Multi-Modal Imaging Genetics Data Fusion via a Hypergraph-Based Manifold Regularization: Application to Schizophrenia Study

Abstract

Recent studies show that multi-modal data fusion techniques combine information from diverse sources for comprehensive diagnosis and prognosis of complex brain disorder, often resulting in improved accuracy compared to single-modality approaches. However, many existing data fusion methods extract features from homogeneous networs, ignoring heterogeneous structural information among multiple modalities. To this end, we propose a Hypergraph-based Multi-modal data Fusion algorithm, namely HMF. Specifically, we first generate a hypergraph similarity matrix to represent the high-order relationships among subjects, and then enforce the regularization term based upon both the inter- and intra-modality relationships of the subjects. Finally, we apply HMF to integrate imaging and genetics datasets. Validation of the proposed method is performed on both synthetic data and real samples from schizophrenia study. Results show that our algorithm outperforms several competing methods, and reveals significant interactions among risk genes, environmental factors and abnormal brain regions.

Fig. 1.

(a) A hypergraph G with vertex set V, hyperedge set E and hyperedge weight vector ψ. (b) Bipartite representation of hypergraph G. (c) The incidence matrix H of hypergraph G.

Fig. 2.

The illustration of the similarity relationship within and between different modalities.

Fig. 3.

The main framework of the proposed algorithm.

Fig. 4.

The classification performance of the proposed algorithm with respect to different parameters’ settings. (a) α ∈ {10⁻², 2 × 10⁻², 3 × 10⁻², …, 10⁻¹}, β ∈ {10⁻³, 2 × 10⁻³, 3 × 10⁻³, …, 10⁻²}, λ₁, λ₂, λ₃ = 0 and Ḱ = 9. (b) α = 0.04, β = 0.006, λ₁ = 0.0002, λ₂ = 0.0004, λ₃ = 0.0005 and Ḱ ∈ {7, 8, …, 12}. (c) α = 0.04, β = 0.006, Ḱ = 9, λ₁, λ₂ ∈ {10⁻⁴, 2 × 10⁻⁴, …, 6 × 10⁻⁴} and λ₃ ∈ {3 × 10⁻⁴, 4 × 10⁻⁴, …, 8 × 10⁻⁴}. (c) α = 0.04, β = 0.006, λ₁ = 0.0002, λ₂ = 0.0004, λ₃ = 0.0005 and Ḱ ∈ {7, 8, …, 12}.

Fig. 5.

(a) The comparison of classification accuracies by HMF and 6 other algorithms. (b) The classification accuracies of HMF tested on different combinations of datasets.

Fig. 6.

(a) The error rates of HMF when testing with the combination of different datasets and added with 5 different SNRs. (b) The error rates of 7 algorithms when testing on three−view datasets with 5 different SNRs.

Fig. 7.

The ROC curves with 7 compared algorithms testing on the MCIC dataset.

Fig. 8.

Visualization of 15 abnormal brain ROIs.