In recent years, the widespreadavailability of large-scale, high-dimensionaldatasets has driven significant interest in clustering algorithms that are both computationally efficient and robust to distributional shifts and outliers. The classical clustering method, K-means, can be seen as an application of the Lloyd-Max quantization algorithm, in which the distribution being quantized is the empirical distribution of the points to be clustered. This empirical distribution generally differs from the true underlying distribution, especially when the number of points to be clustered is small. This induces a distributional shift, which can also arise in many real-world settings, such as image segmentation, biological data analysis, and sensor networks, due to noise variations, sensor inaccuracies, or environmental changes. Distributional shifts can severely impact the performance of clustering algorithms, leading to degraded cluster assignments and unreliable downstream analysis. The field of clustering has a rich history. One of the most popular algorithms in this field is theK-means (KM) algorithm, introduced by [1], which computes centroids by iteratively updating the conditional mean of the data in the Voronoi regions induced by the centroids. However, standardK-means is sensitive to initialization and, in general, converges only to a local minimum.

The increasing availability of real-world conversation data offers exciting opportunities for researchers to study user-chatbot interactions. However, the sheer volume of this data makes manually examining individual conversations impractical. To overcome this challenge, we introduce WildVis, an interactive tool that enables fast, versatile, and large-scale conversation analysis. WildVis provides search and visualization capabilities in the text and embedding spaces based on a list of criteria. To manage million-scale datasets, we implemented optimizations including search index construction, embedding precomputation and compression, and caching to ensure responsive user interactions within seconds. We demonstrate WildVis' utility through three case studies: facilitating chatbot misuse research, visualizing and comparing topic distributions across datasets, and characterizing user-specific conversation patterns. WildVis is open-source and designed to be extendable, supporting additional datasets and customized search and visualization functionalities.

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular heuristics exist, but corresponding theoretical results are scarce. In this paper we investigate the asymptotic value of the normalised cut for an increasing sample assumed to arise from an underlying probability distribution, and based on this result provide recommendations for improving spectral clustering methodology. A corresponding algorithm is proposed with strong empirical performance.

It looks at cluster analysis as an analysis of variance problem. This method involves an agglomerative clustering algorithm. It starts out with n clusters of size 1 and continues until all the observations are included into one cluster. This method is most appropriate for quantitative variables, and not binary variables. Then you can set some threshold for the outlier clusters, like the size of that cluster is smaller then n*0.1%.