Hierarchical Pooling in Graph Neural Networks to Enhance Classification Performance in Large Datasets

Deep learning methods predicated on convolutional neural networks and graph neural networks have enabled significant improvement in node classification and prediction when applied to graph representation with learning node embedding to effectively represent the hierarchical properties of graphs. An interesting approach (DiffPool) utilises a differentiable graph pooling technique which learns ‘differentiable soft cluster assignment’ for nodes at each layer of a deep graph neural network with nodes mapped on sets of clusters. However, effective control of the learning process is difficult given the inherent complexity in an ‘end-to-end’ model with the potential for a large number parameters (including the potential for redundant parameters). In this paper, we propose an approach termed FPool, which is a development of the basic method adopted in DiffPool (where pooling is applied directly to node representations). Techniques designed to enhance data classification have been created and evaluated using a number of popular and publicly available sensor datasets. Experimental results for FPool demonstrate improved classification and prediction performance when compared to alternative methods considered. Moreover, FPool shows a significant reduction in the training time over the basic DiffPool framework.

Deep Graph Mapper: Seeing Graphs Through the Neural Lens

Graph summarization has received much attention lately, with various works tackling the challenge of defining pooling operators on data regions with arbitrary structures. These contrast the grid-like ones encountered in image inputs, where techniques such as max-pooling have been enough to show empirical success. In this work, we merge the Mapper algorithm with the expressive power of graph neural networks to produce topologically grounded graph summaries. We demonstrate the suitability of Mapper as a topological framework for graph pooling by proving that Mapper is a generalization of pooling methods based on soft cluster assignments. Building upon this, we show how easy it is to design novel pooling algorithms that obtain competitive results with other state-of-the-art methods. Additionally, we use our method to produce GNN-aided visualisations of attributed complex networks.

Branch-Price-and-Cut for the Soft-Clustered Capacitated Arc-Routing Problem

The soft-clustered capacitated arc-routing problem (SoftCluCARP) is a variant of the classical capacitated arc-routing problem. The only additional constraint is that the set of required edges, that is, the streets to be serviced, is partitioned into clusters, and feasible routes must respect the soft-cluster constraint, that is, all required edges of the same cluster must be served by the same vehicle. In this article, we design an effective branch-price-and-cut algorithm for the exact solution of the SoftCluCARP. Its new components are a metaheuristic and branch-and-cut-based solvers for the solution of the column-generation subproblem, which is a profitable rural clustered postman tour problem. Although postman problems with these characteristics have been studied before, there is one fundamental difference here: clusters are not necessarily vertex-disjoint, which prohibits many preprocessing and modeling approaches for clustered postman problems from the literature. We present an undirected and a windy formulation for the pricing subproblem and develop and computationally compare two corresponding branch-and-cut algorithms. Cutting is also performed at the master-program level using subset-row inequalities for subsets of size up to five. For the first time, these nonrobust cuts are incorporated into MIP-based routing subproblem solvers using two different modeling approaches. In several computational studies, we calibrate the individual algorithmic components. The final computational experiments prove that the branch-price-and-cut algorithm equipped with these problem-tailored components is effective: The largest SoftCluCARP instances solved to optimality have more than 150 required edges or more than 50 clusters.

Simple and effective neural-free soft-cluster embeddings for item cold-start recommendations

Recommender systems are widely used in online platforms for easy exploration of personalized content. The best available recommendation algorithms are based on using the observed preference information among collaborating entities. A significant challenge in recommender system continues to be item cold-start recommendation: how to effectively recommend items with no observed or past preference information. Here we propose a two-stage algorithm based on soft clustering to provide an efficient solution to this problem. The crux of our approach lies in representing the items as soft-cluster embeddings in the space spanned by the side-information associated with the items. Though many item embedding approaches have been proposed for item cold-start recommendations in the past—and simple as they might appear—to the best of our knowledge, the approach based on soft-cluster embeddings has not been proposed in the research literature. Our experimental results on four benchmark datasets conclusively demonstrate that the proposed algorithm makes accurate recommendations in item cold-start settings compared to the state-of-the-art algorithms according to commonly used ranking metrics like Normalized Discounted Cumulative Gain (NDCG) and Mean Average Precision (MAP). The performance of our proposed algorithm on the MovieLens 20M dataset clearly demonstrates the scalability aspect of our algorithm compared to other popular algorithms. We also propose the metric Cold Items Precision (CIP) to quantify the ability of a system to recommend cold-start items. CIP can be used in conjunction with relevance ranking metrics like NDCG and MAP to measure the effectiveness of the cold-start recommendation algorithm.

ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations

Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4%, compared to current sparse hierarchical state-of-the-art method. We make the source code of ASAP available to encourage reproducible research 1.

Molecular Dynamics Simulation of the Influence Factors of Particle Depositing on Surface during Cold Spray

Using molecular dynamics simulation, the influence factors of deposition process, such as cluster incident velocity, material hardness and so on, were studied. The cluster incident velocity influences the combination strength between the substrate and cluster greatly. The higher the cluster velocity is, the stronger the combination strength is, and the faster the cluster forms the crystalline structure like the substrate. Higher temperature of the substrate and the cluster will improve the combination strength. The size of the cluster influences the effect of combination as well. The larger the cluster is, the stronger the combination strength is. If a soft cluster impacts on a hard substrate, because of lack of enough deformation at the interface of the substrate, it is difficult to form the effective combination. If a hard cluster impacts on a soft substrate, the lattice defects occur and the cluster takes a longer time to form crystalline structure.