A current assumption of most clustering methods is that the training data and future data are taken from the same distribution. However, this assumption may not hold in most real-world scenarios. In this paper, we propose an information theoretical importance sampling based approach for clustering problems (ITISC) which minimizes the worst case of expected distortions under the constraint of distribution deviation. The distribution deviation constraint can be converted to the constraint over a set of weight distributions centered on the uniform distribution derived from importance sampling. The objective of the proposed approach is to minimize the loss under maximum degradation hence the resulting problem is a constrained minimax optimization problem which can be reformulated to an unconstrained problem using the Lagrange method. The optimization problem can be solved by both an alternative optimization algorithm or a general optimization routine by commercially available software. Experiment results on synthetic datasets and a real-world load forecasting problem validate the effectiveness of the proposed model. Furthermore, we show that fuzzy c-means is a special case of ITISC with the logarithmic distortion, and this observation provides an interesting physical interpretation for fuzzy exponent $m$.

The remarkable attention which fair clustering has received in the last few years has resulted in a significant number of different notions of fairness. Despite the fact that these notions are well-justified, they are often motivated and studied in a disjoint manner where one fairness desideratum is considered exclusively in isolation from the others. This leaves the understanding of the relations between different fairness notions as an important open problem in fair clustering. In this paper, we take the first step in this direction. Specifically, we consider the two most prominent demographic representation fairness notions in clustering: (1) Group Fairness (GF), where the different demographic groups are supposed to have close to population-level representation in each cluster and (2) Diversity in Center Selection (DS), where the selected centers are supposed to have close to population-level representation of each group. We show that given a constant approximation algorithm for one constraint (GF or DS only) we can obtain a constant approximation solution that satisfies both constraints simultaneously. Interestingly, we prove that any given solution that satisfies the GF constraint can always be post-processed at a bounded degradation to the clustering cost to additionally satisfy the DS constraint while the reverse is not true. Furthermore, we show that both GF and DS are incompatible (having an empty feasibility set in the worst case) with a collection of other distance-based fairness notions. Finally, we carry experiments to validate our theoretical findings.

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., $\textit{deep constrained clustering}$ (DCC) -- has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under $\textit{unknown}$ annotation confusions, the data membership can still be $\textit{provably}$ identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.

Temporal knowledge graph (TKG) completion models typically rely on having access to the entire graph during training. However, in real-world scenarios, TKG data is often received incrementally as events unfold, leading to a dynamic non-stationary data distribution over time. While one could incorporate fine-tuning to existing methods to allow them to adapt to evolving TKG data, this can lead to forgetting previously learned patterns. Alternatively, retraining the model with the entire updated TKG can mitigate forgetting but is computationally burdensome. To address these challenges, we propose a general continual training framework that is applicable to any TKG completion method, and leverages two key ideas: (i) a temporal regularization that encourages repurposing of less important model parameters for learning new knowledge, and (ii) a clustering-based experience replay that reinforces the past knowledge by selectively preserving only a small portion of the past data. Our experimental results on widely used event-centric TKG datasets demonstrate the effectiveness of our proposed continual training framework in adapting to new events while reducing catastrophic forgetting. Further, we perform ablation studies to show the effectiveness of each component of our proposed framework. Finally, we investigate the relation between the memory dedicated to experience replay and the benefit gained from our clustering-based sampling strategy.

We present a novel approach, in which we learn to cluster data directly from side information, in the form of a small set of pairwise examples. Unlike previous methods, with or without side information, we do not need to know the number of clusters, their centers or any kind of distance metric for similarity. Our method is able to divide the same data points in various ways dependant on the needs of a specific task, defined by the side information. Contrastingly, other work generally finds only the intrinsic, most obvious, clusters. Inspired by the mean shift algorithm, we implement our new clustering approach using a custom iterative neural network to create Differentiable Mean Shift (DMS), a state of the art, dataset agnostic, clustering method. We found that it was possible to train a strong cluster definition without enforcing a constraint that each cluster must be presented during training. DMS outperforms current methods in both the intrinsic and non-intrinsic dataset tasks.

Even when aggregate accuracy is high, state-of-the-art NLP models often fail systematically on specific subgroups of data, resulting in unfair outcomes and eroding user trust. Additional data collection may not help in addressing these weaknesses, as such challenging subgroups may be unknown to users, and underrepresented in the existing and new data. We propose Targeted Data Generation (TDG), a framework that automatically identifies challenging subgroups, and generates new data for those subgroups using large language models (LLMs) with a human in the loop. TDG estimates the expected benefit and potential harm of data augmentation for each subgroup, and selects the ones most likely to improve within group performance without hurting overall performance. In our experiments, TDG significantly improves the accuracy on challenging subgroups for state-of-the-art sentiment analysis and natural language inference models, while also improving overall test accuracy.

Graph Clustering, also known as network clustering, is a technique for partitioning a graph into clusters or communities of nodes based on their structural properties[1]. Graph clustering is used in various applications such as social network analysis, image segmentation, bioinformatics, and more. The goal of graph clustering is to group the nodes in a way to maximizes the similarity within the group and minimizes the similarity between them[2]. These two similarities are usually measured using various metrics such as modularity, Normalized Mutual Information(NMI), Adjusted Rand Index(ARI) and FowlkesMallows Index(FMI).

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed $K$-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including $K$-means, SDP and EM algorithms.

Usage data of a group of users distributed across a number of categories, such as songs, movies, webpages, links, regular household products, mobile apps, games, etc. can be ultra-high dimensional and massive in size. More often this kind of data is categorical and sparse in nature making it even more difficult to interpret any underlying hidden patterns such as clusters of users. However, if this information can be estimated accurately, it will have huge impacts in different business areas such as user recommendations for apps, songs, movies, and other similar products, health analytics using electronic health record (EHR) data, and driver profiling for insurance premium estimation or fleet management. In this work, we propose a clustering strategy of such categorical big data, utilizing the hidden sparsity of the dataset. Most traditional clustering methods fail to give proper clusters for such data and end up giving one big cluster with small clusters around it irrespective of the true structure of the data clusters. We propose a feature transformation, which maps the binary-valued usage vector to a lower dimensional continuous feature space in terms of groups of usage categories, termed as covariate classes. The lower dimensional feature representations in terms of covariate classes can be used for clustering. We implemented the proposed strategy and applied it to a large sized very high-dimensional song playlist dataset for the performance validation. The results are impressive as we achieved similar-sized user clusters with minimal between-cluster overlap in the feature space (8%) on average). As the proposed strategy has a very generic framework, it can be utilized as the analytic engine of many of the above-mentioned business use cases allowing an intelligent and dynamic personal recommendation system or a support system for smart business decision-making.

Self-supervised learning approaches provide a promising direction for clustering multivariate time-series data. However, real-world time-series data often include missing values, and the existing approaches require imputing missing values before clustering, which may cause extensive computations and noise and result in invalid interpretations. To address these challenges, we present a Self-supervised Learning-based Approach to Clustering multivariate Time-series data with missing values (SLAC-Time). SLAC-Time is a Transformer-based clustering method that uses time-series forecasting as a proxy task for leveraging unlabeled data and learning more robust time-series representations. This method jointly learns the neural network parameters and the cluster assignments of the learned representations. It iteratively clusters the learned representations with the K-means method and then utilizes the subsequent cluster assignments as pseudo-labels to update the model parameters. To evaluate our proposed approach, we applied it to clustering and phenotyping Traumatic Brain Injury (TBI) patients in the Transforming Research and Clinical Knowledge in Traumatic Brain Injury (TRACK-TBI) study. Clinical data associated with TBI patients are often measured over time and represented as timeseries variables characterized by missing values and irregular time intervals. We identified three TBI phenotypes that are distinct from one another in terms of clinically significant variables as well as clinical outcomes, including the Extended Glasgow Outcome Scale (GOSE) score, Intensive Care Unit (ICU) length of stay, and mortality rate. The experiments show that the TBI phenotypes identified by SLAC-Time can be potentially used for developing targeted clinical trials and therapeutic strategies. Keywords Self-supervised learning; Clustering; Transformer; Multivariate time-series data; Traumatic brain injury 1. Introduction Multivariate time-series data are frequently observed in many healthcare domains where each patient is represented by a set of clinical measurements recorded over time and present important information spanning the whole course of a patient's care. Clustering approaches are commonly used to extract valuable information and patterns from multivariate time-series data [1]. Such clustering approaches can be broadly divided into two categories: raw data-based approaches and representation-based approaches [2]. Raw data-based approaches perform the clustering on raw input data using well-designed similarity measures that can address the specificities of the temporal dimension, including shifted or stretched patterns (e.g., [3-5]).