ratio (within-subtype vs between-subtype fused similarity) at every T from 0 to 20 in one pass, with the current T marked.
- 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; the network graph, heatmaps and readouts are re-weighted from P_fused at the chosen T.
- 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 2D k-means on the graph layout to color-code the discovered patient subtypes.
- Network graph — drag to pan, scroll/pinch to zoom the force-directed layout.
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.