As one of the most ubiquitously applied unsupervised learning methods, clustering has also been known to have a few disadvantages. More specifically, parameters such as the number of clusters and neighborhood radius are what call the `unsupervised` nature of these algorithms into question. Moreover, the stochastic nature of a great number of these algorithms is also a considerable point of weakness. In order to address these issues, we propose DISCERN which can serve as an initialization algorithm for K-Means, finding suitable centroids that increase the performance of K-Means. Following that, the algorithm can estimate the number of clusters if need be. The algorithm does all of that, while maintaining complete robustness and returning the same results at each separate run. We ran experiments on the proposed method processing multiple datasets and the results show its undeniable superiority in terms of results, computational time and robustness when compared to the randomized K-Means and K-Means++ initialization. In addition, the superiority in estimating the number of clusters is also discussed and we prove the lower complexity when compared to methods such as the elbow and silhouette methods in estimating the number of clusters.

Extracting an understanding of the underlying system from high dimensional data is a growing problem in science. One primary challenge involves clustering the data points into classes with interpretable differences. A challenge in clustering high dimensional data is that multimodal signatures that define clusters may only be present in a small but unknown subspace. Discovering the subspace that defines clusters provides low dimensional representations of the data which capture cluster diversity, and provides greater understanding of the system by identifying the key underlying variables. Here, we define a class of problems in which linear separability of clusters is hidden in a low dimensional space. We propose an unsupervised model-free method to identify the subset of features that define a low dimensional subspace in which clustering can be conducted. This is achieved by averaging over discriminators trained on an ensemble of proposed cluster configurations. We then apply our method to single cell RNA-seq data from mouse gastrulation, and identify 27 key transcription factors (out of 409 total), 18 of which are known to define cell states through their expression levels. In this inferred subspace, we find clear signatures of known cell types that eluded classification prior to discovery of the correct low dimensional subspace. This method can be used as a wrapper for existing clustering algorithms to find low dimensional informative subspaces with multimodal signatures within high dimensional data.

Artificial Intelligence (AI) and Machine Learning (ML) have revolutionized every aspect of our life and disrupted how we do business, unlike any other technology in the the history of mankind. Such disruption brings many challenges for professionals and businesses. In this article, I will provide an introduction to one of the most commonly used machine learning methods, K-Means. Machine learning is a scientific method that utilizes statistical methods along with the computational power of machines to convert data to wisdom that humans or the machine itself can use for taking certain actions. "It is a branch of artificial intelligence based on the idea that systems can learn from data, identify patterns and make decisions with minimal human intervention."

Subspace clustering aims to cluster unlabeled data that lies in a union of low-dimensional linear subspaces. Deep subspace clustering approaches based on auto-encoders have become very popular to solve subspace clustering problems. However, the training of current deep methods converges slowly, which is much less efficient than traditional approaches. We propose a Residual Encoder-Decoder network for deep Subspace Clustering (RED-SC), which symmetrically links convolutional and deconvolutional layers with skip-layer connections, with which the training converges much faster. We use a self-expressive layer to generate more accurate linear representation coefficients through different latent representations from multiple latent spaces. Experiments show the superiority of RED-SC in training efficiency and clustering accuracy. Moreover, we are the first one to apply residual encoder-decoder on unsupervised learning tasks.

A clustering may be considered as fair on pre-specified sensitive attributes if the proportions of sensitive attribute groups in each cluster reflect that in the dataset. In this paper, we consider the task of fair clustering for scenarios involving multiple multi-valued or numeric sensitive attributes. We propose a fair clustering method, FairKM (Fair K-Means), that is inspired by the popular K-Means clustering formulation. We outline a computational notion of fairness which is used along with a cluster coherence objective, to yield the FairKM clustering method. We empirically evaluate our approach, wherein we quantify both the quality and fairness of clusters, over real-world datasets. Our experimental evaluation illustrates that the clusters generated by FairKM fare significantly better on both clustering quality and fair representation of sensitive attribute groups compared to the clusters from a state-of-the-art baseline fair clustering method.

Conventional machine learning algorithms cannot be applied until a data matrix is available to process. When the data matrix needs to be obtained from a relational database via a feature extraction query, the computation cost can be prohibitive, as the data matrix may be (much) larger than the total input relation size. This paper introduces Rk-means, or relational k -means algorithm, for clustering relational data tuples without having to access the full data matrix. As such, we avoid having to run the expensive feature extraction query and storing its output. Our algorithm leverages the underlying structures in relational data. It involves construction of a small {\it grid coreset} of the data matrix for subsequent cluster construction. This gives a constant approximation for the k -means objective, while having asymptotic runtime improvements over standard approaches of first running the database query and then clustering. Empirical results show orders-of-magnitude speedup, and Rk-means can run faster on the database than even just computing the data matrix.

A fundamental problem in computer vision is image segmentation, where the goal is to delineate the boundary of the object in the image. The focus of this work is on the segmentation of grayscale images and its purpose is two-fold. First, we conduct an in-depth study comparing active contour and topologically-based methods, two popular approaches for boundary detection of 2-dimensional images. Certain properties of the image dataset may favor one method over the other, both from an interpretability perspective as well as through evaluation of performance measures. Second, we propose the use of topological knowledge to assist an active contour method, which can potentially incorporate prior shape information. The latter is known to be extremely sensitive to algorithm initialization, and thus, we use a topological model to provide an automatic initialization. In addition, our proposed model can handle objects in images with more complex topological structures. We demonstrate this on artificially-constructed image datasets from computer vision, as well as real medical image data.

Online retail, eCommerce, frequently falls victim to fraud conducted by malicious customers (fraudsters) who obtain goods or services through deception. Fraud coordinated by groups of professional fraudsters that place several fraudulent orders to maximize their gain is referred to as organized fraud. Existing approaches to fraud detection typically analyze orders in isolation and they are not effective at identifying groups of fraudulent orders linked to organized fraud. These also wrongly identify many legitimate orders as fraud, which hinders their usage for automated fraud cancellation. We introduce a novel solution to detect organized fraud by analyzing orders in bulk. Our approach is based on clustering and aims to group together fraudulent orders placed by the same group of fraudsters. It selectively uses two existing techniques, agglomerative clustering and sampling to recursively group orders into small clusters in a reasonable amount of time. We assess our clustering technique on real-world orders placed on the Zalando website, the largest online apparel retailer in Europe1. Our clustering processes 100,000s of orders in a few hours and groups 35-45% of fraudulent orders together. We propose a simple technique built on top of our clustering that detects 26.2% of fraud while raising false alarms for only 0.1% of legitimate orders.

We consider clustering based on significance tests for Gaussian Mixture Models (GMMs). Our starting point is the SigClust method developed by Liu et al. (2008), which introduces a test based on the k-means objective (with k = 2) to decide whether the data should be split into two clusters. When applied recursively, this test yields a method for hierarchical clustering that is equipped with a significance guarantee. We study the limiting distribution and power of this approach in some examples and show that there are large regions of the parameter space where the power is low. We then introduce a new test based on the idea of relative fit. Unlike prior work, we test for whether a mixture of Gaussians provides a better fit relative to a single Gaussian, without assuming that either model is correct. The proposed test has a simple critical value and provides provable error control. One version of our test provides exact, finite sample control of the type I error. We show how our tests can be used for hierarchical clustering as well as in a sequential manner for model selection. We conclude with an extensive simulation study and a cluster analysis of a gene expression dataset.

Clustering ensemble has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering ensemble. One of the arguments for weighted clustering ensemble is that elements (clusterings or clusters) in a clustering ensemble are of different quality, or that objects or features are of varying significance. However, it is not possible to directly apply the weighting mechanisms from classification (supervised) domain to clustering (unsupervised) domain, also because clustering is inherently an ill-posed problem. This paper provides an overview of weighted clustering ensemble by discussing different types of weights, major approaches to determining weight values, and applications of weighted clustering ensemble to complex data. The unifying framework presented in this paper will help clustering practitioners select the most appropriate weighting mechanisms for their own problems.