There are some cases when you have a dataset that is mostly unlabeled. The problems start when you want to structure the datasets and make it valuable by labeling it. In machine learning, there are various methods for labeling these datasets. Clustering is one of them. In this tutorial of "How to", you will learn to do K Means Clustering in Python.

This paper introduces k-splits, an improved hierarchical algorithm based on k-means to cluster data without prior knowledge of the number of clusters. K-splits starts from a small number of clusters and uses the most significant data distribution axis to split these clusters incrementally into better fits if needed. Accuracy and speed are two main advantages of the proposed method. We experiment on six synthetic benchmark datasets plus two real-world datasets MNIST and Fashion-MNIST, to prove that our algorithm has excellent accuracy in finding the correct number of clusters under different conditions. We also show that k-splits is faster than similar methods and can even be faster than the standard k-means in lower dimensions. Finally, we suggest using k-splits to uncover the exact position of centroids and then input them as initial points to the k-means algorithm to fine-tune the results.

Trust calibration is necessary to ensure appropriate user acceptance in advanced automation technologies. A significant challenge to achieve trust calibration is to quantitatively estimate human trust in real-time. Although multiple trust models exist, these models have limited predictive performance partly due to individual differences in trust dynamics. A personalized model for each person can address this issue, but it requires a significant amount of data for each user. We present a methodology to develop customized model by clustering humans based on their trust dynamics. The clustering-based method addresses the individual differences in trust dynamics while requiring significantly less data than personalized model. We show that our clustering-based customized models not only outperform the general model based on entire population, but also outperform simple demographic factor-based customized models. Specifically, we propose that two models based on ``confident'' and ``skeptical'' group of participants, respectively, can represent the trust behavior of the population. The ``confident'' participants, as compared to the ``skeptical'' participants, have higher initial trust levels, lose trust slower when they encounter low reliability operations, and have higher trust levels during trust-repair after the low reliability operations. In summary, clustering-based customized models improve trust prediction performance for further trust calibration considerations.

Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar points. In this paper, we present a wholly different way of clustering points in 2-dimensional space, inspired by how humans cluster data: by training neural networks to perform instance segmentation on plotted data. Our approach, Visual Clustering, has several advantages over traditional clustering algorithms: it is much faster than most existing clustering algorithms (making it suitable for very large datasets), it agrees strongly with human intuition for clusters, and it is by default hyperparameter free (although additional steps with hyperparameters can be introduced for more control of the algorithm). We describe the method and compare it to ten other clustering methods on synthetic data to illustrate its advantages and disadvantages. We then demonstrate how our approach can be extended to higher dimensional data and illustrate its performance on real-world data. The implementation of Visual Clustering is publicly available and can be applied to any dataset in a few lines of code.

Network-valued data are encountered in a wide range of applications, and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of protein structures and social networks. Various methods, ranging from graph kernels to graph neural networks, have been proposed that achieve some success in graph classification problems. However, most methods have limited theoretical justification, and their applicability beyond classification remains unexplored. In this work, we propose methods for clustering multiple graphs, without vertex correspondence, that are inspired by the recent literature on estimating graphons-- symmetric functions corresponding to infinite vertex limit of graphs. We propose a novel graph distance based on sorting-and-smoothing graphon estimators. Using the proposed graph distance, we present two clustering algorithms and show that they achieve state-of-the-art results. We prove the statistical consistency of both algorithms under Lipschitz assumptions on the graph degrees. We further study the applicability of the proposed distance for graph two-sample testing problems. Machine learning on graphs has evolved considerably over the past two decades. The traditional view towards network analysis is limited to modelling interactions among entities of interest, for instance social networks or world wide web, and learning algorithms based on graph theory have been commonly used to solve these problems (Von Luxburg, 2007; Yan et al., 2006).

Design of experiments (DOE) is playing an essential role in learning and improving a variety of objects and processes. The article discusses the application of unsupervised machine learning to support the pragmatic designs of complex experiments. Complex experiments are characterized by having a large number of factors, mixed-level designs, and may be subject to constraints that eliminate some unfeasible trials for various reasons. Having such attributes, it is very challenging to design pragmatic experiments that are economically, operationally, and timely sound. It means a significant decrease in the number of required trials from a full factorial design, while still attempting to achieve the defined objectives. A beta variational autoencoder (beta-VAE) has been applied to represent trials of the initial full factorial design after filtering out unfeasible trials on the low dimensional latent space. Regarding visualization and interpretability, the paper is limited to 2D representations. Beta-VAE supports (1) orthogonality of the latent space dimensions, (2) isotropic multivariate standard normal distribution of the representation on the latent space, (3) disentanglement of the latent space representation by levels of factors, (4) propagation of the applied constraints of the initial design into the latent space, and (5) generation of trials by decoding latent space points. Having an initial design representation on the latent space with such properties, it allows for the generation of pragmatic design of experiments (G-DOE) by specifying the number of trials and their pattern on the latent space, such as square or polar grids. Clustering and aggregated gradient metrics have been shown to guide grid specification.

The existing person search methods use the annotated labels of person identities to train deep networks in a supervised manner that requires a huge amount of time and effort for human labeling. In this paper, we first introduce a novel framework of person search that is able to train the network in the absence of the person identity labels, and propose efficient unsupervised clustering methods to substitute the supervision process using annotated person identity labels. Specifically, we propose a hard negative mining scheme based on the uniqueness property that only a single person has the same identity to a given query person in each image. We also propose a hard positive mining scheme by using the contextual information of co-appearance that neighboring persons in one image tend to appear simultaneously in other images. The experimental results show that the proposed method achieves comparable performance to that of the state-of-the-art supervised person search methods, and furthermore outperforms the extended unsupervised person re-identification methods on the benchmark person search datasets.

Structured point process data harvested from various platforms poses new challenges to the machine learning community. By imposing a matrix structure to repeatedly observed marked point processes, we propose a novel mixture model of multi-level marked point processes for identifying potential heterogeneity in the observed data. Specifically, we study a matrix whose entries are marked log-Gaussian Cox processes and cluster rows of such a matrix. An efficient semi-parametric Expectation-Solution (ES) algorithm combined with functional principal component analysis (FPCA) of point processes is proposed for model estimation. The effectiveness of the proposed framework is demonstrated through simulation studies and a real data analysis.

\textbf{A}ccuracy, \textbf{R}obustness to noises and scales, \textbf{I}nterpretability, \textbf{S}peed, and \textbf{E}asy to use (ARISE) are crucial requirements of a good clustering algorithm. However, achieving these goals simultaneously is challenging, and most advanced approaches only focus on parts of them. Towards an overall consideration of these aspects, we propose a novel clustering algorithm, namely GIT (Clustering Based on \textbf{G}raph of \textbf{I}ntensity \textbf{T}opology). GIT considers both local and global data structures: firstly forming local clusters based on intensity peaks of samples, and then estimating the global topological graph (topo-graph) between these local clusters. We use the Wasserstein Distance between the predicted and prior class proportions to automatically cut noisy edges in the topo-graph and merge connected local clusters as final clusters. Then, we compare GIT with seven competing algorithms on five synthetic datasets and nine real-world datasets. With fast local cluster detection, robust topo-graph construction and accurate edge-cutting, GIT shows attractive ARISE performance and significantly exceeds other non-convex clustering methods. For example, GIT outperforms its counterparts about $10\%$ (F1-score) on MNIST and FashionMNIST. Code is available at \color{red}{https://github.com/gaozhangyang/GIT}.

We investigate a clustering problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and derive a Max-Cut integer program based on maximum likelihood estimation. We prove its solutions achieve the optimal misclassification rate when the number of samples grows linearly in the dimension, up to a logarithmic factor. However, solving the Max-cut problem appears to be computationally intractable. To overcome this, we develop an efficient spectral algorithm that attains the optimal rate but requires a quadratic sample size. Although this sample complexity is worse than that of the Max-cut problem, we conjecture that no polynomial-time method can perform better. Furthermore, we gather numerical and theoretical evidence that supports the existence of a statistical-computational gap. Finally, we generalize the Max-Cut program to a $k$-means program that handles multi-component mixtures with possibly unequal weights. It enjoys similar optimality guarantees for mixtures of distributions that satisfy a transportation-cost inequality, encompassing Gaussian and strongly log-concave distributions.