In this paper, we study the problem of k-center clustering with outliers. The problem has many important applications in real world, but the presence of outliers can significantly increase the computational complexity. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez's algorithm, that was developed for solving the ordinary k-center clustering problem. Based on some novel observations, we show that a simple randomized version of this greedy strategy actually can handle outliers efficiently. We further show that this randomized greedy approach also yields small coreset for the problem in doubling metrics (even if the doubling dimension is not given), which can greatly reduce the computational complexity. Moreover, together with the partial clustering framework proposed by Guha et al. (2019), we prove that our coreset method can be applied to distributed data with a low communication complexity. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower complexities comparing with the existing methods.

In this article, we are going to talk in detail about hierarchical clustering like Why we need hierarchical clustering?, How hierarchical clustering works?, Types of hierarchical clustering?, On which dataset it is applicable? . Before moving forward to hierarchal clustering, we should know why we are talking about hierarchical clustering? even when we have K Means clustering. If you have studied K Means then you know that this algorithm works on the distance to centroid method to create a cluster. Although it works well if you have well defined boundaries type dataset that has less outliers. In above picture, K Means is working well but when we move towards some complex datasets then the problem arises and K Means don't work properly. As you can see in below picture, K Means is failing in making clusters.

Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of high-dimensional data. Diffusion condensation is constructed as a time-inhomogeneous process where each step first computes and then applies a diffusion operator to the data. We theoretically analyze the convergence and evolution of this process from geometric, spectral, and topological perspectives. From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel. Our spectral results are of particular interest since most of the literature on data diffusion is focused on homogeneous processes. From a topological perspective, we show diffusion condensation generalizes centroid-based hierarchical clustering. We use this perspective to obtain a bound based on the number of data points, independent of their location. To understand the evolution of the data geometry beyond convergence, we use topological data analysis. We show that the condensation process itself defines an intrinsic condensation homology. We use this intrinsic topology as well as the ambient persistent homology of the condensation process to study how the data changes over diffusion time. We demonstrate both types of topological information in well-understood toy examples. Our work gives theoretical insights into the convergence of diffusion condensation, and shows that it provides a link between topological and geometric data analysis.

With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate time series and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this paper, we propose a group-based method to cluster a collection of multivariate time series via a Bayesian mixture of smoothing splines. Our method assumes each multivariate time series is a mixture of multiple components with different mixing weights. Time-independent covariates are assumed to be associated with the mixture components and are incorporated via logistic weights of a mixture-of-experts model. We formulate this approach under a fully Bayesian framework using Gibbs sampling where the number of components is selected based on a deviance information criterion. The proposed method is compared to existing methods via simulation studies and is applied to a study on functional near-infrared spectroscopy (fNIRS), which aims to understand infant emotional reactivity and recovery from stress. The results reveal distinct patterns of brain activity, as well as associations between these patterns and selected covariates.

Benefiting from the intrinsic supervision information exploitation capability, contrastive learning has achieved promising performance in the field of deep graph clustering recently. However, we observe that two drawbacks of the positive and negative sample construction mechanisms limit the performance of existing algorithms from further improvement. 1) The quality of positive samples heavily depends on the carefully designed data augmentations, while inappropriate data augmentations would easily lead to the semantic drift and indiscriminative positive samples. 2) The constructed negative samples are not reliable for ignoring important clustering information. To solve these problems, we propose a Cluster-guided Contrastive deep Graph Clustering network (CCGC) by mining the intrinsic supervision information in the high-confidence clustering results. Specifically, instead of conducting complex node or edge perturbation, we construct two views of the graph by designing special Siamese encoders whose weights are not shared between the sibling sub-networks. Then, guided by the high-confidence clustering information, we carefully select and construct the positive samples from the same high-confidence cluster in two views. Moreover, to construct semantic meaningful negative sample pairs, we regard the centers of different high-confidence clusters as negative samples, thus improving the discriminative capability and reliability of the constructed sample pairs. Lastly, we design an objective function to pull close the samples from the same cluster while pushing away those from other clusters by maximizing and minimizing the cross-view cosine similarity between positive and negative samples. Extensive experimental results on six datasets demonstrate the effectiveness of CCGC compared with the existing state-of-the-art algorithms.

This article charts the work of a 4 month project aimed at automatically identifying patterns of tweets' popularity evolution using Machine Learning and Deep Learning techniques. To apprehend both the data and the extent of the problem, a straightforward clustering algorithm based on a point to point distance is used. Then, in an attempt to refine the algorithm, various analyses especially using feature extraction techniques are conducted. Although the algorithm eventually fails to automate such a task, this exercise raises a complex but necessary issue touching on the impact of virality on social networks.

Text clustering and topic extraction are two important tasks in text mining. Usually, these two tasks are performed separately. For topic extraction to facilitate clustering, we can first project texts into a topic space and then perform a clustering algorithm to obtain clusters. To promote topic extraction by clustering, we can first obtain clusters with a clustering algorithm and then extract cluster-specific topics. However, this naive strategy ignores the fact that text clustering and topic extraction are strongly correlated and follow a chicken-and-egg relationship. Performing them separately fails to make them mutually benefit each other to achieve the best overall performance. In this paper, we propose an unsupervised text clustering and topic extraction framework (ClusTop) which integrates text clustering and topic extraction into a unified framework and can achieve high-quality clustering result and extract topics from each cluster simultaneously. Our framework includes four components: enhanced language model training, dimensionality reduction, clustering and topic extraction, where the enhanced language model can be viewed as a bridge between clustering and topic extraction. On one hand, it provides text embeddings with a strong cluster structure which facilitates effective text clustering; on the other hand, it pays high attention on the topic related words for topic extraction because of its self-attention architecture. Moreover, the training of enhanced language model is unsupervised. Experiments on two datasets demonstrate the effectiveness of our framework and provide benchmarks for different model combinations in this framework.

Application of machine learning may be understood as deriving new knowledge for practical use through explaining accumulated observations, training set. Peirce used the term abduction for this kind of inference. Here I formalize the concept of abduction for real valued hypotheses, and show that 14 of the most popular textbook ML learners (every learner I tested), covering classification, regression and clustering, implement this concept of abduction inference. The approach is proposed as an alternative to statistical learning theory, which requires an impractical assumption of indefinitely increasing training set for its justification.

Clustering is one of the most studied problems in machine learning with various applications in analyzing and visualizing large datasets. There are various models and technique to obtain a partition of elements, such that elements belonging to different partitions are dissimilar to each other and the elements in the same partition are very similar to each other. The problem of correlation clustering, introduced in [1], is known to be an NP-hard problem for the disagree minimization. Therefore, several different approximation solutions based on its IP formulation exist in the literature. Recently, the idea of a 2-approximation algorithm in [1] is extended in [4] for constructing a O (1)-approximation algorithm. The experiments in [4] show acceptable performance for this algorithm in practice, although its theoretical guarantee can be too high, e.g. 1 442 for β = λ =

Mixtures of von Mises-Fisher distributions can be used to cluster data on the unit hypersphere. This is particularly adapted for high-dimensional directional data such as texts. We propose in this article to estimate a von Mises mixture using a l 1 penalized likelihood. This leads to sparse prototypes that improve clustering interpretability. We introduce an expectation-maximisation (EM) algorithm for this estimation and explore the trade-off between the sparsity term and the likelihood one with a path following algorithm. The model's behaviour is studied on simulated data and, we show the advantages of the approach on real data benchmark. We also introduce a new data set on financial reports and exhibit the benefits of our method for exploratory analysis.