Put three and three together: Triangle-driven community detection

Community detection has arisen as one of the most relevant topics in the field of graph data mining due to its applications in many fields such as biology, social networks, or network traffic analysis. Although the existing metrics used to quantify the quality of a community work well in general, under some circumstances, they fail at correctly capturing such notion. The main reason is that these metrics consider the internal community edges as a set, but ignore how these actually connect the vertices of the community. We propose the Weighted Community Clustering (WCC), which is a new community metric that takes the triangle instead of the edge as the minimal structural motif indicating the presence of a strong relation in a graph. We theoretically analyse WCC in depth and formally prove, by means of a set of properties, that the maximization of WCC guarantees communities with cohesion and structure. In addition, we propose Scalable Community Detection (SCD), a community detection algorithm based on WCC, which is designed to be fast and scalable on SMP machines, showing experimentally that WCC correctly captures the concept of community in social networks using real datasets. Finally, using ground-truth data, we show that SCD provides better quality than the best disjoint community detection algorithms of the state of the art while performing faster.Peer ReviewedPostprint (author's final draft

Fast Robust PCA on Graphs

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(nlog(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data

A Degeneracy Framework for Scalable Graph Autoencoders

In this paper, we present a general framework to scale graph autoencoders (AE) and graph variational autoencoders (VAE). This framework leverages graph degeneracy concepts to train models only from a dense subset of nodes instead of using the entire graph. Together with a simple yet effective propagation mechanism, our approach significantly improves scalability and training speed while preserving performance. We evaluate and discuss our method on several variants of existing graph AE and VAE, providing the first application of these models to large graphs with up to millions of nodes and edges. We achieve empirically competitive results w.r.t. several popular scalable node embedding methods, which emphasizes the relevance of pursuing further research towards more scalable graph AE and VAE.Comment: International Joint Conference on Artificial Intelligence (IJCAI 2019

Low-Rank Matrices on Graphs: Generalized Recovery & Applications

Many real world datasets subsume a linear or non-linear low-rank structure in a very low-dimensional space. Unfortunately, one often has very little or no information about the geometry of the space, resulting in a highly under-determined recovery problem. Under certain circumstances, state-of-the-art algorithms provide an exact recovery for linear low-rank structures but at the expense of highly inscalable algorithms which use nuclear norm. However, the case of non-linear structures remains unresolved. We revisit the problem of low-rank recovery from a totally different perspective, involving graphs which encode pairwise similarity between the data samples and features. Surprisingly, our analysis confirms that it is possible to recover many approximate linear and non-linear low-rank structures with recovery guarantees with a set of highly scalable and efficient algorithms. We call such data matrices as \textit{Low-Rank matrices on graphs} and show that many real world datasets satisfy this assumption approximately due to underlying stationarity. Our detailed theoretical and experimental analysis unveils the power of the simple, yet very novel recovery framework \textit{Fast Robust PCA on Graphs

Cache Serializability: Reducing Inconsistency in Edge Transactions

Read-only caches are widely used in cloud infrastructures to reduce access latency and load on backend databases. Operators view coherent caches as impractical at genuinely large scale and many client-facing caches are updated in an asynchronous manner with best-effort pipelines. Existing solutions that support cache consistency are inapplicable to this scenario since they require a round trip to the database on every cache transaction. Existing incoherent cache technologies are oblivious to transactional data access, even if the backend database supports transactions. We propose T-Cache, a novel caching policy for read-only transactions in which inconsistency is tolerable (won't cause safety violations) but undesirable (has a cost). T-Cache improves cache consistency despite asynchronous and unreliable communication between the cache and the database. We define cache-serializability, a variant of serializability that is suitable for incoherent caches, and prove that with unbounded resources T-Cache implements this new specification. With limited resources, T-Cache allows the system manager to choose a trade-off between performance and consistency. Our evaluation shows that T-Cache detects many inconsistencies with only nominal overhead. We use synthetic workloads to demonstrate the efficacy of T-Cache when data accesses are clustered and its adaptive reaction to workload changes. With workloads based on the real-world topologies, T-Cache detects 43-70% of the inconsistencies and increases the rate of consistent transactions by 33-58%.Comment: Ittay Eyal, Ken Birman, Robbert van Renesse, "Cache Serializability: Reducing Inconsistency in Edge Transactions," Distributed Computing Systems (ICDCS), IEEE 35th International Conference on, June~29 2015--July~2 201