K-Means Clustering is an unsupervised learning algorithm that is used to solve the clustering problems in machine learning or data science. In this article, I would be giving you a detailed explanation and how this model works. Unsupervised Learning method K-Means Clustering divides the unlabeled dataset into various clusters. K specifies the number of pre-defined clusters that must be produced throughout the process; for example, if K 2, two clusters will be created, and if K 3, three clusters will be created, and so on. It allows us to cluster data into distinct groups and provides a simple technique to determine the categories of groups in an unlabeled dataset without any training. It's a centroid-based approach, which means that each cluster has its own centroid.

Deep Learning (DL) has shown great promise in the unsupervised task of clustering. That said, while in classical (i.e., non-deep) clustering the benefits of the nonparametric approach are well known, most deep-clustering methods are parametric: namely, they require a predefined and fixed number of clusters, denoted by K. When K is unknown, however, using model-selection criteria to choose its optimal value might become computationally expensive, especially in DL as the training process would have to be repeated numerous times. In this work, we bridge this gap by introducing an effective deep-clustering method that does not require knowing the value of K as it infers it during the learning. Using a split/merge framework, a dynamic architecture that adapts to the changing K, and a novel loss, our proposed method outperforms existing nonparametric methods (both classical and deep ones). While the very few existing deep nonparametric methods lack scalability, we demonstrate ours by being the first to report the performance of such a method on ImageNet. We also demonstrate the importance of inferring K by showing how methods that fix it deteriorate in performance when their assumed K value gets further from the ground-truth one, especially on imbalanced datasets. Our code is available at https://github.com/BGU-CS-VIL/DeepDPM.

Deep neural networks (DNNs) have found their way into many applications with potential impact on the safety, security, and fairness of human-machine-systems. Such require basic understanding and sufficient trust by the users. This motivated the research field of explainable artificial intelligence (XAI), i.e. finding methods for opening the "black-boxes" DNNs represent. For the computer vision domain in specific, practical assessment of DNNs requires a globally valid association of human interpretable concepts with internals of the model. The research field of concept (embedding) analysis (CA) tackles this problem: CA aims to find global, assessable associations of humanly interpretable semantic concepts (e.g., eye, bearded) with internal representations of a DNN. This work establishes a general definition of CA and a taxonomy for CA methods, uniting several ideas from literature. That allows to easily position and compare CA approaches. Guided by the defined notions, the current state-of-the-art research regarding CA methods and interesting applications are reviewed. More than thirty relevant methods are discussed, compared, and categorized. Finally, for practitioners, a survey of fifteen datasets is provided that have been used for supervised concept analysis. Open challenges and research directions are pointed out at the end.

With the rising use of the Internet in today's society, the quantity of data created is incomprehensibly huge. Even though the nature of individual data is straightforward, the sheer amount of data to be analyzed makes processing difficult for even computers. To manage such procedures, we need large data analysis tools. Data mining methods and techniques, in conjunction with machine learning, enable us to analyze large amounts of data in an intelligible manner. It is capable of classifying unlabeled data into a predetermined number of clusters based on similarities (k).

When trained on diverse labeled data, machine learning models have proven themselves to be a powerful tool in all facets of society. However, due to budget limitations, deliberate or non-deliberate censorship, and other problems during data collection and curation, the labeled training set might exhibit a systematic shortage of data for certain groups. We investigate a scenario in which the absence of certain data is linked to the second level of a two-level hierarchy in the data. Inspired by the idea of protected groups from algorithmic fairness, we refer to the partitions carved by this second level as "subgroups"; we refer to combinations of subgroups and classes, or leaves of the hierarchy, as "sources". To characterize the problem, we introduce the concept of classes with incomplete subgroup support. The representational bias in the training set can give rise to spurious correlations between the classes and the subgroups which render standard classification models ungeneralizable to unseen sources. To overcome this bias, we make use of an additional, diverse but unlabeled dataset, called the "deployment set", to learn a representation that is invariant to subgroup. This is done by adversarially matching the support of the training and deployment sets in representation space. In order to learn the desired invariance, it is paramount that the sets of samples observed by the discriminator are balanced by class; this is easily achieved for the training set, but requires using semi-supervised clustering for the deployment set. We demonstrate the effectiveness of our method with experiments on several datasets and variants of the problem.

Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of must-link and cannot-link pairs, arise naturally in many applications and are intuitive for users to provide. However, the common practice of relaxing discrete constraints to a continuous domain to ease optimization when learning kernels or metrics can harm generalization, as information which only encodes linkage is transformed to informing distances. We introduce a new constrained clustering algorithm that jointly clusters data and learns a kernel in accordance with the available pairwise constraints. To generalize well, our method is designed to maximize constraint satisfaction without relaxing pairwise constraints to a continuous domain where they inform distances. We show that the proposed method outperforms existing approaches on a large number of diverse publicly available datasets, and we discuss how our method can scale to handling large data.

We present a clustering method and provide a theoretical analysis and an explanation to a phenomenon encountered in the applied statistical literature since the 1990's. This phenomenon is the natural adaptability of the order when using a clustering method derived from the famous EM algorithm. We define a new statistic, the relative entropic order, that represents the number of clumps in the target distribution. We prove in particular that the empirical version of this relative entropic order is consistent. Our approach is easy to implement and has a high potential of applications. Perspectives of this works are algorithmic and theoretical, with possible natural extensions to various cases such as dependent or multidimensional data.

In this paper with study phase transitions of the $q$-state Potts model, through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), $k$-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures $T_c(q)$, for $q = 3, 4$ and $5$, results show that non-linear methods as UMAP and TDA are less dependent on finite size effects, while still being able to distinguish between first and second order phase transitions. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.

World Input-Output (I/O) matrices provide the networks of within- and cross-country economic relations. In the context of I/O analysis, the methodology adopted by national statistical offices in data collection raises the issue of obtaining reliable data in a timely fashion and it makes the reconstruction of (part of) the I/O matrices of particular interest. In this work, we propose a method combining hierarchical clustering and Matrix Completion (MC) with a LASSO-like nuclear norm penalty, to impute missing entries of a partially unknown I/O matrix. Through simulations based on synthetic matrices we study the effectiveness of the proposed method to predict missing values from both previous years data and current data related to countries similar to the one for which current data are obscured. To show the usefulness of our method, an application based on World Input-Output Database (WIOD) tables - which are an example of industry-by-industry I/O tables - is provided. Strong similarities in structure between WIOD and other I/O tables are also found, which make the proposed approach easily generalizable to them.

We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the iterative working of the algorithm, in the sense that the partitions of the hierarchical clusters are purely defined in accordance with the input dataset. Our method is a universal hierarchical clustering approach since it can be implemented as bottom up or top down versions, both of which result in the same clustering. We show that for certain types of datasets, our algorithm has near-linear time and space complexity.