Similarity Network Fusion (SNF)

For each omics data type (e.g., genomics, proteomics), SNF constructs a patient-by-patient similarity network. A node represents a patient, and edge weights quantify the similarity between patients based on that specific molecular profile. Typically, a scaled exponential similarity kernel is used, where Euclidean distance between patients determines the edge weight. This kernel emphasizes local neighborhoods, making it robust to data heterogeneity and noise. The result is a set of independent networks, each capturing a different molecular view of the same cohort.

The core innovation of SNF is the non-linear, message-passing fusion of individual similarity networks. In each iteration, a network is updated by diffusing information from the other networks while preserving its own strong similarities. This is achieved by interleaving two operations:

• Diffusion: Spreading similarity information along the network's own structure.
• Cross-network averaging: Making the current network more similar to the others. This iterative process converges to a single fused network that captures both shared and complementary signals across all omics layers.

Once the fused patient similarity network is generated, spectral clustering is applied to identify clinically meaningful patient subtypes. This technique uses the eigenvectors of the network's Laplacian matrix to perform dimensionality reduction before clustering. The key advantage is that spectral clustering can capture non-convex cluster shapes and is highly effective on graph-structured data. The number of clusters is often determined by analyzing the eigengap—the difference between consecutive eigenvalues—or by assessing the stability of the clustering solution.

SNF is inherently robust to non-informative features and measurement noise because of its focus on local patient neighborhoods. By constructing networks where only the strongest similarities are retained (via K-nearest neighbors), random noise has minimal impact on the global fused structure. Furthermore, because each omics network is built independently before fusion, SNF does not require complex batch effect normalization across different data types. This makes it particularly effective for integrating data from diverse experimental platforms and laboratories.

A critical strength of SNF is its ability to capture complementary molecular signals. If a subgroup of patients is similar in their methylation profiles but not in their gene expression, the fusion process will strengthen the weak expression-based similarity using the strong methylation signal. This means the final fused network reflects a consensus that is stronger than any single omics view. This property is essential for identifying disease subtypes that are defined by complex, multi-factorial molecular signatures rather than a single genomic aberration.

The patient clusters derived from SNF are typically validated using Kaplan-Meier survival analysis and a log-rank test to determine if the identified subtypes have significantly different clinical outcomes. Strong separation of survival curves indicates that the fused molecular network has captured biologically and clinically meaningful patient stratifications. This step is crucial for translating computational clusters into actionable biomarkers for prognosis or treatment selection in precision medicine.

An unsupervised statistical framework that decomposes variation across multiple omics data types into a sparse set of latent factors. Unlike SNF's network-based fusion, MOFA identifies the principal sources of biological and technical variability, making it highly effective for uncovering hidden drivers of disease heterogeneity.

• Key Strength: Directly interprets factors driving multi-omics variance
• Use Case: Identifying latent sources of patient variability in cancer cohorts

A machine learning paradigm that learns an optimal composite kernel by combining multiple kernel functions, each representing a different omics data type or similarity measure. MKL shares SNF's philosophy of leveraging patient similarities but uses a different mathematical optimization to find the best weighted combination for a specific prediction task.

• Key Strength: Task-specific optimization of data type weights
• Use Case: Supervised classification of disease subtypes using heterogeneous molecular data

A supervised multi-omics integration framework extending sparse generalized canonical correlation analysis. DIABLO simultaneously discriminates between phenotypic outcome classes while selecting correlated molecular features across data blocks. It extends the unsupervised fusion concept of SNF into a discriminative analysis for biomarker identification.

• Key Strength: Simultaneous feature selection and class discrimination
• Use Case: Identifying multi-omics biomarker panels predictive of treatment response

A probabilistic integrative clustering approach that combines multiple clustering results from individual omics data types within a Bayesian framework. While SNF fuses similarity networks, this method finds a robust consensus partition of patient subgroups by statistically modeling the agreement and disagreement between individual omics clusterings.

• Key Strength: Quantifies uncertainty in patient subgroup assignments
• Use Case: Robust identification of clinically meaningful patient subtypes across discordant omics data

A neural network architecture that operates directly on graph-structured data. In multi-omics, GCNs can model molecular interactions by propagating feature information across biological networks like protein-protein interaction graphs. This provides a deep learning complement to SNF's spectral graph approach for integrating structured biological knowledge.

• Key Strength: Learns hierarchical representations from graph topology
• Use Case: Predicting patient outcomes by integrating omics data with known molecular interaction networks

A dimensionality reduction technique that decomposes a non-negative data matrix into additive, parts-based representations. Applied to multi-omics, NMF identifies coherent molecular signatures and mutational processes across data types. It offers an alternative to SNF's network-based logic by focusing on additive latent components rather than patient similarities.

• Key Strength: Highly interpretable, parts-based decomposition
• Use Case: Extracting mutational signatures and expression programs from integrated cancer genomics data