Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as batch algorithms that incur a high overhead as they cluster all the objects in the database from scratch or assume an incremental workload. In practice, database objects are updated, added, and removed from databases continuously which makes previous results stale. Running batch algorithms is infeasible in such scenarios as it would incur a significant overhead if performed continuously. This is particularly the case for high-velocity scenarios such as ones in Internet of Things applications. In this paper, we tackle the problem of clustering in high-velocity dynamic scenarios, where the objects are continuously updated, inserted, and deleted. Specifically, we propose a generally dynamic approach to clustering that utilizes previous clustering results. Our system, DynamicC, uses a machine learning model that is augmented with an existing batch algorithm. The DynamicC model trains by observing the clustering decisions made by the batch algorithm. After training, the DynamicC model is usedin cooperation with the batch algorithm to achieve both accurate and fast clustering decisions. The experimental results on four real-world and one synthetic datasets show that our approach has a better performance compared to the state-of-the-art method while achieving similarly accurate clustering results to the baseline batch algorithm.

In the pharmaceutical industry, the maintenance of production machines must be audited by the regulator. In this context, the problem of predictive maintenance is not when to maintain a machine, but what parts to maintain at a given point in time. The focus shifts from the entire machine to its component parts and prediction becomes a classification problem. In this paper, we focus on rolling-elements bearings and we propose a framework for predicting their degradation stages automatically. Our main contribution is a k-means bearing lifetime segmentation method based on high-frequency bearing vibration signal embedded in a latent low-dimensional subspace using an AutoEncoder. Given high-frequency vibration data, our framework generates a labeled dataset that is used to train a supervised model for bearing degradation stage detection. Our experimental results, based on the FEMTO Bearing dataset, show that our framework is scalable and that it provides reliable and actionable predictions for a range of different bearings.

The particle filter (PF) is a powerful inference tool widely used to estimate the filtering distribution in non-linear and/or non-Gaussian problems. To overcome the curse of dimensionality of PF, the block PF (BPF) inserts a blocking step to partition the state space into several subspaces or blocks of smaller dimension so that the correction and resampling steps can be performed independently on each subspace. Using blocks of small size reduces the variance of the filtering distribution estimate, but in turn the correlation between blocks is broken and a bias is introduced. When the dependence relationships between state variables are unknown, it is not obvious to decide how to split the state space into blocks and a significant error overhead may arise from a poor choice of partitioning. In this paper, we formulate the partitioning problem in the BPF as a clustering problem and we propose a state space partitioning method based on spectral clustering (SC). We design a generalized BPF algorithm that contains two new steps: (i) estimation of the state vector correlation matrix from predicted particles, (ii) SC using this estimate as the similarity matrix to determine an appropriate partition. In addition, a constraint is imposed on the maximal cluster size to prevent SC from providing too large blocks. We show that the proposed method can bring together in the same blocks the most correlated state variables while successfully escaping the curse of dimensionality.

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under population-level constraints. These constraints are specified by additional information available in the form of auxiliary categorical node attributes. In this paper, we consider a scenario where these attributes may not be observable, but manifest as latent features of an auxiliary graph. Motivated by this, we study constrained spectral clustering with the aim of finding balanced clusters in a given \textit{similarity graph} $\mathcal{G}$, such that each individual is adequately represented with respect to an auxiliary graph $\mathcal{R}$ (we refer to this as representation graph). We propose an individual-level balancing constraint that formalizes this idea. Our work leads to an interesting stochastic block model that not only plants the given partitions in $\mathcal{G}$ but also plants the auxiliary information encoded in the representation graph $\mathcal{R}$. We develop unnormalized and normalized variants of spectral clustering in this setting. These algorithms use $\mathcal{R}$ to find clusters in $\mathcal{G}$ that approximately satisfy the proposed constraint. We also establish the first statistical consistency result for constrained spectral clustering under individual-level constraints for graphs sampled from the above-mentioned variant of the stochastic block model. Our experimental results corroborate our theoretical findings.

We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of the polyhedron to be refined. This strategy is a variation of the well known Centroidal Voronoi Tessellation. The second one employs Convolutional Neural Networks to classify the "shape" of an element so that "ad-hoc" refinement criteria can be defined. This strategy can be used to enhance existing refinement strategies, including the k-means strategy, at a low online computational cost. We test the proposed algorithms considering two families of finite element methods that support arbitrarily shaped polyhedral elements, namely the Virtual Element Method (VEM) and the Polygonal Discontinuous Galerkin (PolyDG) method. We demonstrate that these strategies do preserve the structure and the quality of the underlaying grids, reducing the overall computational cost and mesh complexity.

We introduce a class of clustering procedures which includes $k$-means and $k$-medians, as well as variants of these where the domain of the cluster centers can be chosen adaptively (for example, $k$-medoids) and where the number of cluster centers can be chosen adaptively (for example, according to the elbow method). In the non-parametric setting and assuming only the finiteness of certain moments, we show that all clustering procedures in this class are strongly consistent under IID samples. Our method of proof is to directly study the continuity of various deterministic maps associated with these clustering procedures, and to show that strong consistency simply descends from analogous strong consistency of the empirical measures. In the adaptive setting, our work provides a strong consistency result that is the first of its kind. In the non-adaptive setting, our work strengthens Pollard's classical result by dispensing with various unnecessary technical hypotheses, by upgrading the particular notion of strong consistency, and by using the same methods to prove further limit theorems.

Practical tools for clustering streaming data must be fast enough to handle the arrival rate of the observations. Typically, they also must adapt on the fly to possible lack of stationarity; i.e., the data statistics may be time-dependent due to various forms of drifts, changes in the number of clusters, etc. The Dirichlet Process Mixture Model (DPMM), whose Bayesian nonparametric nature allows it to adapt its complexity to the data, seems a natural choice for the streaming-data case. In its classical formulation, however, the DPMM cannot capture common types of drifts in the data statistics. Moreover, and regardless of that limitation, existing methods for online DPMM inference are too slow to handle rapid data streams. In this work we propose adapting both the DPMM and a known DPMM sampling-based non-streaming inference method for streaming-data clustering. We demonstrate the utility of the proposed method on several challenging settings, where it obtains state-of-the-art results while being on par with other methods in terms of speed.

Subtyping of Alzheimer's disease (AD) can facilitate diagnosis, treatment, prognosis and disease management. It can also support the testing of new prevention and treatment strategies through clinical trials. In this study, we employed spectral clustering to cluster 29,922 AD patients in the OneFlorida Data Trust using their longitudinal EHR data of diagnosis and conditions into four subtypes. In addition, according to the results of various statistical tests, these subtypes are also significantly different with respect to demographics, mortality, and prescription medications after the AD diagnosis. This study could potentially facilitate early detection and personalized treatment of AD as well as data-driven generalizability assessment of clinical trials for AD. Introduction Alzheimer's disease (AD) is a progressive neurodegenerative disorder that affects an estimated 6.2 million Americans age 65 and older in 2021. This number is likely to reach 13.8 million by 2060.

Markov chain Monte Carlo (MCMC) methods are often used in clustering since they guarantee asymptotically exact expectations in the infinite-time limit. In finite time, though, slow mixing often leads to poor performance. Modern computing environments offer massive parallelism, but naive implementations of parallel MCMC can exhibit substantial bias. In MCMC samplers of continuous random variables, Markov chain couplings can overcome bias. But these approaches depend crucially on paired chains meetings after a small number of transitions. We show that straightforward applications of existing coupling ideas to discrete clustering variables fail to meet quickly. This failure arises from the "label-switching problem": semantically equivalent cluster relabelings impede fast meeting of coupled chains. We instead consider chains as exploring the space of partitions rather than partitions' (arbitrary) labelings. Using a metric on the partition space, we formulate a practical algorithm using optimal transport couplings. Our theory confirms our method is accurate and efficient. In experiments ranging from clustering of genes or seeds to graph colorings, we show the benefits of our coupling in the highly parallel, time-limited regime.

We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's. We study both continuous-space and discrete-space (i.e., medoid) variants and establish their consistency.