Identifying Cancer Subtypes Using a Residual Graph Convolution Model on a Sample Similarity Network

Cancer subtype classification helps us to understand the pathogenesis of cancer and develop new cancer drugs, treatment from which patients would benefit most. Most previous studies detect cancer subtypes by extracting features from individual samples, ignoring their associations with others. We believe that the interactions of cancer samples can help identify cancer subtypes. This work proposes a cancer subtype classification method based on a residual graph convolutional network and a sample similarity network. First, we constructed a sample similarity network regarding cancer gene co-expression patterns. Then, the gene expression profiles of cancer samples as initial features and the sample similarity network were passed into a two-layer graph convolutional network (GCN) model. We introduced the initial features to the GCN model to avoid over-smoothing during the training process. Finally, the classification of cancer subtypes was obtained through a softmax activation function. Our model was applied to breast invasive carcinoma (BRCA), glioblastoma multiforme (GBM) and lung cancer (LUNG) datasets. The accuracy values of our model reached 82.58%, 85.13% and 79.18% for BRCA, GBM and LUNG, respectively, which outperformed the existing methods. The survival analysis of our results proves the significant clinical features of the cancer subtypes identified by our model. Moreover, we can leverage our model to detect the essential genes enriched in gene ontology (GO) terms and the biological pathways related to a cancer subtype.

Power System Small-signal Stability Assessment Model Based on Residual Graph Convolutional Networks

Small-signal stability (SSA) is important to power system security. A data-driven approach is established for rapid prediction of the power system oscillation characteristics. The key of the approach is the Graph Convolution Networks (GCN) with residual mechanism, which works to aggregate features from high-dimension steady-state operation information and is denoted as ResGCN (RESidual GCN) in the paper. The residual mechanism helps to overcome the network degradation phenomenon. Both the oscillation frequency and damping ratio of multiple modes can be predicted by the proposed model. The performance of the proposed scheme as well as its adaptability to the power system topological changes is verified on the IEEE 39 Bus system.

LRGCPND: Predicting Associations between ncRNA and Drug Resistance via Linear Residual Graph Convolution

Accurate inference of the relationship between non-coding RNAs (ncRNAs) and drug resistance is essential for understanding the complicated mechanisms of drug actions and clinical treatment. Traditional biological experiments are time-consuming, laborious, and minor in scale. Although several databases provide relevant resources, computational method for predicting this type of association has not yet been developed. In this paper, we leverage the verified association data of ncRNA and drug resistance to construct a bipartite graph and then develop a linear residual graph convolution approach for predicting associations between non-coding RNA and drug resistance (LRGCPND) without introducing or defining additional data. LRGCPND first aggregates the potential features of neighboring nodes per graph convolutional layer. Next, we transform the information between layers through a linear function. Eventually, LRGCPND unites the embedding representations of each layer to complete the prediction. Results of comparison experiments demonstrate that LRGCPND has more reliable performance than seven other state-of-the-art approaches with an average AUC value of 0.8987. Case studies illustrate that LRGCPND is an effective tool for inferring the associations between ncRNA and drug resistance.

ResGCN: attention-based deep residual modeling for anomaly detection on attributed networks

Effectively detecting anomalous nodes in attributed networks is crucial for the success of many real-world applications such as fraud and intrusion detection. Existing approaches have difficulties with three major issues: sparsity and nonlinearity capturing, residual modeling, and network smoothing. We propose Residual Graph Convolutional Network (ResGCN), an attention-based deep residual modeling approach that can tackle these issues: modeling the attributed networks with GCN allows to capture the sparsity and nonlinearity, utilizing a deep neural network allows direct residual ing from the input, and a residual-based attention mechanism reduces the adverse effect from anomalous nodes and prevents over-smoothing. Extensive experiments on several real-world attributed networks demonstrate the effectiveness of ResGCN in detecting anomalies.

The Critical Node Problem Based on Connectivity Index and Properties of Components on Trees

We deal with the critical node problem (CNP) in a graph [Formula: see text], in which a given number [Formula: see text] of nodes are removed to minimize the connectivity of the residual graph in some sense. Several ways to minimize some connectivity measurement have been proposed, including minimizing the connectivity index(MinCI), maximizing the number of components, minimizing the maximal component size. We propose two classes of CNPs by combining the above measurements together. The objective is to minimize the sum of connectivity indexes and the total degrees in the residual graph. The CNP with an upper-bound [Formula: see text] on the maximal component size is denoted by MSCID-CS and the one with an extra upper-bound [Formula: see text] on the number of components is denoted by MSCID-CSN. They are generalizations of the MinCI, which has been shown NP-hard for general graphs. In particular, we study the case where [Formula: see text] is a tree. Two dynamic programming algorithms are proposed to solve the two classes of CNPs. The time complexities of the algorithms for MSCID-CS and MSCID-CSN are [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is the number of nodes in [Formula: see text]. Computational experiments are presented which show the effectiveness of the algorithms.

A Spanner for the Day After

We show how to construct a $$(1+\varepsilon )$$ ( 1 + ε ) -spanner over a set $${P}$$ P of n points in $${\mathbb {R}}^d$$ R d that is resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters $${\vartheta },\varepsilon \in (0,1)$$ ϑ , ε ∈ ( 0 , 1 ) , the computed spanner $${G}$$ G has $$\begin{aligned} {{\mathcal {O}}}\bigl (\varepsilon ^{-O(d)} {\vartheta }^{-6} n(\log \log n)^6 \log n \bigr ) \end{aligned}$$ O ( ε - O ( d ) ϑ - 6 n ( log log n ) 6 log n ) edges. Furthermore, for anyk, and any deleted set $${{B}}\subseteq {P}$$ B ⊆ P of k points, the residual graph $${G}\setminus {{B}}$$ G \ B is a $$(1+\varepsilon )$$ ( 1 + ε ) -spanner for all the points of $${P}$$ P except for $$(1+{\vartheta })k$$ ( 1 + ϑ ) k of them. No previous constructions, beyond the trivial clique with $${{\mathcal {O}}}(n^2)$$ O ( n 2 ) edges, were known with this resilience property (i.e., only a tiny additional fraction of vertices, $$\vartheta |B|$$ ϑ | B | , lose their distance preserving connectivity). Our construction works by first solving the exact problem in one dimension, and then showing a surprisingly simple and elegant construction in higher dimensions, that uses the one-dimensional construction in a black-box fashion.