We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.

In this work, we propose a multi-armed bandit-based framework for identifying a compact set of informative data instances (i.e., the prototypes) from a source dataset $S$ that best represents a given target set $T$. Prototypical examples of a given dataset offer interpretable insights into the underlying data distribution and assist in example-based reasoning, thereby influencing every sphere of human decision-making. Current state-of-the-art prototype selection approaches require $O(|S||T|)$ similarity comparisons between source and target data points, which becomes prohibitively expensive for large-scale settings. We propose to mitigate this limitation by employing stochastic greedy search in the space of prototypical examples and multi-armed bandits for reducing the number of similarity comparisons. Our randomized algorithm, ProtoBandit, identifies a set of $k$ prototypes incurring $O(k^3|S|)$ similarity comparisons, which is independent of the size of the target set. An interesting outcome of our analysis is for the $k$-medoids clustering problem $T = S$ setting) in which we show that our algorithm ProtoBandit approximates the BUILD step solution of the partitioning around medoids (PAM) method in $O(k^3|S|)$ complexity. Empirically, we observe that ProtoBandit reduces the number of similarity computation calls by several orders of magnitudes ($100-1000$ times) while obtaining solutions similar in quality to those from state-of-the-art approaches.

The choice to participate in a data-driven service, often made on the basis of quality of that service, influences the ability of the service to learn and improve. We study the participation and retraining dynamics that arise when both the learners and sub-populations of users are \emph{risk-reducing}, which cover a broad class of updates including gradient descent, multiplicative weights, etc. Suppose, for example, that individuals choose to spend their time amongst social media platforms proportionally to how well each platform works for them. Each platform also gathers data about its active users, which it uses to update parameters with a gradient step. For this example and for our general class of dynamics, we show that the only asymptotically stable equilibria are segmented, with sub-populations allocated to a single learner. Under mild assumptions, the utilitarian social optimum is a stable equilibrium. In contrast to previous work, which shows that repeated risk minimization can result in representation disparity and high overall loss for a single learner \citep{hashimoto2018fairness,miller2021outside}, we find that repeated myopic updates with multiple learners lead to better outcomes. We illustrate the phenomena via a simulated example initialized from real data.

We introduce a novel profile-based patient clustering model designed for clinical data in healthcare. By utilizing a method grounded on constrained low-rank approximation, our model takes advantage of patients' clinical data and digital interaction data, including browsing and search, to construct patient profiles. As a result of the method, nonnegative embedding vectors are generated, serving as a low-dimensional representation of the patients. Our model was assessed using real-world patient data from a healthcare web portal, with a comprehensive evaluation approach which considered clustering and recommendation capabilities. In comparison to other baselines, our approach demonstrated superior performance in terms of clustering coherence and recommendation accuracy.

Graph contrastive learning algorithms have demonstrated remarkable success in various applications such as node classification, link prediction, and graph clustering. However, in unsupervised graph contrastive learning, some contrastive pairs may contradict the truths in downstream tasks and thus the decrease of losses on these pairs undesirably harms the performance in the downstream tasks. To assess the discrepancy between the prediction and the ground-truth in the downstream tasks for these contrastive pairs, we adapt the expected calibration error (ECE) to graph contrastive learning. The analysis of ECE motivates us to propose a novel regularization method, Contrast-Reg, to ensure that decreasing the contrastive loss leads to better performance in the downstream tasks. As a plug-in regularizer, Contrast-Reg effectively improves the performance of existing graph contrastive learning algorithms. We provide both theoretical and empirical results to demonstrate the effectiveness of Contrast-Reg in enhancing the generalizability of the Graph Neural Network(GNN) model and improving the performance of graph contrastive algorithms with different similarity definitions and encoder backbones across various downstream tasks.

Image segmentation is a fundamental task in computer vision. Data annotation for training supervised methods can be labor-intensive, motivating unsupervised methods. Current approaches often rely on extracting deep features from pre-trained networks to construct a graph, and classical clustering methods like k-means and normalized-cuts are then applied as a post-processing step. However, this approach reduces the high-dimensional information encoded in the features to pair-wise scalar affinities. To address this limitation, this study introduces a lightweight Graph Neural Network (GNN) to replace classical clustering methods while optimizing for the same clustering objective function. Unlike existing methods, our GNN takes both the pair-wise affinities between local image features and the raw features as input. This direct connection between the raw features and the clustering objective enables us to implicitly perform classification of the clusters between different graphs, resulting in part semantic segmentation without the need for additional post-processing steps. We demonstrate how classical clustering objectives can be formulated as self-supervised loss functions for training an image segmentation GNN. Furthermore, we employ the Correlation-Clustering (CC) objective to perform clustering without defining the number of clusters, allowing for k-less clustering. We apply the proposed method for object localization, segmentation, and semantic part segmentation tasks, surpassing state-of-the-art performance on multiple benchmarks.

Machine learning (ML) models are increasingly pivotal in automating clinical decisions. Yet, a glaring oversight in prior research has been the lack of proper processing of Electronic Medical Record (EMR) data in the clinical context for errors and outliers. Addressing this oversight, we introduce an innovative projections-based method that seamlessly integrates clinical expertise as domain constraints, generating important meta-data that can be used in ML workflows. In particular, by using high-dimensional mixed-integer programs that capture physiological and biological constraints on patient vitals and lab values, we can harness the power of mathematical "projections" for the EMR data to correct patient data. Consequently, we measure the distance of corrected data from the constraints defining a healthy range of patient data, resulting in a unique predictive metric we term as "trust-scores". These scores provide insight into the patient's health status and significantly boost the performance of ML classifiers in real-life clinical settings. We validate the impact of our framework in the context of early detection of sepsis using ML. We show an AUROC of 0.865 and a precision of 0.922, that surpasses conventional ML models without such projections.

The 2019-2020 Australia bushfire season was catastrophic in the scale of damage caused to agricultural resources, property, infrastructure, and ecological systems. By the end of 2020, the devastation attributable to these Black Summer fires totalled 33 lives lost, almost 19 million hectares of land burned, over 3,000 homes destroyed and AUD $1.7 billion in insurance losses, as well as an estimated 1 billion animals killed, including half of Kangaroo Island's population of koalas (Filkov et al. 2020). According to the Australian Government Bureau of Meteorology (2021), 2019 was the warmest year on record in Australia, and the period from 2013-2020 represents eight of the ten warmest years in recorded history. There is concern and expectation that impacts of climate change - including more extreme temperatures, persistent drought, and changes in plant growth and landscape drying - will worsen conditions for extreme bushfires (CSIRO and Australian Government Bureau of Meteorology 2020; Deb et al. 2020). Contributing to the problem is that dry lightning represents the main source of natural ignition, and fires that start in remote areas deep in the temperate forests are difficult to access and monitor (Abram et al. 2021). Therefore, opportunities to detect fire ignitions, monitor bushfire spread, and understand movement patterns in remote areas are important for developing effective strategies to mitigate bushfire impact.

Pre-trained language models (pLMs) learn intricate patterns and contextual dependencies via unsupervised learning on vast text data, driving breakthroughs across NLP tasks. Despite these achievements, these models remain black boxes, necessitating research into understanding their decision-making processes. Recent studies explore representation analysis by clustering latent spaces within pre-trained models. However, these approaches are limited in terms of scalability and the scope of interpretation because of high computation costs of clustering algorithms. This study focuses on comparing clustering algorithms for the purpose of scaling encoded concept discovery of representations from pLMs. Specifically, we compare three algorithms in their capacity to unveil the encoded concepts through their alignment to human-defined ontologies: Agglomerative Hierarchical Clustering, Leaders Algorithm, and K-Means Clustering. Our results show that K-Means has the potential to scale to very large datasets, allowing rich latent concept discovery, both on the word and phrase level.

In modern day industry, clustering algorithms are daily routines of algorithm engineers. Although clustering algorithms experienced rapid growth before 2010. Innovation related to the research topic has stagnated after deep learning became the de facto industrial standard for machine learning applications. In 2007, a density-based clustering algorithm named DENCLUE was invented to solve clustering problem for nonlinear data structures. However, its parameter selection problem was largely neglected until 2011. In this paper, we propose a new approach to compute the optimal parameters for the DENCLUE algorithm, and discuss its performance in the experiment section.