There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the type of the graph, the clustering approach, the inference approach, and whether the number of groups is selected or estimated. We then review unsupervised learning of texts, also known as topic modelling, as the two areas are closely related. Also reviewed are the models that combine block modelling with topic modelling, as such incorporations are natural because both areas have the same goal of model-based clustering. How different approaches cope with various issues will be summarised and compared, to facilitate the demand of practitioners for a concise overview of the current status of these two areas of literature.

Cluster analysis is a staple of unsupervised machine learning and data science. It is very useful for data mining and big data because it automatically finds patterns in the data, without the need for labels, unlike supervised machine learning. In a real-world environment, you can imagine that a robot or an artificial intelligence won't always have access to the optimal answer, or maybe there isn't an optimal correct answer. You'd want that robot to be able to explore the world on its own, and learn things just by looking for patterns. In this course we are first going to talk about clustering.

Consider a supervised dataset $D=[A\mid \textbf{b}]$, where $\textbf{b}$ is the outcome column, rows of $D$ correspond to observations, and columns of $A$ are the features of the dataset. A central problem in machine learning and pattern recognition is to select the most important features from $D$ to be able to predict the outcome. In this paper, we provide a new feature selection method where we use perturbation theory to detect correlations between features. We solve $AX=\textbf{b}$ using the method of least squares and singular value decomposition of $A$. In practical applications, such as in bioinformatics, the number of rows of $A$ (observations) are much less than the number of columns of $A$ (features). So we are dealing with singular matrices with big condition numbers. Although it is known that the solutions of least square problems in singular case are very sensitive to perturbations in $A$, our novel approach in this paper is to prove that the correlations between features can be detected by applying perturbations to $A$. The effectiveness of our method is verified by performing a series of comparisons with conventional and novel feature selection methods in the literature. It is demonstrated that in most situations, our method chooses considerably less number of features while attaining or exceeding the accuracy of the other methods.

Let's say you want to classify hundreds (or thousands) of documents based on their content and topics, or you wish to group together different images for some reason. Or what's even more, let's think you have that same data already classified but you want to challenge that labeling. You want to know if that data categorization makes sense or not, or can be improved. Well, my advice is that you cluster your data. Information is often darkened by noise and redundancy, and grouping data into clusters (clustering) with similar features is an efficient way to bring some light on.

Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A common practice for dealing with missing values in the context of clustering is to first impute the missing values, and then apply the clustering algorithm on the completed data. We consider missing values in the context of optimal clustering, which finds an optimal clustering operator with reference to an underlying random labeled point process (RLPP). We show how the missing-value problem fits neatly into the overall framework of optimal clustering by incorporating the missing value mechanism into the random labeled point process and then marginalizing out the missing-value process. In particular, we demonstrate the proposed framework for the Gaussian model with arbitrary covariance structures. Comprehensive experimental studies on both synthetic and real-world RNA-seq data show the superior performance of the proposed optimal clustering with missing values when compared to various clustering approaches. Optimal clustering with missing values obviates the need for imputation-based pre-processing of the data, while at the same time possessing smaller clustering errors.

Data is one of the essential ingredients to power deep learning research. Small datasets, especially specific to medical institutes, bring challenges to deep learning training stage. This work aims to develop a practical deep multimodal that can classify patients into abnormal and normal categories accurately as well as assist radiologists to detect visual and textual anomalies by locating areas of interest. The detection of the anomalies is achieved through a novel technique which extends the integrated gradients methodology with an unsupervised clustering algorithm. This technique also introduces a tuning parameter which trades off true positive signals to denoise false positive signals in the detection process. To overcome the challenges of the small training dataset which only has 3K frontal X-ray images and medical reports in pairs, we have adopted transfer learning for the multimodal which concatenates the layers of image and text submodels. The image submodel was trained on the vast ChestX-ray14 dataset, while the text submodel transferred a pertained word embedding layer from a hospital-specific corpus. Experimental results show that our multimodal improves the accuracy of the classification by 4% and 7% on average of 50 epochs, compared to the individual text and image model, respectively.

Traditional clustering algorithms such as K-means rely heavily on the nature of the chosen metric or data representation. To get meaningful clusters, these representations need to be tailored to the downstream task (e.g. cluster photos by object category, cluster faces by identity). Therefore, we frame clustering as a meta-learning task, few-shot clustering, which allows us to specify how to cluster the data at the meta-training level, despite the clustering algorithm itself being unsupervised. We propose Centroid Networks, a simple and efficient few-shot clustering method based on learning representations which are tailored both to the task to solve and to its internal clustering module. We also introduce unsupervised few-shot classification, which is conceptually similar to few-shot clustering, but is strictly harder than supervised* few-shot classification and therefore allows direct comparison with existing supervised few-shot classification methods. On Omniglot and miniImageNet, our method achieves accuracy competitive with popular supervised few-shot classification algorithms, despite using *no labels* from the support set. We also show performance competitive with state-of-the-art learning-to-cluster methods.

Mixture models are a standard approach to dealing with heterogeneous data with non-i.i.d. structure. However, when the dimension $p$ is large relative to sample size $n$ and where either or both of means and covariances/graphical models may differ between the latent groups, mixture models face statistical and computational difficulties and currently available methods cannot realistically go beyond $p \! \sim \! 10^4$ or so. We propose an approach called Model-based Clustering via Adaptive Projections (MCAP). Instead of estimating mixtures in the original space, we work with a low-dimensional representation obtained by linear projection. The projection dimension itself plays an important role and governs a type of bias-variance tradeoff with respect to recovery of the relevant signals. MCAP sets the projection dimension automatically in a data-adaptive manner, using a proxy for the assignment risk. Combining a full covariance formulation with the adaptive projection allows detection of both mean and covariance signals in very high dimensional problems. We show real-data examples in which covariance signals are reliably detected in problems with $p \! \sim \! 10^4$ or more, and simulations going up to $p = 10^6$. In some examples, MCAP performs well even when the mean signal is entirely removed, leaving differential covariance structure in the high-dimensional space as the only signal. Across a number of regimes, MCAP performs as well or better than a range of existing methods, including a recently-proposed $\ell_1$-penalized approach; and performance remains broadly stable with increasing dimension. MCAP can be run "out of the box" and is fast enough for interactive use on large-$p$ problems using standard desktop computing resources.

Traditional load analysis is facing challenges with the new electricity usage patterns due to demand response as well as increasing deployment of distributed generations, including photovoltaics (PV), electric vehicles (EV), and energy storage systems (ESS). At the transmission system, despite of irregular load behaviors at different areas, highly aggregated load shapes still share similar characteristics. Load clustering is to discover such intrinsic patterns and provide useful information to other load applications, such as load forecasting and load modeling. This paper proposes an efficient submodular load clustering method for transmission-level load areas. Robust principal component analysis (R-PCA) firstly decomposes the annual load profiles into low-rank components and sparse components to extract key features. A novel submodular cluster center selection technique is then applied to determine the optimal cluster centers through constructed similarity graph. Following the selection results, load areas are efficiently assigned to different clusters for further load analysis and applications. Numerical results obtained from PJM load demonstrate the effectiveness of the proposed approach.

Generative Adversarial Networks (GANs) have achieved great success in generating realistic images. Most of these are conditional models, although acquisition of class labels is expensive and time-consuming in practice. To reduce the dependence on labeled data, we propose an un-conditional generative adversarial model, called K-Means-GAN (KM-GAN), which incorporates the idea of updating centers in K-Means into GANs. Specifically, we redesign the framework of GANs by applying K-Means on the features extracted from the discriminator. With obtained labels from K-Means, we propose new objective functions from the perspective of deep metric learning (DML). Distinct from previous works, the discriminator is treated as a feature extractor rather than a classifier in KM-GAN, meanwhile utilization of K-Means makes features of the discriminator more representative. Experiments are conducted on various datasets, such as MNIST, Fashion-10, CIFAR-10 and CelebA, and show that the quality of samples generated by KM-GAN is comparable to some conditional generative adversarial models.