Graph clustering and community detection are central problems in modern data mining. The increasing need for analyzing billion-scale data calls for faster and more scalable algorithms for these problems. There are certain trade-offs between the quality and speed of such clustering algorithms. In this paper, we design scalable algorithms that achieve high quality when evaluated based on ground truth. We develop a generalized sequential and shared-memory parallel framework based on the LambdaCC objective (introduced by Veldt et al.), which encompasses modularity and correlation clustering. Our framework consists of highly-optimized implementations that scale to large data sets of billions of edges and that obtain high-quality clusters compared to ground-truth data, on both unweighted and weighted graphs. Our empirical evaluation shows that this framework improves the state-of-the-art trade-offs between speed and quality of scalable community detection. For example, on a 30-core machine with two-way hyper-threading, our implementations achieve orders of magnitude speedups over other correlation clustering baselines, and up to 28.44x speedups over our own sequential baselines while maintaining or improving quality.

We present a framework for the unsupervised learning of neurosymbolic encoders, i.e., encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Such a framework can naturally incorporate symbolic expert knowledge into the learning process and lead to more interpretable and factorized latent representations than fully neural encoders. Also, models learned this way can have downstream impact, as many analysis workflows can benefit from having clean programmatic descriptions. We ground our learning algorithm in the variational autoencoding (VAE) framework, where we aim to learn a neurosymbolic encoder in conjunction with a standard decoder. Our algorithm integrates standard VAE-style training with modern program synthesis techniques. We evaluate our method on learning latent representations for real-world trajectory data from animal biology and sports analytics. We show that our approach offers significantly better separation than standard VAEs and leads to practical gains on downstream tasks.

In this work we propose a new biophysical computational model of brain regions relevant to Parkinson's Disease based on local field potential data collected from the brain of marmoset monkeys. Parkinson's disease is a neurodegenerative disorder, linked to the death of dopaminergic neurons at the substantia nigra pars compacta, which affects the normal dynamics of the basal ganglia-thalamus-cortex neuronal circuit of the brain. Although there are multiple mechanisms underlying the disease, a complete description of those mechanisms and molecular pathogenesis are still missing, and there is still no cure. To address this gap, computational models that resemble neurobiological aspects found in animal models have been proposed. In our model, we performed a data-driven approach in which a set of biologically constrained parameters is optimised using differential evolution. Evolved models successfully resembled single-neuron mean firing rates and spectral signatures of local field potentials from healthy and parkinsonian marmoset brain data. As far as we are concerned, this is the first computational model of Parkinson's Disease based on simultaneous electrophysiological recordings from seven brain regions of Marmoset monkeys. Results show that the proposed model could facilitate the investigation of the mechanisms of PD and support the development of techniques that can indicate new therapies. It could also be applied to other computational neuroscience problems in which biological data could be used to fit multi-scale models of brain circuits.

The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction methods have been proposed but they have hyper-parameters to determine beforehand, which requires strong experience and lead to difficulty in real applications especially when the inter-cluster similarity is high or/and the dataset is large. On the other hand, we often have to determine to use a linear model or a nonlinear model, which still depends on experience. To solve these two problems, in this paper, we present an eigen-gap guided search method for subspace clustering. The main idea is to find the most reliable affinity matrix among a set of candidates constructed by linear and kernel regressions, where the reliability is quantified by the \textit{relative-eigen-gap} of graph Laplacian defined in this paper. We show, theoretically and numerically, that the Laplacian matrix with a larger relative-eigen-gap often yields a higher clustering accuracy and stability. Our method is able to automatically search the best model and hyper-parameters in a pre-defined space. The search space is very easy to determine and can be arbitrarily large, though a relatively compact search space can reduce the highly unnecessary computation. Our method has high flexibility and convenience in real applications, and also has low computational cost because the affinity matrix is not computed by iterative optimization. We extend the method to large-scale datasets such as MNIST, on which the time cost is less than 90s and the clustering accuracy is state-of-the-art. Extensive experiments of natural image clustering show that our method is more stable, accurate, and efficient than baseline methods.

We propose a novel framework for image clustering that incorporates joint representation learning and clustering. Our method consists of two heads that share the same backbone network - a "representation learning" head and a "clustering" head. The "representation learning" head captures fine-grained patterns of objects at the instance level which serve as clues for the "clustering" head to extract coarse-grain information that separates objects into clusters. The whole model is trained in an end-to-end manner by minimizing the weighted sum of two sample-oriented contrastive losses applied to the outputs of the two heads. To ensure that the contrastive loss corresponding to the "clustering" head is optimal, we introduce a novel critic function called "log-of-dot-product". Extensive experimental results demonstrate that our method significantly outperforms state-of-the-art single-stage clustering methods across a variety of image datasets, improving over the best baseline by about 5-7% in accuracy on CIFAR10/20, STL10, and ImageNet-Dogs. Further, the "two-stage" variant of our method also achieves better results than baselines on three challenging ImageNet subsets.

Content delivery networks (CDNs) provide efficient content distribution over the Internet. CDNs improve the connectivity and efficiency of global communications, but their caching mechanisms may be breached by cyber-attackers. Among the security mechanisms, effective anomaly detection forms an important part of CDN security enhancement. In this work, we propose a multi-perspective unsupervised learning framework for anomaly detection in CDNs. In the proposed framework, a multi-perspective feature engineering approach, an optimized unsupervised anomaly detection model that utilizes an isolation forest and a Gaussian mixture model, and a multi-perspective validation method, are developed to detect abnormal behaviors in CDNs mainly from the client Internet Protocol (IP) and node perspectives, therefore to identify the denial of service (DoS) and cache pollution attack (CPA) patterns. Experimental results are presented based on the analytics of eight days of real-world CDN log data provided by a major CDN operator. Through experiments, the abnormal contents, compromised nodes, malicious IPs, as well as their corresponding attack types, are identified effectively by the proposed framework and validated by multiple cybersecurity experts. This shows the effectiveness of the proposed method when applied to real-world CDN data.

Federated learning has emerged as an important paradigm for training machine learning models in different domains. For graph-level tasks such as graph classification, graphs can also be regarded as a special type of data samples, which can be collected and stored in separate local systems. Similar to other domains, multiple local systems, each holding a small set of graphs, may benefit from collaboratively training a powerful graph mining model, such as the popular graph neural networks (GNNs). To provide more motivation towards such endeavors, we analyze real-world graphs from different domains to confirm that they indeed share certain graph properties that are statistically significant compared with random graphs. However, we also find that different sets of graphs, even from the same domain or same dataset, are non-IID regarding both graph structures and node features. To handle this, we propose a graph clustered federated learning (GCFL) framework that dynamically finds clusters of local systems based on the gradients of GNNs, and theoretically justify that such clusters can reduce the structure and feature heterogeneity among graphs owned by the local systems. Moreover, we observe the gradients of GNNs to be rather fluctuating in GCFL which impedes high-quality clustering, and design a gradient sequence-based clustering mechanism based on dynamic time warping (GCFL+). Extensive experimental results and in-depth analysis demonstrate the effectiveness of our proposed frameworks.

Frequently, the parameter space, chosen for shape design or other applications that involve the definition of a surrogate model, present subdomains where the objective function of interest is highly regular or well behaved. So, it could be approximated more accurately if restricted to those subdomains and studied separately. The drawback of this approach is the possible scarcity of data in some applications, but in those, where a quantity of data, moderately abundant considering the parameter space dimension and the complexity of the objective function, is available, partitioned or local studies are beneficial. In this work we propose a new method called local active subspaces (LAS), which explores the synergies of active subspaces with supervised clustering techniques in order to perform a more efficient dimension reduction in the parameter space for the design of accurate response surfaces. We also developed a procedure to exploit the local active subspace information for classification tasks. Using this technique as a preprocessing step onto the parameter space, or output space in case of vectorial outputs, brings remarkable results for the purpose of surrogate modelling.

The neural ordinary differential equation (neural ODE) model has attracted increasing attention in time series analysis for its capability to process irregular time steps, i.e., data are not observed over equally-spaced time intervals. In multi-dimensional time series analysis, a task is to conduct evolutionary subspace clustering, aiming at clustering temporal data according to their evolving low-dimensional subspace structures. Many existing methods can only process time series with regular time steps while time series are unevenly sampled in many situations such as missing data. In this paper, we propose a neural ODE model for evolutionary subspace clustering to overcome this limitation and a new objective function with subspace self-expressiveness constraint is introduced. We demonstrate that this method can not only interpolate data at any time step for the evolutionary subspace clustering task, but also achieve higher accuracy than other state-of-the-art evolutionary subspace clustering methods. Both synthetic and real-world data are used to illustrate the efficacy of our proposed method.

Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic. The clause selection heuristics in such systems are, however, often evaluating clauses in isolation, ignoring other clauses. This has changed recently by equipping the E/ENIGMA system with a graph neural network (GNN) that chooses the next given clause based on its evaluation in the context of previously selected clauses. In this work, we describe several algorithms and experiments with ENIGMA, advancing the idea of contextual evaluation based on learning important components of the graph of clauses.