There is a long history of research into time series clustering using distance-based partitional clustering. Many of the most popular algorithms adapt k-means (also known as Lloyd's algorithm) to exploit time dependencies in the data by specifying a time series distance function. However, these algorithms are often presented with k-means configured in various ways, altering key parameters such as the initialisation strategy. This variability makes it difficult to compare studies because k-means is known to be highly sensitive to its configuration. To address this, we propose a standard Lloyd's-based model for TSCL that adopts an end-to-end approach, incorporating a specialised distance function not only in the assignment step but also in the initialisation and stopping criteria. By doing so, we create a unified structure for comparing seven popular Lloyd's-based TSCL algorithms. This common framework enables us to more easily attribute differences in clustering performance to the distance function itself, rather than variations in the k-means configuration.

Compactness in deep learning can be critical to a model's viability in low-resource applications, and a common approach to extreme model compression is quantization. We consider Iterative Product Quantization (iPQ) with Quant-Noise (Fan et al., 2020) to be state-of-the-art in this area, but this quantization framework suffers from preventable inference quality degradation due to prevalent empty clusters. In this paper, we propose several novel enhancements aiming to improve the accuracy of iPQ with Quant-Noise by focusing on resolving empty clusters. Our contribution, which we call Partitioning-Guided k-means (PG k-means), is a heavily augmented k-means implementation composed of three main components. First, we propose a partitioning-based pre-assignment strategy that ensures no initial empty clusters and encourages an even weight-to-cluster distribution. Second, we propose an empirically superior empty cluster resolution heuristic executed via cautious partitioning of large clusters. Finally, we construct an optional optimization step that consolidates intuitively dense clusters of weights to ensure shared representation. The proposed approach consistently reduces the number of empty clusters in iPQ with Quant-Noise by 100x on average, uses 8x fewer iterations during empty cluster resolution, and improves overall model accuracy by up to 12%, when applied to RoBERTa on a variety of tasks in the GLUE benchmark.

Classical model-based partitional clustering algorithms, such ask-means or mixture of Gaussians, provide only loose and indirect control over the size of the resulting clusters. In this work, we present a family of probabilistic clustering models that can be steered towards clusters of desired size by providing a prior distribution over the possible sizes, allowing the analyst to fine-tune exploratory analysis or to produce clusters of suitable size for future down-stream processing.Our formulation supports arbitrary multimodal prior distributions, generalizing the previous work on clustering algorithms searching for clusters of equal size or algorithms designed for the microclustering task of finding small clusters. We provide practical methods for solving the problem, using integer programming for making the cluster assignments, and demonstrate that we can also automatically infer the number of clusters.