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.

Predicting the political leaning of social media users is an increasingly popular task, given its usefulness for electoral forecasts, opinion dynamics models and for studying the political dimension of polarization and disinformation. Here, we propose a novel unsupervised technique for learning fine-grained political leaning from the textual content of social media posts. Our technique leverages a deep neural network for learning latent political ideologies in a representation learning task. Then, users are projected in a low-dimensional ideology space where they are subsequently clustered. The political leaning of a user is automatically derived from the cluster to which the user is assigned. We evaluated our technique in two challenging classification tasks and we compared it to baselines and other state-of-the-art approaches. Our technique obtains the best results among all unsupervised techniques, with micro F1 = 0.426 in the 8-class task and micro F1 = 0.772 in the 3-class task. Other than being interesting on their own, our results also pave the way for the development of new and better unsupervised approaches for the detection of fine-grained political leaning.

When we need to cluster a data set, the first couple of algorithms we might look into are K means, DB scan, or hierarchical clustering algorithm. Those classic clustering algorithms always treat each data point as a dot. However, those data points usually have size or boundary(bounding box) in real life. Ignoring the edge of points might cause further bias. RVN algorithm is a method that considers points and the bounding box of each point.

Development of new algorithms in the area of machine learning, especially clustering, comparative studies of such algorithms as well as testing according to software engineering principles requires availability of labeled data sets. While standard benchmarks are made available, a broader range of such data sets is necessary in order to avoid the problem of overfitting. In this context, theoretical works on axiomatization of clustering algorithms, especially axioms on clustering preserving transformations are quite a cheap way to produce labeled data sets from existing ones. However, the frequently cited axiomatic system of Kleinberg:2002, as we show in this paper, is not applicable for finite dimensional Euclidean spaces, in which many algorithms like $k$-means, operate. In particular, the so-called outer-consistency axiom fails upon making small changes in datapoint positions and inner-consistency axiom is valid only for identity transformation in general settings. Hence we propose an alternative axiomatic system, in which Kleinberg's inner consistency axiom is replaced by a centric consistency axiom and outer consistency axiom is replaced by motion consistency axiom. We demonstrate that the new system is satisfiable for a hierarchical version of $k$-means with auto-adjusted $k$, hence it is not contradictory. Additionally, as $k$-means creates convex clusters only, we demonstrate that it is possible to create a version detecting concave clusters and still the axiomatic system can be satisfied. The practical application area of such an axiomatic system may be the generation of new labeled test data from existent ones for clustering algorithm testing. %We propose the gravitational consistency as a replacement which does not have this deficiency.

Existing work (Ji and Grishman, we consider the attention weight between 2008; McClosky et al., 2011; Li et al., 2013; two event mentions as a learned similarity, and we Chen et al., 2015; Du and Cardie, 2020; Li et al., ensure that the attention mechanism learns to align 2021a) traditionally uses a predefined list of event similar events using a semi-supervised contrastive types and their respective annotations to learn an loss. By doing this, we are able to leverage the event extraction model. However, these annotations large variety of semantic information in pretrained are both expensive and time-consuming to language models for clustering unseen types by using create. This problem is amplified when considering a trained attention head. Unlike (Huang and specialization-intensive domains such as scientific Ji, 2020), we are able to separate clustering from literature, which requires years of specialized experience learning, allowing specific task-suited clustering to understand even a specific niche. For algorithms to be selected.