This article will answer these questions. Apart from all this, we will also learn more about K-means clustering and its implementation by defining K-means fit function. Clustering is an unsupervised learning technique. It is used to group different data points based on similar features or characteristics. For example, A company wants to know to whom they should display a particular ad such the chances of clicking it increases. Now suppose you have all the user's clusters with the ads each group mostly clicks.

Datasets containing natural clusters or batch effects are ubiquitous across most biological applications, necessitating the advent of prediction algorithms that can adapt to the particular challenges of handling possible heterogeneity in the distribution of the features. Numerous learning algorithms have been created to address the setting in which the covariate-outcome relationship varies across clusters, including mixed-effects regression, sequential ensembling approaches, the mixture of experts framework, and dynamic co-clustering learning algorithms [1] [2] [3]. This context is in fact analogous to the multi-study framework formalized by Patil and Parmigiani (2018), in which separate clusters can be thought of as individual studies [4]. Multi-study learning handles the availability of multiple training studies that measure the same outcome and many of the same covariates by building ensembles of learners each trained on a single study to form the final predictor. Several learning algorithms have been shown to be highly effective in this scheme, including regularized regression, neural networks, and Random Forest.

Unsupervised domain adaptation has been widely adopted to generalize models for unlabeled data in a target domain, given labeled data in a source domain, whose data distributions differ from the target domain. However, existing works are inapplicable to face recognition under privacy constraints because they require sharing sensitive face images between two domains. To address this problem, we propose a novel unsupervised federated face recognition approach (FedFR). FedFR improves the performance in the target domain by iteratively aggregating knowledge from the source domain through federated learning. It protects data privacy by transferring models instead of raw data between domains. Besides, we propose a new domain constraint loss (DCL) to regularize source domain training. DCL suppresses the data volume dominance of the source domain. We also enhance a hierarchical clustering algorithm to predict pseudo labels for the unlabeled target domain accurately. To this end, FedFR forms an end-to-end training pipeline: (1) pre-train in the source domain; (2) predict pseudo labels by clustering in the target domain; (3) conduct domain-constrained federated learning across two domains. Extensive experiments and analysis on two newly constructed benchmarks demonstrate the effectiveness of FedFR. It outperforms the baseline and classic methods in the target domain by over 4% on the more realistic benchmark. We believe that FedFR will shed light on applying federated learning to more computer vision tasks under privacy constraints.

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques crucially rely on accurate estimation of pairwise distance between records. However, computing exact features of the records, and their pairwise distances is often challenging, and sometimes not possible. We circumvent this challenge by leveraging weak supervision in the form of a comparison oracle that compares the relative distance between the queried points such as `Is point u closer to v or w closer to x?'. However, it is possible that some queries are easier to answer than others using a comparison oracle. We capture this by introducing two different noise models called adversarial and probabilistic noise. In this paper, we study various problems that include finding maximum, nearest/farthest neighbor search under these noise models. Building upon the techniques we develop for these comparison operations, we give robust algorithms for k-center clustering and agglomerative hierarchical clustering. We prove that our algorithms achieve good approximation guarantees with a high probability and analyze their query complexity. We evaluate the effectiveness and efficiency of our techniques empirically on various real-world datasets.

This work addresses the problem of optimizing communications between server and clients in federated learning (FL). Current sampling approaches in FL are either biased, or non optimal in terms of server-clients communications and training stability. To overcome this issue, we introduce \textit{clustered sampling} for clients selection. We prove that clustered sampling leads to better clients representatitivity and to reduced variance of the clients stochastic aggregation weights in FL. Compatibly with our theory, we provide two different clustering approaches enabling clients aggregation based on 1) sample size, and 2) models similarity. Through a series of experiments in non-iid and unbalanced scenarios, we demonstrate that model aggregation through clustered sampling consistently leads to better training convergence and variability when compared to standard sampling approaches. Our approach does not require any additional operation on the clients side, and can be seamlessly integrated in standard FL implementations. Finally, clustered sampling is compatible with existing methods and technologies for privacy enhancement, and for communication reduction through model compression.

This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph stochastic block model (d-HSBM), wherein n nodes are partitioned into k disjoint communities with relative sizes (p1,..., pk). Each subset of nodes with cardinality d is generated independently as an order-d hyperedge with a certain probability that depends on the ground-truth communities that the d nodes belong to. The goal is to exactly recover the k hidden communities based on the observed hypergraph. We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below the threshold (apart from a small regime of parameters that will be specified precisely). This threshold is represented in terms of a quantity which we term as the generalized Chernoff-Hellinger divergence between communities. Our result for this general model recovers prior results for the standard SBM and d-HSBM with two symmetric communities as special cases. En route to proving our achievability results, we develop a polynomial-time two-stage algorithm that meets the threshold. The first stage adopts a certain hypergraph spectral clustering method to obtain a coarse estimate of communities, and the second stage refines each node individually via local refinement steps to ensure exact recovery.

Multi-view clustering (MVC) has been extensively studied to collect multiple source information in recent years. One typical type of MVC methods is based on matrix factorization to effectively perform dimension reduction and clustering. However, the existing approaches can be further improved with following considerations: i) The current one-layer matrix factorization framework cannot fully exploit the useful data representations. ii) Most algorithms only focus on the shared information while ignore the view-specific structure leading to suboptimal solutions. iii) The partition level information has not been utilized in existing work. To solve the above issues, we propose a novel multi-view clustering algorithm via deep matrix decomposition and partition alignment. To be specific, the partition representations of each view are obtained through deep matrix decomposition, and then are jointly utilized with the optimal partition representation for fusing multi-view information. Finally, an alternating optimization algorithm is developed to solve the optimization problem with proven convergence. The comprehensive experimental results conducted on six benchmark multi-view datasets clearly demonstrates the effectiveness of the proposed algorithm against the SOTA methods.

Classification of imbalanced data is one of the common problems in the recent field of data mining. Imbalanced data substantially affects the performance of standard classification models. Data-level approaches mainly use the oversampling methods to solve the problem, such as synthetic minority oversampling Technique (SMOTE). However, since the methods such as SMOTE generate instances by linear interpolation, synthetic data space may look like a polygonal. Also, the oversampling methods generate outliers of the minority class. In this paper, we proposed Gaussian based minority oversampling technique (GMOTE) with a statistical perspective for imbalanced datasets. To avoid linear interpolation and to consider outliers, this proposed method generates instances by the Gaussian Mixture Model. Motivated by clustering-based multivariate Gaussian outlier score (CMGOS), we propose to adapt tail probability of instances through the Mahalanobis distance to consider local outliers. The experiment was carried out on a representative set of benchmark datasets. The performance of the GMOTE is compared with other methods such as SMOTE. When the GMOTE is combined with classification and regression tree (CART) or support vector machine (SVM), it shows better accuracy and F1-Score. Experimental results demonstrate the robust performance.

Studies related to fairness in machine learning have recently gained traction due to its ever-expanding role in high-stakes decision making. For example, it may be desirable to ensure that all clusters discovered by an algorithm have high gender diversity. Previously, these problems have been studied under a setting where sensitive attributes, with respect to which fairness conditions impose diversity across clusters, are assumed to be observable; hence, protected groups are readily available. Most often, this may not be true, and diversity or individual interests can manifest as an intrinsic or latent feature of a social network. For example, depending on latent sensitive attributes, individuals interact with each other and represent each other's interests, resulting in a network, which we refer to as a representation graph. Motivated by this, we propose an individual fairness criterion for clustering a graph $\mathcal{G}$ that requires each cluster to contain an adequate number of members connected to the individual under a representation graph $\mathcal{R}$. We devise a spectral clustering algorithm to find fair clusters under a given representation graph. We further propose a variant of the stochastic block model and establish our algorithm's weak consistency under this model. Finally, we present experimental results to corroborate our theoretical findings.

With recent advances in data collection from multiple sources, multi-view data has received significant attention. In multi-view data, each view represents a different perspective of data. Since label information is often expensive to acquire, multi-view clustering has gained growing interest, which aims to obtain better clustering solution by exploiting complementary and consistent information across all views rather than only using an individual view. Due to inevitable sensor failures, data in each view may contain error. Error often exhibits as noise or feature-specific corruptions or outliers. Multi-view data may contain any or combination of these error types. Blindly clustering multi-view data i.e., without considering possible error in view(s) could significantly degrade the performance. The goal of error-robust multi-view clustering is to obtain useful outcome even if the multi-view data is corrupted. Existing error-robust multi-view clustering approaches with explicit error removal formulation can be structured into five broad research categories - sparsity norm based approaches, graph based methods, subspace based learning approaches, deep learning based methods and hybrid approaches, this survey summarizes and reviews recent advances in error-robust clustering for multi-view data. Finally, we highlight the challenges and provide future research opportunities.